1
Macroeconomics
Malthus’s Model of Growth
Practice Problems #0
• Questions?
2
“Guard your manhood”
• https://www.depend.com/guard-your-manhood/#home
3
Malthus & his model
Malthus
• English “philosopher” and “political economist”
• Lived 1766-1834
• Ordained minister
– Concerned with the poor
– England had lots of poor
• Original “dismal scientist”
• Dead wrong – afterwards
5
Models
• Model = a specific implementation of a theory
– A way of organizing our thoughts
– Uses equations to be precise
– Simplicity is good: strip away details [we can always add them back in later]
– A laboratory for asking “what if?”
6
2
What Malthus knew
• J Hatcher:
– Between Domesday [1086] and the Black Death, the population of England rose from just under 2 million to about 4 million. Land was scarce, wages and the standard of living were low. Then in 1348-1349 the Black Death reduced the population by about 60%. [In the century that followed] wage levels rose to previously unknown heights, as did the general standard of living.
• What’s going on? Why did living standards rise?
7
Malthus’s growth model
• Picture of the world
– Everyone’s a farmer
– Growing food to eat
• Ingredient 1: production function
– Relate output to labor input
– Larger population => more workers => higher output => lower income per person
• Ingredient 2: population dynamics
– Population adds births, subtracts deaths
– Death rate lower if incomes are higher
8
Malthus’s model: production
• Production function
Y = A Kα L1-α
Y/L = A (K/L)α
• Questions
– What is α?
– What happens to Y/L as we increase L?
9
Malthus’s model: production
• To keep things simple
– Everyone works (L=POP)
– Capital K =1000 is constant (land)
– Productivity A = 79.37 also constant (don’t ask)
– Initial population L0 arbitrary (millions)
• See spreadsheet
10
Malthus’s model: production
11
Malthus’s model: production
12
3
Malthus’s model: population
• Things that change population
– Births (B) increase population (L)
– Deaths (D) decrease population (L)
• Population
Lt+1 = Lt + Bt − Dt
13
Malthus’s model: population
• To keep things simple
– Birth rate constant
– Death rate declines with income (increases with population)
• Birth and death rates
Bt /Lt = b
Dt/Lt = d0 + d1 (1000 − Lt)
• Numbers: b = 0.05, d0 = 0.05, d1 = 0.0001
14
Malthus’s model: population
15
Malthus’s model: population
• Questions for the figure
– On the left (right), is population high or low
– Is population increasing or decreasing?
– Is income per person increasing or decreasing?
– Which way are we moving in the figure?
– Where do we end up?
16
Experiments
What if we start with low population?
• Where is that on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
18
4
Malthus’s model: population
19
Malthus’s model: production
20
What if we reduce mortality?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
21
Malthus’s model: population
22
What if we increase productivity?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
23
Malthus’s model: production
24
5
Malthus’s model: population
25
Bottom line
• None of these things raise long-term living standards
• If there’s a lot to eat, more people will arrive to eat it [“If you grow it, they will come”]
• Biologists have similar models for flies, rabbits, etc
26
Assessment
What happened?
• In the UK
– Population increased by a factor of 5
– Income per person increased by a factor of 20!
– Agriculture became less important
• Oops!
• Where did we go wrong?
28
Where did Malthus go wrong?
• Incomes rose (massive increases in productivity) [unprecedented]
• Demographics changed: as people became richer, they had fewer children [also unprecedented – see Gapminder]
• Something to think about
– How important was China’s one-child policy to its rapid growth?
29
Takeaways
• Malthus had a nice theory for the period before 1800
• Since then, not so much
– Enormous productivity growth
– Dramatic change in demographics
• How should we think about that?
Y/L = A (K/L)α
30
6
For next class
• Should we save more?
– As individuals or as countries?
– Why? Or why not?
– Examples?
31
1
Macroeconomics
Malthus’s Model of Growth
Practice Problems #0
• Questions?
2
“Guard your manhood”
• https://www.depend.com/guard-your-manhood/#home
3
Malthus & his model
Malthus
• English “philosopher” and “political economist”
• Lived 1766-1834
• Ordained minister
– Concerned with the poor
– England had lots of poor
• Original “dismal scientist”
• Dead wrong – afterwards
5
Models
• Model = a specific implementation of a theory
– A way of organizing our thoughts
– Uses equations to be precise
– Simplicity is good: strip away details [we can always add them back in later]
– A laboratory for asking “what if?”
6
2
What Malthus knew
• J Hatcher:
– Between Domesday [1086] and the Black Death, the population of England rose from just under 2 million to about 4 million. Land was scarce, wages and the standard of living were low. Then in 1348-1349 the Black Death reduced the population by about 60%. [In the century that followed] wage levels rose to previously unknown heights, as did the general standard of living.
• What’s going on? Why did living standards rise?
7
Malthus’s growth model
• Picture of the world
– Everyone’s a farmer
– Growing food to eat
• Ingredient 1: production function
– Relate output to labor input
– Larger population => more workers => higher output => lower income per person
• Ingredient 2: population dynamics
– Population adds births, subtracts deaths
– Death rate lower if incomes are higher
8
Malthus’s model: production
• Production function
Y = A Kα L1-α
Y/L = A (K/L)α
• Questions
– What is α?
– What happens to Y/L as we increase L?
9
Malthus’s model: production
• To keep things simple
– Everyone works (L=POP)
– Capital K =1000 is constant (land)
– Productivity A = 79.37 also constant (don’t ask)
– Initial population L0 arbitrary (millions)
• See spreadsheet
10
Malthus’s model: production
11
Malthus’s model: production
12
3
Malthus’s model: population
• Things that change population
– Births (B) increase population (L)
– Deaths (D) decrease population (L)
• Population
Lt+1 = Lt + Bt − Dt
13
Malthus’s model: population
• To keep things simple
– Birth rate constant
– Death rate declines with income (increases with population)
• Birth and death rates
Bt /Lt = b
Dt/Lt = d0 + d1 (1000 − Lt)
• Numbers: b = 0.05, d0 = 0.05, d1 = 0.0001
14
Malthus’s model: population
15
Malthus’s model: population
• Questions for the figure
– On the left (right), is population high or low
– Is population increasing or decreasing?
– Is income per person increasing or decreasing?
– Which way are we moving in the figure?
– Where do we end up?
16
Experiments
What if we start with low population?
• Where is that on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
18
4
Malthus’s model: population
19
Malthus’s model: production
20
What if we reduce mortality?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
21
Malthus’s model: population
22
What if we increase productivity?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
23
Malthus’s model: production
24
5
Malthus’s model: population
25
Bottom line
• None of these things raise long-term living standards
• If there’s a lot to eat, more people will arrive to eat it [“If you grow it, they will come”]
• Biologists have similar models for flies, rabbits, etc
26
Assessment
What happened?
• In the UK
– Population increased by a factor of 5
– Income per person increased by a factor of 20!
– Agriculture became less important
• Oops!
• Where did we go wrong?
28
Where did Malthus go wrong?
• Incomes rose (massive increases in productivity) [unprecedented]
• Demographics changed: as people became richer, they had fewer children [also unprecedented – see Gapminder]
• Something to think about
– How important was China’s one-child policy to its rapid growth?
29
Takeaways
• Malthus had a nice theory for the period before 1800
• Since then, not so much
– Enormous productivity growth
– Dramatic change in demographics
• How should we think about that?
Y/L = A (K/L)α
30
6
For next class
• Should we save more?
– As individuals or as countries?
– Why? Or why not?
– Examples?
31
1
Macroeconomics
Malthus’s Model of Growth
Practice Problems #0
• Questions?
2
“Guard your manhood”
• https://www.depend.com/guard-your-manhood/#home
3
Malthus & his model
Malthus
• English “philosopher” and “political economist”
• Lived 1766-1834
• Ordained minister
– Concerned with the poor
– England had lots of poor
• Original “dismal scientist”
• Dead wrong – afterwards
5
Models
• Model = a specific implementation of a theory
– A way of organizing our thoughts
– Uses equations to be precise
– Simplicity is good: strip away details [we can always add them back in later]
– A laboratory for asking “what if?”
6
2
What Malthus knew
• J Hatcher:
– Between Domesday [1086] and the Black Death, the population of England rose from just under 2 million to about 4 million. Land was scarce, wages and the standard of living were low. Then in 1348-1349 the Black Death reduced the population by about 60%. [In the century that followed] wage levels rose to previously unknown heights, as did the general standard of living.
• What’s going on? Why did living standards rise?
7
Malthus’s growth model
• Picture of the world
– Everyone’s a farmer
– Growing food to eat
• Ingredient 1: production function
– Relate output to labor input
– Larger population => more workers => higher output => lower income per person
• Ingredient 2: population dynamics
– Population adds births, subtracts deaths
– Death rate lower if incomes are higher
8
Malthus’s model: production
• Production function
Y = A Kα L1-α
Y/L = A (K/L)α
• Questions
– What is α?
– What happens to Y/L as we increase L?
9
Malthus’s model: production
• To keep things simple
– Everyone works (L=POP)
– Capital K =1000 is constant (land)
– Productivity A = 79.37 also constant (don’t ask)
– Initial population L0 arbitrary (millions)
• See spreadsheet
10
Malthus’s model: production
11
Malthus’s model: production
12
3
Malthus’s model: population
• Things that change population
– Births (B) increase population (L)
– Deaths (D) decrease population (L)
• Population
Lt+1 = Lt + Bt − Dt
13
Malthus’s model: population
• To keep things simple
– Birth rate constant
– Death rate declines with income (increases with population)
• Birth and death rates
Bt /Lt = b
Dt/Lt = d0 + d1 (1000 − Lt)
• Numbers: b = 0.05, d0 = 0.05, d1 = 0.0001
14
Malthus’s model: population
15
Malthus’s model: population
• Questions for the figure
– On the left (right), is population high or low
– Is population increasing or decreasing?
– Is income per person increasing or decreasing?
– Which way are we moving in the figure?
– Where do we end up?
16
Experiments
What if we start with low population?
• Where is that on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
18
4
Malthus’s model: population
19
Malthus’s model: production
20
What if we reduce mortality?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
21
Malthus’s model: population
22
What if we increase productivity?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
23
Malthus’s model: production
24
5
Malthus’s model: population
25
Bottom line
• None of these things raise long-term living standards
• If there’s a lot to eat, more people will arrive to eat it [“If you grow it, they will come”]
• Biologists have similar models for flies, rabbits, etc
26
Assessment
What happened?
• In the UK
– Population increased by a factor of 5
– Income per person increased by a factor of 20!
– Agriculture became less important
• Oops!
• Where did we go wrong?
28
Where did Malthus go wrong?
• Incomes rose (massive increases in productivity) [unprecedented]
• Demographics changed: as people became richer, they had fewer children [also unprecedented – see Gapminder]
• Something to think about
– How important was China’s one-child policy to its rapid growth?
29
Takeaways
• Malthus had a nice theory for the period before 1800
• Since then, not so much
– Enormous productivity growth
– Dramatic change in demographics
• How should we think about that?
Y/L = A (K/L)α
30
6
For next class
• Should we save more?
– As individuals or as countries?
– Why? Or why not?
– Examples?
31
1
Macroeconomics
Malthus’s Model of Growth
Practice Problems #0
• Questions?
2
“Guard your manhood”
• https://www.depend.com/guard-your-manhood/#home
3
Malthus & his model
Malthus
• English “philosopher” and “political economist”
• Lived 1766-1834
• Ordained minister
– Concerned with the poor
– England had lots of poor
• Original “dismal scientist”
• Dead wrong – afterwards
5
Models
• Model = a specific implementation of a theory
– A way of organizing our thoughts
– Uses equations to be precise
– Simplicity is good: strip away details [we can always add them back in later]
– A laboratory for asking “what if?”
6
2
What Malthus knew
• J Hatcher:
– Between Domesday [1086] and the Black Death, the population of England rose from just under 2 million to about 4 million. Land was scarce, wages and the standard of living were low. Then in 1348-1349 the Black Death reduced the population by about 60%. [In the century that followed] wage levels rose to previously unknown heights, as did the general standard of living.
• What’s going on? Why did living standards rise?
7
Malthus’s growth model
• Picture of the world
– Everyone’s a farmer
– Growing food to eat
• Ingredient 1: production function
– Relate output to labor input
– Larger population => more workers => higher output => lower income per person
• Ingredient 2: population dynamics
– Population adds births, subtracts deaths
– Death rate lower if incomes are higher
8
Malthus’s model: production
• Production function
Y = A Kα L1-α
Y/L = A (K/L)α
• Questions
– What is α?
– What happens to Y/L as we increase L?
9
Malthus’s model: production
• To keep things simple
– Everyone works (L=POP)
– Capital K =1000 is constant (land)
– Productivity A = 79.37 also constant (don’t ask)
– Initial population L0 arbitrary (millions)
• See spreadsheet
10
Malthus’s model: production
11
Malthus’s model: production
12
3
Malthus’s model: population
• Things that change population
– Births (B) increase population (L)
– Deaths (D) decrease population (L)
• Population
Lt+1 = Lt + Bt − Dt
13
Malthus’s model: population
• To keep things simple
– Birth rate constant
– Death rate declines with income (increases with population)
• Birth and death rates
Bt /Lt = b
Dt/Lt = d0 + d1 (1000 − Lt)
• Numbers: b = 0.05, d0 = 0.05, d1 = 0.0001
14
Malthus’s model: population
15
Malthus’s model: population
• Questions for the figure
– On the left (right), is population high or low
– Is population increasing or decreasing?
– Is income per person increasing or decreasing?
– Which way are we moving in the figure?
– Where do we end up?
16
Experiments
What if we start with low population?
• Where is that on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
18
4
Malthus’s model: population
19
Malthus’s model: production
20
What if we reduce mortality?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
21
Malthus’s model: population
22
What if we increase productivity?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
23
Malthus’s model: production
24
5
Malthus’s model: population
25
Bottom line
• None of these things raise long-term living standards
• If there’s a lot to eat, more people will arrive to eat it [“If you grow it, they will come”]
• Biologists have similar models for flies, rabbits, etc
26
Assessment
What happened?
• In the UK
– Population increased by a factor of 5
– Income per person increased by a factor of 20!
– Agriculture became less important
• Oops!
• Where did we go wrong?
28
Where did Malthus go wrong?
• Incomes rose (massive increases in productivity) [unprecedented]
• Demographics changed: as people became richer, they had fewer children [also unprecedented – see Gapminder]
• Something to think about
– How important was China’s one-child policy to its rapid growth?
29
Takeaways
• Malthus had a nice theory for the period before 1800
• Since then, not so much
– Enormous productivity growth
– Dramatic change in demographics
• How should we think about that?
Y/L = A (K/L)α
30
6
For next class
• Should we save more?
– As individuals or as countries?
– Why? Or why not?
– Examples?
31
1
Macroeconomics
Malthus’s Model of Growth
Practice Problems #0
• Questions?
2
“Guard your manhood”
• https://www.depend.com/guard-your-manhood/#home
3
Malthus & his model
Malthus
• English “philosopher” and “political economist”
• Lived 1766-1834
• Ordained minister
– Concerned with the poor
– England had lots of poor
• Original “dismal scientist”
• Dead wrong – afterwards
5
Models
• Model = a specific implementation of a theory
– A way of organizing our thoughts
– Uses equations to be precise
– Simplicity is good: strip away details [we can always add them back in later]
– A laboratory for asking “what if?”
6
2
What Malthus knew
• J Hatcher:
– Between Domesday [1086] and the Black Death, the population of England rose from just under 2 million to about 4 million. Land was scarce, wages and the standard of living were low. Then in 1348-1349 the Black Death reduced the population by about 60%. [In the century that followed] wage levels rose to previously unknown heights, as did the general standard of living.
• What’s going on? Why did living standards rise?
7
Malthus’s growth model
• Picture of the world
– Everyone’s a farmer
– Growing food to eat
• Ingredient 1: production function
– Relate output to labor input
– Larger population => more workers => higher output => lower income per person
• Ingredient 2: population dynamics
– Population adds births, subtracts deaths
– Death rate lower if incomes are higher
8
Malthus’s model: production
• Production function
Y = A Kα L1-α
Y/L = A (K/L)α
• Questions
– What is α?
– What happens to Y/L as we increase L?
9
Malthus’s model: production
• To keep things simple
– Everyone works (L=POP)
– Capital K =1000 is constant (land)
– Productivity A = 79.37 also constant (don’t ask)
– Initial population L0 arbitrary (millions)
• See spreadsheet
10
Malthus’s model: production
11
Malthus’s model: production
12
3
Malthus’s model: population
• Things that change population
– Births (B) increase population (L)
– Deaths (D) decrease population (L)
• Population
Lt+1 = Lt + Bt − Dt
13
Malthus’s model: population
• To keep things simple
– Birth rate constant
– Death rate declines with income (increases with population)
• Birth and death rates
Bt /Lt = b
Dt/Lt = d0 + d1 (1000 − Lt)
• Numbers: b = 0.05, d0 = 0.05, d1 = 0.0001
14
Malthus’s model: population
15
Malthus’s model: population
• Questions for the figure
– On the left (right), is population high or low
– Is population increasing or decreasing?
– Is income per person increasing or decreasing?
– Which way are we moving in the figure?
– Where do we end up?
16
Experiments
What if we start with low population?
• Where is that on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
18
4
Malthus’s model: population
19
Malthus’s model: production
20
What if we reduce mortality?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
21
Malthus’s model: population
22
What if we increase productivity?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
23
Malthus’s model: production
24
5
Malthus’s model: population
25
Bottom line
• None of these things raise long-term living standards
• If there’s a lot to eat, more people will arrive to eat it [“If you grow it, they will come”]
• Biologists have similar models for flies, rabbits, etc
26
Assessment
What happened?
• In the UK
– Population increased by a factor of 5
– Income per person increased by a factor of 20!
– Agriculture became less important
• Oops!
• Where did we go wrong?
28
Where did Malthus go wrong?
• Incomes rose (massive increases in productivity) [unprecedented]
• Demographics changed: as people became richer, they had fewer children [also unprecedented – see Gapminder]
• Something to think about
– How important was China’s one-child policy to its rapid growth?
29
Takeaways
• Malthus had a nice theory for the period before 1800
• Since then, not so much
– Enormous productivity growth
– Dramatic change in demographics
• How should we think about that?
Y/L = A (K/L)α
30
6
For next class
• Should we save more?
– As individuals or as countries?
– Why? Or why not?
– Examples?
31
1
Macroeconomics
Malthus’s Model of Growth
Practice Problems #0
• Questions?
2
“Guard your manhood”
• https://www.depend.com/guard-your-manhood/#home
3
Malthus & his model
Malthus
• English “philosopher” and “political economist”
• Lived 1766-1834
• Ordained minister
– Concerned with the poor
– England had lots of poor
• Original “dismal scientist”
• Dead wrong – afterwards
5
Models
• Model = a specific implementation of a theory
– A way of organizing our thoughts
– Uses equations to be precise
– Simplicity is good: strip away details [we can always add them back in later]
– A laboratory for asking “what if?”
6
2
What Malthus knew
• J Hatcher:
– Between Domesday [1086] and the Black Death, the population of England rose from just under 2 million to about 4 million. Land was scarce, wages and the standard of living were low. Then in 1348-1349 the Black Death reduced the population by about 60%. [In the century that followed] wage levels rose to previously unknown heights, as did the general standard of living.
• What’s going on? Why did living standards rise?
7
Malthus’s growth model
• Picture of the world
– Everyone’s a farmer
– Growing food to eat
• Ingredient 1: production function
– Relate output to labor input
– Larger population => more workers => higher output => lower income per person
• Ingredient 2: population dynamics
– Population adds births, subtracts deaths
– Death rate lower if incomes are higher
8
Malthus’s model: production
• Production function
Y = A Kα L1-α
Y/L = A (K/L)α
• Questions
– What is α?
– What happens to Y/L as we increase L?
9
Malthus’s model: production
• To keep things simple
– Everyone works (L=POP)
– Capital K =1000 is constant (land)
– Productivity A = 79.37 also constant (don’t ask)
– Initial population L0 arbitrary (millions)
• See spreadsheet
10
Malthus’s model: production
11
Malthus’s model: production
12
3
Malthus’s model: population
• Things that change population
– Births (B) increase population (L)
– Deaths (D) decrease population (L)
• Population
Lt+1 = Lt + Bt − Dt
13
Malthus’s model: population
• To keep things simple
– Birth rate constant
– Death rate declines with income (increases with population)
• Birth and death rates
Bt /Lt = b
Dt/Lt = d0 + d1 (1000 − Lt)
• Numbers: b = 0.05, d0 = 0.05, d1 = 0.0001
14
Malthus’s model: population
15
Malthus’s model: population
• Questions for the figure
– On the left (right), is population high or low
– Is population increasing or decreasing?
– Is income per person increasing or decreasing?
– Which way are we moving in the figure?
– Where do we end up?
16
Experiments
What if we start with low population?
• Where is that on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
18
4
Malthus’s model: population
19
Malthus’s model: production
20
What if we reduce mortality?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
21
Malthus’s model: population
22
What if we increase productivity?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
23
Malthus’s model: production
24
5
Malthus’s model: population
25
Bottom line
• None of these things raise long-term living standards
• If there’s a lot to eat, more people will arrive to eat it [“If you grow it, they will come”]
• Biologists have similar models for flies, rabbits, etc
26
Assessment
What happened?
• In the UK
– Population increased by a factor of 5
– Income per person increased by a factor of 20!
– Agriculture became less important
• Oops!
• Where did we go wrong?
28
Where did Malthus go wrong?
• Incomes rose (massive increases in productivity) [unprecedented]
• Demographics changed: as people became richer, they had fewer children [also unprecedented – see Gapminder]
• Something to think about
– How important was China’s one-child policy to its rapid growth?
29
Takeaways
• Malthus had a nice theory for the period before 1800
• Since then, not so much
– Enormous productivity growth
– Dramatic change in demographics
• How should we think about that?
Y/L = A (K/L)α
30
6
For next class
• Should we save more?
– As individuals or as countries?
– Why? Or why not?
– Examples?
31
1
Macroeconomics
Malthus’s Model of Growth
Practice Problems #0
• Questions?
2
“Guard your manhood”
• https://www.depend.com/guard-your-manhood/#home
3
Malthus & his model
Malthus
• English “philosopher” and “political economist”
• Lived 1766-1834
• Ordained minister
– Concerned with the poor
– England had lots of poor
• Original “dismal scientist”
• Dead wrong – afterwards
5
Models
• Model = a specific implementation of a theory
– A way of organizing our thoughts
– Uses equations to be precise
– Simplicity is good: strip away details [we can always add them back in later]
– A laboratory for asking “what if?”
6
2
What Malthus knew
• J Hatcher:
– Between Domesday [1086] and the Black Death, the population of England rose from just under 2 million to about 4 million. Land was scarce, wages and the standard of living were low. Then in 1348-1349 the Black Death reduced the population by about 60%. [In the century that followed] wage levels rose to previously unknown heights, as did the general standard of living.
• What’s going on? Why did living standards rise?
7
Malthus’s growth model
• Picture of the world
– Everyone’s a farmer
– Growing food to eat
• Ingredient 1: production function
– Relate output to labor input
– Larger population => more workers => higher output => lower income per person
• Ingredient 2: population dynamics
– Population adds births, subtracts deaths
– Death rate lower if incomes are higher
8
Malthus’s model: production
• Production function
Y = A Kα L1-α
Y/L = A (K/L)α
• Questions
– What is α?
– What happens to Y/L as we increase L?
9
Malthus’s model: production
• To keep things simple
– Everyone works (L=POP)
– Capital K =1000 is constant (land)
– Productivity A = 79.37 also constant (don’t ask)
– Initial population L0 arbitrary (millions)
• See spreadsheet
10
Malthus’s model: production
11
Malthus’s model: production
12
3
Malthus’s model: population
• Things that change population
– Births (B) increase population (L)
– Deaths (D) decrease population (L)
• Population
Lt+1 = Lt + Bt − Dt
13
Malthus’s model: population
• To keep things simple
– Birth rate constant
– Death rate declines with income (increases with population)
• Birth and death rates
Bt /Lt = b
Dt/Lt = d0 + d1 (1000 − Lt)
• Numbers: b = 0.05, d0 = 0.05, d1 = 0.0001
14
Malthus’s model: population
15
Malthus’s model: population
• Questions for the figure
– On the left (right), is population high or low
– Is population increasing or decreasing?
– Is income per person increasing or decreasing?
– Which way are we moving in the figure?
– Where do we end up?
16
Experiments
What if we start with low population?
• Where is that on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
18
4
Malthus’s model: population
19
Malthus’s model: production
20
What if we reduce mortality?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
21
Malthus’s model: population
22
What if we increase productivity?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
23
Malthus’s model: production
24
5
Malthus’s model: population
25
Bottom line
• None of these things raise long-term living standards
• If there’s a lot to eat, more people will arrive to eat it [“If you grow it, they will come”]
• Biologists have similar models for flies, rabbits, etc
26
Assessment
What happened?
• In the UK
– Population increased by a factor of 5
– Income per person increased by a factor of 20!
– Agriculture became less important
• Oops!
• Where did we go wrong?
28
Where did Malthus go wrong?
• Incomes rose (massive increases in productivity) [unprecedented]
• Demographics changed: as people became richer, they had fewer children [also unprecedented – see Gapminder]
• Something to think about
– How important was China’s one-child policy to its rapid growth?
29
Takeaways
• Malthus had a nice theory for the period before 1800
• Since then, not so much
– Enormous productivity growth
– Dramatic change in demographics
• How should we think about that?
Y/L = A (K/L)α
30
6
For next class
• Should we save more?
– As individuals or as countries?
– Why? Or why not?
– Examples?
31
1
Macroeconomics
Malthus’s Model of Growth
Practice Problems #0
• Questions?
2
“Guard your manhood”
• https://www.depend.com/guard-your-manhood/#home
3
Malthus & his model
Malthus
• English “philosopher” and “political economist”
• Lived 1766-1834
• Ordained minister
– Concerned with the poor
– England had lots of poor
• Original “dismal scientist”
• Dead wrong – afterwards
5
Models
• Model = a specific implementation of a theory
– A way of organizing our thoughts
– Uses equations to be precise
– Simplicity is good: strip away details [we can always add them back in later]
– A laboratory for asking “what if?”
6
2
What Malthus knew
• J Hatcher:
– Between Domesday [1086] and the Black Death, the population of England rose from just under 2 million to about 4 million. Land was scarce, wages and the standard of living were low. Then in 1348-1349 the Black Death reduced the population by about 60%. [In the century that followed] wage levels rose to previously unknown heights, as did the general standard of living.
• What’s going on? Why did living standards rise?
7
Malthus’s growth model
• Picture of the world
– Everyone’s a farmer
– Growing food to eat
• Ingredient 1: production function
– Relate output to labor input
– Larger population => more workers => higher output => lower income per person
• Ingredient 2: population dynamics
– Population adds births, subtracts deaths
– Death rate lower if incomes are higher
8
Malthus’s model: production
• Production function
Y = A Kα L1-α
Y/L = A (K/L)α
• Questions
– What is α?
– What happens to Y/L as we increase L?
9
Malthus’s model: production
• To keep things simple
– Everyone works (L=POP)
– Capital K =1000 is constant (land)
– Productivity A = 79.37 also constant (don’t ask)
– Initial population L0 arbitrary (millions)
• See spreadsheet
10
Malthus’s model: production
11
Malthus’s model: production
12
3
Malthus’s model: population
• Things that change population
– Births (B) increase population (L)
– Deaths (D) decrease population (L)
• Population
Lt+1 = Lt + Bt − Dt
13
Malthus’s model: population
• To keep things simple
– Birth rate constant
– Death rate declines with income (increases with population)
• Birth and death rates
Bt /Lt = b
Dt/Lt = d0 + d1 (1000 − Lt)
• Numbers: b = 0.05, d0 = 0.05, d1 = 0.0001
14
Malthus’s model: population
15
Malthus’s model: population
• Questions for the figure
– On the left (right), is population high or low
– Is population increasing or decreasing?
– Is income per person increasing or decreasing?
– Which way are we moving in the figure?
– Where do we end up?
16
Experiments
What if we start with low population?
• Where is that on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
18
4
Malthus’s model: population
19
Malthus’s model: production
20
What if we reduce mortality?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
21
Malthus’s model: population
22
What if we increase productivity?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
23
Malthus’s model: production
24
5
Malthus’s model: population
25
Bottom line
• None of these things raise long-term living standards
• If there’s a lot to eat, more people will arrive to eat it [“If you grow it, they will come”]
• Biologists have similar models for flies, rabbits, etc
26
Assessment
What happened?
• In the UK
– Population increased by a factor of 5
– Income per person increased by a factor of 20!
– Agriculture became less important
• Oops!
• Where did we go wrong?
28
Where did Malthus go wrong?
• Incomes rose (massive increases in productivity) [unprecedented]
• Demographics changed: as people became richer, they had fewer children [also unprecedented – see Gapminder]
• Something to think about
– How important was China’s one-child policy to its rapid growth?
29
Takeaways
• Malthus had a nice theory for the period before 1800
• Since then, not so much
– Enormous productivity growth
– Dramatic change in demographics
• How should we think about that?
Y/L = A (K/L)α
30
6
For next class
• Should we save more?
– As individuals or as countries?
– Why? Or why not?
– Examples?
31
1
Macroeconomics
Malthus’s Model of Growth
Practice Problems #0
• Questions?
2
“Guard your manhood”
• https://www.depend.com/guard-your-manhood/#home
3
Malthus & his model
Malthus
• English “philosopher” and “political economist”
• Lived 1766-1834
• Ordained minister
– Concerned with the poor
– England had lots of poor
• Original “dismal scientist”
• Dead wrong – afterwards
5
Models
• Model = a specific implementation of a theory
– A way of organizing our thoughts
– Uses equations to be precise
– Simplicity is good: strip away details [we can always add them back in later]
– A laboratory for asking “what if?”
6
2
What Malthus knew
• J Hatcher:
– Between Domesday [1086] and the Black Death, the population of England rose from just under 2 million to about 4 million. Land was scarce, wages and the standard of living were low. Then in 1348-1349 the Black Death reduced the population by about 60%. [In the century that followed] wage levels rose to previously unknown heights, as did the general standard of living.
• What’s going on? Why did living standards rise?
7
Malthus’s growth model
• Picture of the world
– Everyone’s a farmer
– Growing food to eat
• Ingredient 1: production function
– Relate output to labor input
– Larger population => more workers => higher output => lower income per person
• Ingredient 2: population dynamics
– Population adds births, subtracts deaths
– Death rate lower if incomes are higher
8
Malthus’s model: production
• Production function
Y = A Kα L1-α
Y/L = A (K/L)α
• Questions
– What is α?
– What happens to Y/L as we increase L?
9
Malthus’s model: production
• To keep things simple
– Everyone works (L=POP)
– Capital K =1000 is constant (land)
– Productivity A = 79.37 also constant (don’t ask)
– Initial population L0 arbitrary (millions)
• See spreadsheet
10
Malthus’s model: production
11
Malthus’s model: production
12
3
Malthus’s model: population
• Things that change population
– Births (B) increase population (L)
– Deaths (D) decrease population (L)
• Population
Lt+1 = Lt + Bt − Dt
13
Malthus’s model: population
• To keep things simple
– Birth rate constant
– Death rate declines with income (increases with population)
• Birth and death rates
Bt /Lt = b
Dt/Lt = d0 + d1 (1000 − Lt)
• Numbers: b = 0.05, d0 = 0.05, d1 = 0.0001
14
Malthus’s model: population
15
Malthus’s model: population
• Questions for the figure
– On the left (right), is population high or low
– Is population increasing or decreasing?
– Is income per person increasing or decreasing?
– Which way are we moving in the figure?
– Where do we end up?
16
Experiments
What if we start with low population?
• Where is that on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
18
4
Malthus’s model: population
19
Malthus’s model: production
20
What if we reduce mortality?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
21
Malthus’s model: population
22
What if we increase productivity?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
23
Malthus’s model: production
24
5
Malthus’s model: population
25
Bottom line
• None of these things raise long-term living standards
• If there’s a lot to eat, more people will arrive to eat it [“If you grow it, they will come”]
• Biologists have similar models for flies, rabbits, etc
26
Assessment
What happened?
• In the UK
– Population increased by a factor of 5
– Income per person increased by a factor of 20!
– Agriculture became less important
• Oops!
• Where did we go wrong?
28
Where did Malthus go wrong?
• Incomes rose (massive increases in productivity) [unprecedented]
• Demographics changed: as people became richer, they had fewer children [also unprecedented – see Gapminder]
• Something to think about
– How important was China’s one-child policy to its rapid growth?
29
Takeaways
• Malthus had a nice theory for the period before 1800
• Since then, not so much
– Enormous productivity growth
– Dramatic change in demographics
• How should we think about that?
Y/L = A (K/L)α
30
6
For next class
• Should we save more?
– As individuals or as countries?
– Why? Or why not?
– Examples?
31
1
Macroeconomics
Malthus’s Model of Growth
Practice Problems #0
• Questions?
2
“Guard your manhood”
• https://www.depend.com/guard-your-manhood/#home
3
Malthus & his model
Malthus
• English “philosopher” and “political economist”
• Lived 1766-1834
• Ordained minister
– Concerned with the poor
– England had lots of poor
• Original “dismal scientist”
• Dead wrong – afterwards
5
Models
• Model = a specific implementation of a theory
– A way of organizing our thoughts
– Uses equations to be precise
– Simplicity is good: strip away details [we can always add them back in later]
– A laboratory for asking “what if?”
6
2
What Malthus knew
• J Hatcher:
– Between Domesday [1086] and the Black Death, the population of England rose from just under 2 million to about 4 million. Land was scarce, wages and the standard of living were low. Then in 1348-1349 the Black Death reduced the population by about 60%. [In the century that followed] wage levels rose to previously unknown heights, as did the general standard of living.
• What’s going on? Why did living standards rise?
7
Malthus’s growth model
• Picture of the world
– Everyone’s a farmer
– Growing food to eat
• Ingredient 1: production function
– Relate output to labor input
– Larger population => more workers => higher output => lower income per person
• Ingredient 2: population dynamics
– Population adds births, subtracts deaths
– Death rate lower if incomes are higher
8
Malthus’s model: production
• Production function
Y = A Kα L1-α
Y/L = A (K/L)α
• Questions
– What is α?
– What happens to Y/L as we increase L?
9
Malthus’s model: production
• To keep things simple
– Everyone works (L=POP)
– Capital K =1000 is constant (land)
– Productivity A = 79.37 also constant (don’t ask)
– Initial population L0 arbitrary (millions)
• See spreadsheet
10
Malthus’s model: production
11
Malthus’s model: production
12
3
Malthus’s model: population
• Things that change population
– Births (B) increase population (L)
– Deaths (D) decrease population (L)
• Population
Lt+1 = Lt + Bt − Dt
13
Malthus’s model: population
• To keep things simple
– Birth rate constant
– Death rate declines with income (increases with population)
• Birth and death rates
Bt /Lt = b
Dt/Lt = d0 + d1 (1000 − Lt)
• Numbers: b = 0.05, d0 = 0.05, d1 = 0.0001
14
Malthus’s model: population
15
Malthus’s model: population
• Questions for the figure
– On the left (right), is population high or low
– Is population increasing or decreasing?
– Is income per person increasing or decreasing?
– Which way are we moving in the figure?
– Where do we end up?
16
Experiments
What if we start with low population?
• Where is that on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
18
4
Malthus’s model: population
19
Malthus’s model: production
20
What if we reduce mortality?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
21
Malthus’s model: population
22
What if we increase productivity?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
23
Malthus’s model: production
24
5
Malthus’s model: population
25
Bottom line
• None of these things raise long-term living standards
• If there’s a lot to eat, more people will arrive to eat it [“If you grow it, they will come”]
• Biologists have similar models for flies, rabbits, etc
26
Assessment
What happened?
• In the UK
– Population increased by a factor of 5
– Income per person increased by a factor of 20!
– Agriculture became less important
• Oops!
• Where did we go wrong?
28
Where did Malthus go wrong?
• Incomes rose (massive increases in productivity) [unprecedented]
• Demographics changed: as people became richer, they had fewer children [also unprecedented – see Gapminder]
• Something to think about
– How important was China’s one-child policy to its rapid growth?
29
Takeaways
• Malthus had a nice theory for the period before 1800
• Since then, not so much
– Enormous productivity growth
– Dramatic change in demographics
• How should we think about that?
Y/L = A (K/L)α
30
6
For next class
• Should we save more?
– As individuals or as countries?
– Why? Or why not?
– Examples?
31
1
Macroeconomics
Malthus’s Model of Growth
Practice Problems #0
• Questions?
2
“Guard your manhood”
• https://www.depend.com/guard-your-manhood/#home
3
Malthus & his model
Malthus
• English “philosopher” and “political economist”
• Lived 1766-1834
• Ordained minister
– Concerned with the poor
– England had lots of poor
• Original “dismal scientist”
• Dead wrong – afterwards
5
Models
• Model = a specific implementation of a theory
– A way of organizing our thoughts
– Uses equations to be precise
– Simplicity is good: strip away details [we can always add them back in later]
– A laboratory for asking “what if?”
6
2
What Malthus knew
• J Hatcher:
– Between Domesday [1086] and the Black Death, the population of England rose from just under 2 million to about 4 million. Land was scarce, wages and the standard of living were low. Then in 1348-1349 the Black Death reduced the population by about 60%. [In the century that followed] wage levels rose to previously unknown heights, as did the general standard of living.
• What’s going on? Why did living standards rise?
7
Malthus’s growth model
• Picture of the world
– Everyone’s a farmer
– Growing food to eat
• Ingredient 1: production function
– Relate output to labor input
– Larger population => more workers => higher output => lower income per person
• Ingredient 2: population dynamics
– Population adds births, subtracts deaths
– Death rate lower if incomes are higher
8
Malthus’s model: production
• Production function
Y = A Kα L1-α
Y/L = A (K/L)α
• Questions
– What is α?
– What happens to Y/L as we increase L?
9
Malthus’s model: production
• To keep things simple
– Everyone works (L=POP)
– Capital K =1000 is constant (land)
– Productivity A = 79.37 also constant (don’t ask)
– Initial population L0 arbitrary (millions)
• See spreadsheet
10
Malthus’s model: production
11
Malthus’s model: production
12
3
Malthus’s model: population
• Things that change population
– Births (B) increase population (L)
– Deaths (D) decrease population (L)
• Population
Lt+1 = Lt + Bt − Dt
13
Malthus’s model: population
• To keep things simple
– Birth rate constant
– Death rate declines with income (increases with population)
• Birth and death rates
Bt /Lt = b
Dt/Lt = d0 + d1 (1000 − Lt)
• Numbers: b = 0.05, d0 = 0.05, d1 = 0.0001
14
Malthus’s model: population
15
Malthus’s model: population
• Questions for the figure
– On the left (right), is population high or low
– Is population increasing or decreasing?
– Is income per person increasing or decreasing?
– Which way are we moving in the figure?
– Where do we end up?
16
Experiments
What if we start with low population?
• Where is that on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
18
4
Malthus’s model: population
19
Malthus’s model: production
20
What if we reduce mortality?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
21
Malthus’s model: population
22
What if we increase productivity?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
23
Malthus’s model: production
24
5
Malthus’s model: population
25
Bottom line
• None of these things raise long-term living standards
• If there’s a lot to eat, more people will arrive to eat it [“If you grow it, they will come”]
• Biologists have similar models for flies, rabbits, etc
26
Assessment
What happened?
• In the UK
– Population increased by a factor of 5
– Income per person increased by a factor of 20!
– Agriculture became less important
• Oops!
• Where did we go wrong?
28
Where did Malthus go wrong?
• Incomes rose (massive increases in productivity) [unprecedented]
• Demographics changed: as people became richer, they had fewer children [also unprecedented – see Gapminder]
• Something to think about
– How important was China’s one-child policy to its rapid growth?
29
Takeaways
• Malthus had a nice theory for the period before 1800
• Since then, not so much
– Enormous productivity growth
– Dramatic change in demographics
• How should we think about that?
Y/L = A (K/L)α
30
6
For next class
• Should we save more?
– As individuals or as countries?
– Why? Or why not?
– Examples?
31
1
Macroeconomics
Malthus’s Model of Growth
Practice Problems #0
• Questions?
2
“Guard your manhood”
• https://www.depend.com/guard-your-manhood/#home
3
Malthus & his model
Malthus
• English “philosopher” and “political economist”
• Lived 1766-1834
• Ordained minister
– Concerned with the poor
– England had lots of poor
• Original “dismal scientist”
• Dead wrong – afterwards
5
Models
• Model = a specific implementation of a theory
– A way of organizing our thoughts
– Uses equations to be precise
– Simplicity is good: strip away details [we can always add them back in later]
– A laboratory for asking “what if?”
6
2
What Malthus knew
• J Hatcher:
– Between Domesday [1086] and the Black Death, the population of England rose from just under 2 million to about 4 million. Land was scarce, wages and the standard of living were low. Then in 1348-1349 the Black Death reduced the population by about 60%. [In the century that followed] wage levels rose to previously unknown heights, as did the general standard of living.
• What’s going on? Why did living standards rise?
7
Malthus’s growth model
• Picture of the world
– Everyone’s a farmer
– Growing food to eat
• Ingredient 1: production function
– Relate output to labor input
– Larger population => more workers => higher output => lower income per person
• Ingredient 2: population dynamics
– Population adds births, subtracts deaths
– Death rate lower if incomes are higher
8
Malthus’s model: production
• Production function
Y = A Kα L1-α
Y/L = A (K/L)α
• Questions
– What is α?
– What happens to Y/L as we increase L?
9
Malthus’s model: production
• To keep things simple
– Everyone works (L=POP)
– Capital K =1000 is constant (land)
– Productivity A = 79.37 also constant (don’t ask)
– Initial population L0 arbitrary (millions)
• See spreadsheet
10
Malthus’s model: production
11
Malthus’s model: production
12
3
Malthus’s model: population
• Things that change population
– Births (B) increase population (L)
– Deaths (D) decrease population (L)
• Population
Lt+1 = Lt + Bt − Dt
13
Malthus’s model: population
• To keep things simple
– Birth rate constant
– Death rate declines with income (increases with population)
• Birth and death rates
Bt /Lt = b
Dt/Lt = d0 + d1 (1000 − Lt)
• Numbers: b = 0.05, d0 = 0.05, d1 = 0.0001
14
Malthus’s model: population
15
Malthus’s model: population
• Questions for the figure
– On the left (right), is population high or low
– Is population increasing or decreasing?
– Is income per person increasing or decreasing?
– Which way are we moving in the figure?
– Where do we end up?
16
Experiments
What if we start with low population?
• Where is that on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
18
4
Malthus’s model: population
19
Malthus’s model: production
20
What if we reduce mortality?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
21
Malthus’s model: population
22
What if we increase productivity?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
23
Malthus’s model: production
24
5
Malthus’s model: population
25
Bottom line
• None of these things raise long-term living standards
• If there’s a lot to eat, more people will arrive to eat it [“If you grow it, they will come”]
• Biologists have similar models for flies, rabbits, etc
26
Assessment
What happened?
• In the UK
– Population increased by a factor of 5
– Income per person increased by a factor of 20!
– Agriculture became less important
• Oops!
• Where did we go wrong?
28
Where did Malthus go wrong?
• Incomes rose (massive increases in productivity) [unprecedented]
• Demographics changed: as people became richer, they had fewer children [also unprecedented – see Gapminder]
• Something to think about
– How important was China’s one-child policy to its rapid growth?
29
Takeaways
• Malthus had a nice theory for the period before 1800
• Since then, not so much
– Enormous productivity growth
– Dramatic change in demographics
• How should we think about that?
Y/L = A (K/L)α
30
6
For next class
• Should we save more?
– As individuals or as countries?
– Why? Or why not?
– Examples?
31
1
Macroeconomics
Malthus’s Model of Growth
Practice Problems #0
• Questions?
2
“Guard your manhood”
• https://www.depend.com/guard-your-manhood/#home
3
Malthus & his model
Malthus
• English “philosopher” and “political economist”
• Lived 1766-1834
• Ordained minister
– Concerned with the poor
– England had lots of poor
• Original “dismal scientist”
• Dead wrong – afterwards
5
Models
• Model = a specific implementation of a theory
– A way of organizing our thoughts
– Uses equations to be precise
– Simplicity is good: strip away details [we can always add them back in later]
– A laboratory for asking “what if?”
6
2
What Malthus knew
• J Hatcher:
– Between Domesday [1086] and the Black Death, the population of England rose from just under 2 million to about 4 million. Land was scarce, wages and the standard of living were low. Then in 1348-1349 the Black Death reduced the population by about 60%. [In the century that followed] wage levels rose to previously unknown heights, as did the general standard of living.
• What’s going on? Why did living standards rise?
7
Malthus’s growth model
• Picture of the world
– Everyone’s a farmer
– Growing food to eat
• Ingredient 1: production function
– Relate output to labor input
– Larger population => more workers => higher output => lower income per person
• Ingredient 2: population dynamics
– Population adds births, subtracts deaths
– Death rate lower if incomes are higher
8
Malthus’s model: production
• Production function
Y = A Kα L1-α
Y/L = A (K/L)α
• Questions
– What is α?
– What happens to Y/L as we increase L?
9
Malthus’s model: production
• To keep things simple
– Everyone works (L=POP)
– Capital K =1000 is constant (land)
– Productivity A = 79.37 also constant (don’t ask)
– Initial population L0 arbitrary (millions)
• See spreadsheet
10
Malthus’s model: production
11
Malthus’s model: production
12
3
Malthus’s model: population
• Things that change population
– Births (B) increase population (L)
– Deaths (D) decrease population (L)
• Population
Lt+1 = Lt + Bt − Dt
13
Malthus’s model: population
• To keep things simple
– Birth rate constant
– Death rate declines with income (increases with population)
• Birth and death rates
Bt /Lt = b
Dt/Lt = d0 + d1 (1000 − Lt)
• Numbers: b = 0.05, d0 = 0.05, d1 = 0.0001
14
Malthus’s model: population
15
Malthus’s model: population
• Questions for the figure
– On the left (right), is population high or low
– Is population increasing or decreasing?
– Is income per person increasing or decreasing?
– Which way are we moving in the figure?
– Where do we end up?
16
Experiments
What if we start with low population?
• Where is that on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
18
4
Malthus’s model: population
19
Malthus’s model: production
20
What if we reduce mortality?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
21
Malthus’s model: population
22
What if we increase productivity?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
23
Malthus’s model: production
24
5
Malthus’s model: population
25
Bottom line
• None of these things raise long-term living standards
• If there’s a lot to eat, more people will arrive to eat it [“If you grow it, they will come”]
• Biologists have similar models for flies, rabbits, etc
26
Assessment
What happened?
• In the UK
– Population increased by a factor of 5
– Income per person increased by a factor of 20!
– Agriculture became less important
• Oops!
• Where did we go wrong?
28
Where did Malthus go wrong?
• Incomes rose (massive increases in productivity) [unprecedented]
• Demographics changed: as people became richer, they had fewer children [also unprecedented – see Gapminder]
• Something to think about
– How important was China’s one-child policy to its rapid growth?
29
Takeaways
• Malthus had a nice theory for the period before 1800
• Since then, not so much
– Enormous productivity growth
– Dramatic change in demographics
• How should we think about that?
Y/L = A (K/L)α
30
6
For next class
• Should we save more?
– As individuals or as countries?
– Why? Or why not?
– Examples?
31
1
Macroeconomics
Malthus’s Model of Growth
Practice Problems #0
• Questions?
2
“Guard your manhood”
• https://www.depend.com/guard-your-manhood/#home
3
Malthus & his model
Malthus
• English “philosopher” and “political economist”
• Lived 1766-1834
• Ordained minister
– Concerned with the poor
– England had lots of poor
• Original “dismal scientist”
• Dead wrong – afterwards
5
Models
• Model = a specific implementation of a theory
– A way of organizing our thoughts
– Uses equations to be precise
– Simplicity is good: strip away details [we can always add them back in later]
– A laboratory for asking “what if?”
6
2
What Malthus knew
• J Hatcher:
– Between Domesday [1086] and the Black Death, the population of England rose from just under 2 million to about 4 million. Land was scarce, wages and the standard of living were low. Then in 1348-1349 the Black Death reduced the population by about 60%. [In the century that followed] wage levels rose to previously unknown heights, as did the general standard of living.
• What’s going on? Why did living standards rise?
7
Malthus’s growth model
• Picture of the world
– Everyone’s a farmer
– Growing food to eat
• Ingredient 1: production function
– Relate output to labor input
– Larger population => more workers => higher output => lower income per person
• Ingredient 2: population dynamics
– Population adds births, subtracts deaths
– Death rate lower if incomes are higher
8
Malthus’s model: production
• Production function
Y = A Kα L1-α
Y/L = A (K/L)α
• Questions
– What is α?
– What happens to Y/L as we increase L?
9
Malthus’s model: production
• To keep things simple
– Everyone works (L=POP)
– Capital K =1000 is constant (land)
– Productivity A = 79.37 also constant (don’t ask)
– Initial population L0 arbitrary (millions)
• See spreadsheet
10
Malthus’s model: production
11
Malthus’s model: production
12
3
Malthus’s model: population
• Things that change population
– Births (B) increase population (L)
– Deaths (D) decrease population (L)
• Population
Lt+1 = Lt + Bt − Dt
13
Malthus’s model: population
• To keep things simple
– Birth rate constant
– Death rate declines with income (increases with population)
• Birth and death rates
Bt /Lt = b
Dt/Lt = d0 + d1 (1000 − Lt)
• Numbers: b = 0.05, d0 = 0.05, d1 = 0.0001
14
Malthus’s model: population
15
Malthus’s model: population
• Questions for the figure
– On the left (right), is population high or low
– Is population increasing or decreasing?
– Is income per person increasing or decreasing?
– Which way are we moving in the figure?
– Where do we end up?
16
Experiments
What if we start with low population?
• Where is that on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
18
4
Malthus’s model: population
19
Malthus’s model: production
20
What if we reduce mortality?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
21
Malthus’s model: population
22
What if we increase productivity?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
23
Malthus’s model: production
24
5
Malthus’s model: population
25
Bottom line
• None of these things raise long-term living standards
• If there’s a lot to eat, more people will arrive to eat it [“If you grow it, they will come”]
• Biologists have similar models for flies, rabbits, etc
26
Assessment
What happened?
• In the UK
– Population increased by a factor of 5
– Income per person increased by a factor of 20!
– Agriculture became less important
• Oops!
• Where did we go wrong?
28
Where did Malthus go wrong?
• Incomes rose (massive increases in productivity) [unprecedented]
• Demographics changed: as people became richer, they had fewer children [also unprecedented – see Gapminder]
• Something to think about
– How important was China’s one-child policy to its rapid growth?
29
Takeaways
• Malthus had a nice theory for the period before 1800
• Since then, not so much
– Enormous productivity growth
– Dramatic change in demographics
• How should we think about that?
Y/L = A (K/L)α
30
6
For next class
• Should we save more?
– As individuals or as countries?
– Why? Or why not?
– Examples?
31
1
Macroeconomics
Malthus’s Model of Growth
Practice Problems #0
• Questions?
2
“Guard your manhood”
• https://www.depend.com/guard-your-manhood/#home
3
Malthus & his model
Malthus
• English “philosopher” and “political economist”
• Lived 1766-1834
• Ordained minister
– Concerned with the poor
– England had lots of poor
• Original “dismal scientist”
• Dead wrong – afterwards
5
Models
• Model = a specific implementation of a theory
– A way of organizing our thoughts
– Uses equations to be precise
– Simplicity is good: strip away details [we can always add them back in later]
– A laboratory for asking “what if?”
6
2
What Malthus knew
• J Hatcher:
– Between Domesday [1086] and the Black Death, the population of England rose from just under 2 million to about 4 million. Land was scarce, wages and the standard of living were low. Then in 1348-1349 the Black Death reduced the population by about 60%. [In the century that followed] wage levels rose to previously unknown heights, as did the general standard of living.
• What’s going on? Why did living standards rise?
7
Malthus’s growth model
• Picture of the world
– Everyone’s a farmer
– Growing food to eat
• Ingredient 1: production function
– Relate output to labor input
– Larger population => more workers => higher output => lower income per person
• Ingredient 2: population dynamics
– Population adds births, subtracts deaths
– Death rate lower if incomes are higher
8
Malthus’s model: production
• Production function
Y = A Kα L1-α
Y/L = A (K/L)α
• Questions
– What is α?
– What happens to Y/L as we increase L?
9
Malthus’s model: production
• To keep things simple
– Everyone works (L=POP)
– Capital K =1000 is constant (land)
– Productivity A = 79.37 also constant (don’t ask)
– Initial population L0 arbitrary (millions)
• See spreadsheet
10
Malthus’s model: production
11
Malthus’s model: production
12
3
Malthus’s model: population
• Things that change population
– Births (B) increase population (L)
– Deaths (D) decrease population (L)
• Population
Lt+1 = Lt + Bt − Dt
13
Malthus’s model: population
• To keep things simple
– Birth rate constant
– Death rate declines with income (increases with population)
• Birth and death rates
Bt /Lt = b
Dt/Lt = d0 + d1 (1000 − Lt)
• Numbers: b = 0.05, d0 = 0.05, d1 = 0.0001
14
Malthus’s model: population
15
Malthus’s model: population
• Questions for the figure
– On the left (right), is population high or low
– Is population increasing or decreasing?
– Is income per person increasing or decreasing?
– Which way are we moving in the figure?
– Where do we end up?
16
Experiments
What if we start with low population?
• Where is that on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
18
4
Malthus’s model: population
19
Malthus’s model: production
20
What if we reduce mortality?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
21
Malthus’s model: population
22
What if we increase productivity?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
23
Malthus’s model: production
24
5
Malthus’s model: population
25
Bottom line
• None of these things raise long-term living standards
• If there’s a lot to eat, more people will arrive to eat it [“If you grow it, they will come”]
• Biologists have similar models for flies, rabbits, etc
26
Assessment
What happened?
• In the UK
– Population increased by a factor of 5
– Income per person increased by a factor of 20!
– Agriculture became less important
• Oops!
• Where did we go wrong?
28
Where did Malthus go wrong?
• Incomes rose (massive increases in productivity) [unprecedented]
• Demographics changed: as people became richer, they had fewer children [also unprecedented – see Gapminder]
• Something to think about
– How important was China’s one-child policy to its rapid growth?
29
Takeaways
• Malthus had a nice theory for the period before 1800
• Since then, not so much
– Enormous productivity growth
– Dramatic change in demographics
• How should we think about that?
Y/L = A (K/L)α
30
6
For next class
• Should we save more?
– As individuals or as countries?
– Why? Or why not?
– Examples?
31
1
Macroeconomics
Malthus’s Model of Growth
Practice Problems #0
• Questions?
2
“Guard your manhood”
• https://www.depend.com/guard-your-manhood/#home
3
Malthus & his model
Malthus
• English “philosopher” and “political economist”
• Lived 1766-1834
• Ordained minister
– Concerned with the poor
– England had lots of poor
• Original “dismal scientist”
• Dead wrong – afterwards
5
Models
• Model = a specific implementation of a theory
– A way of organizing our thoughts
– Uses equations to be precise
– Simplicity is good: strip away details [we can always add them back in later]
– A laboratory for asking “what if?”
6
2
What Malthus knew
• J Hatcher:
– Between Domesday [1086] and the Black Death, the population of England rose from just under 2 million to about 4 million. Land was scarce, wages and the standard of living were low. Then in 1348-1349 the Black Death reduced the population by about 60%. [In the century that followed] wage levels rose to previously unknown heights, as did the general standard of living.
• What’s going on? Why did living standards rise?
7
Malthus’s growth model
• Picture of the world
– Everyone’s a farmer
– Growing food to eat
• Ingredient 1: production function
– Relate output to labor input
– Larger population => more workers => higher output => lower income per person
• Ingredient 2: population dynamics
– Population adds births, subtracts deaths
– Death rate lower if incomes are higher
8
Malthus’s model: production
• Production function
Y = A Kα L1-α
Y/L = A (K/L)α
• Questions
– What is α?
– What happens to Y/L as we increase L?
9
Malthus’s model: production
• To keep things simple
– Everyone works (L=POP)
– Capital K =1000 is constant (land)
– Productivity A = 79.37 also constant (don’t ask)
– Initial population L0 arbitrary (millions)
• See spreadsheet
10
Malthus’s model: production
11
Malthus’s model: production
12
3
Malthus’s model: population
• Things that change population
– Births (B) increase population (L)
– Deaths (D) decrease population (L)
• Population
Lt+1 = Lt + Bt − Dt
13
Malthus’s model: population
• To keep things simple
– Birth rate constant
– Death rate declines with income (increases with population)
• Birth and death rates
Bt /Lt = b
Dt/Lt = d0 + d1 (1000 − Lt)
• Numbers: b = 0.05, d0 = 0.05, d1 = 0.0001
14
Malthus’s model: population
15
Malthus’s model: population
• Questions for the figure
– On the left (right), is population high or low
– Is population increasing or decreasing?
– Is income per person increasing or decreasing?
– Which way are we moving in the figure?
– Where do we end up?
16
Experiments
What if we start with low population?
• Where is that on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
18
4
Malthus’s model: population
19
Malthus’s model: production
20
What if we reduce mortality?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
21
Malthus’s model: population
22
What if we increase productivity?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
23
Malthus’s model: production
24
5
Malthus’s model: population
25
Bottom line
• None of these things raise long-term living standards
• If there’s a lot to eat, more people will arrive to eat it [“If you grow it, they will come”]
• Biologists have similar models for flies, rabbits, etc
26
Assessment
What happened?
• In the UK
– Population increased by a factor of 5
– Income per person increased by a factor of 20!
– Agriculture became less important
• Oops!
• Where did we go wrong?
28
Where did Malthus go wrong?
• Incomes rose (massive increases in productivity) [unprecedented]
• Demographics changed: as people became richer, they had fewer children [also unprecedented – see Gapminder]
• Something to think about
– How important was China’s one-child policy to its rapid growth?
29
Takeaways
• Malthus had a nice theory for the period before 1800
• Since then, not so much
– Enormous productivity growth
– Dramatic change in demographics
• How should we think about that?
Y/L = A (K/L)α
30
6
For next class
• Should we save more?
– As individuals or as countries?
– Why? Or why not?
– Examples?
31
1
Macroeconomics
Malthus’s Model of Growth
Practice Problems #0
• Questions?
2
“Guard your manhood”
• https://www.depend.com/guard-your-manhood/#home
3
Malthus & his model
Malthus
• English “philosopher” and “political economist”
• Lived 1766-1834
• Ordained minister
– Concerned with the poor
– England had lots of poor
• Original “dismal scientist”
• Dead wrong – afterwards
5
Models
• Model = a specific implementation of a theory
– A way of organizing our thoughts
– Uses equations to be precise
– Simplicity is good: strip away details [we can always add them back in later]
– A laboratory for asking “what if?”
6
2
What Malthus knew
• J Hatcher:
– Between Domesday [1086] and the Black Death, the population of England rose from just under 2 million to about 4 million. Land was scarce, wages and the standard of living were low. Then in 1348-1349 the Black Death reduced the population by about 60%. [In the century that followed] wage levels rose to previously unknown heights, as did the general standard of living.
• What’s going on? Why did living standards rise?
7
Malthus’s growth model
• Picture of the world
– Everyone’s a farmer
– Growing food to eat
• Ingredient 1: production function
– Relate output to labor input
– Larger population => more workers => higher output => lower income per person
• Ingredient 2: population dynamics
– Population adds births, subtracts deaths
– Death rate lower if incomes are higher
8
Malthus’s model: production
• Production function
Y = A Kα L1-α
Y/L = A (K/L)α
• Questions
– What is α?
– What happens to Y/L as we increase L?
9
Malthus’s model: production
• To keep things simple
– Everyone works (L=POP)
– Capital K =1000 is constant (land)
– Productivity A = 79.37 also constant (don’t ask)
– Initial population L0 arbitrary (millions)
• See spreadsheet
10
Malthus’s model: production
11
Malthus’s model: production
12
3
Malthus’s model: population
• Things that change population
– Births (B) increase population (L)
– Deaths (D) decrease population (L)
• Population
Lt+1 = Lt + Bt − Dt
13
Malthus’s model: population
• To keep things simple
– Birth rate constant
– Death rate declines with income (increases with population)
• Birth and death rates
Bt /Lt = b
Dt/Lt = d0 + d1 (1000 − Lt)
• Numbers: b = 0.05, d0 = 0.05, d1 = 0.0001
14
Malthus’s model: population
15
Malthus’s model: population
• Questions for the figure
– On the left (right), is population high or low
– Is population increasing or decreasing?
– Is income per person increasing or decreasing?
– Which way are we moving in the figure?
– Where do we end up?
16
Experiments
What if we start with low population?
• Where is that on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
18
4
Malthus’s model: population
19
Malthus’s model: production
20
What if we reduce mortality?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
21
Malthus’s model: population
22
What if we increase productivity?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
23
Malthus’s model: production
24
5
Malthus’s model: population
25
Bottom line
• None of these things raise long-term living standards
• If there’s a lot to eat, more people will arrive to eat it [“If you grow it, they will come”]
• Biologists have similar models for flies, rabbits, etc
26
Assessment
What happened?
• In the UK
– Population increased by a factor of 5
– Income per person increased by a factor of 20!
– Agriculture became less important
• Oops!
• Where did we go wrong?
28
Where did Malthus go wrong?
• Incomes rose (massive increases in productivity) [unprecedented]
• Demographics changed: as people became richer, they had fewer children [also unprecedented – see Gapminder]
• Something to think about
– How important was China’s one-child policy to its rapid growth?
29
Takeaways
• Malthus had a nice theory for the period before 1800
• Since then, not so much
– Enormous productivity growth
– Dramatic change in demographics
• How should we think about that?
Y/L = A (K/L)α
30
6
For next class
• Should we save more?
– As individuals or as countries?
– Why? Or why not?
– Examples?
31
1
Macroeconomics
Malthus’s Model of Growth
Practice Problems #0
• Questions?
2
“Guard your manhood”
• https://www.depend.com/guard-your-manhood/#home
3
Malthus & his model
Malthus
• English “philosopher” and “political economist”
• Lived 1766-1834
• Ordained minister
– Concerned with the poor
– England had lots of poor
• Original “dismal scientist”
• Dead wrong – afterwards
5
Models
• Model = a specific implementation of a theory
– A way of organizing our thoughts
– Uses equations to be precise
– Simplicity is good: strip away details [we can always add them back in later]
– A laboratory for asking “what if?”
6
2
What Malthus knew
• J Hatcher:
– Between Domesday [1086] and the Black Death, the population of England rose from just under 2 million to about 4 million. Land was scarce, wages and the standard of living were low. Then in 1348-1349 the Black Death reduced the population by about 60%. [In the century that followed] wage levels rose to previously unknown heights, as did the general standard of living.
• What’s going on? Why did living standards rise?
7
Malthus’s growth model
• Picture of the world
– Everyone’s a farmer
– Growing food to eat
• Ingredient 1: production function
– Relate output to labor input
– Larger population => more workers => higher output => lower income per person
• Ingredient 2: population dynamics
– Population adds births, subtracts deaths
– Death rate lower if incomes are higher
8
Malthus’s model: production
• Production function
Y = A Kα L1-α
Y/L = A (K/L)α
• Questions
– What is α?
– What happens to Y/L as we increase L?
9
Malthus’s model: production
• To keep things simple
– Everyone works (L=POP)
– Capital K =1000 is constant (land)
– Productivity A = 79.37 also constant (don’t ask)
– Initial population L0 arbitrary (millions)
• See spreadsheet
10
Malthus’s model: production
11
Malthus’s model: production
12
3
Malthus’s model: population
• Things that change population
– Births (B) increase population (L)
– Deaths (D) decrease population (L)
• Population
Lt+1 = Lt + Bt − Dt
13
Malthus’s model: population
• To keep things simple
– Birth rate constant
– Death rate declines with income (increases with population)
• Birth and death rates
Bt /Lt = b
Dt/Lt = d0 + d1 (1000 − Lt)
• Numbers: b = 0.05, d0 = 0.05, d1 = 0.0001
14
Malthus’s model: population
15
Malthus’s model: population
• Questions for the figure
– On the left (right), is population high or low
– Is population increasing or decreasing?
– Is income per person increasing or decreasing?
– Which way are we moving in the figure?
– Where do we end up?
16
Experiments
What if we start with low population?
• Where is that on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
18
4
Malthus’s model: population
19
Malthus’s model: production
20
What if we reduce mortality?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
21
Malthus’s model: population
22
What if we increase productivity?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
23
Malthus’s model: production
24
5
Malthus’s model: population
25
Bottom line
• None of these things raise long-term living standards
• If there’s a lot to eat, more people will arrive to eat it [“If you grow it, they will come”]
• Biologists have similar models for flies, rabbits, etc
26
Assessment
What happened?
• In the UK
– Population increased by a factor of 5
– Income per person increased by a factor of 20!
– Agriculture became less important
• Oops!
• Where did we go wrong?
28
Where did Malthus go wrong?
• Incomes rose (massive increases in productivity) [unprecedented]
• Demographics changed: as people became richer, they had fewer children [also unprecedented – see Gapminder]
• Something to think about
– How important was China’s one-child policy to its rapid growth?
29
Takeaways
• Malthus had a nice theory for the period before 1800
• Since then, not so much
– Enormous productivity growth
– Dramatic change in demographics
• How should we think about that?
Y/L = A (K/L)α
30
6
For next class
• Should we save more?
– As individuals or as countries?
– Why? Or why not?
– Examples?
31
1
Macroeconomics
Malthus’s Model of Growth
Practice Problems #0
• Questions?
2
“Guard your manhood”
• https://www.depend.com/guard-your-manhood/#home
3
Malthus & his model
Malthus
• English “philosopher” and “political economist”
• Lived 1766-1834
• Ordained minister
– Concerned with the poor
– England had lots of poor
• Original “dismal scientist”
• Dead wrong – afterwards
5
Models
• Model = a specific implementation of a theory
– A way of organizing our thoughts
– Uses equations to be precise
– Simplicity is good: strip away details [we can always add them back in later]
– A laboratory for asking “what if?”
6
2
What Malthus knew
• J Hatcher:
– Between Domesday [1086] and the Black Death, the population of England rose from just under 2 million to about 4 million. Land was scarce, wages and the standard of living were low. Then in 1348-1349 the Black Death reduced the population by about 60%. [In the century that followed] wage levels rose to previously unknown heights, as did the general standard of living.
• What’s going on? Why did living standards rise?
7
Malthus’s growth model
• Picture of the world
– Everyone’s a farmer
– Growing food to eat
• Ingredient 1: production function
– Relate output to labor input
– Larger population => more workers => higher output => lower income per person
• Ingredient 2: population dynamics
– Population adds births, subtracts deaths
– Death rate lower if incomes are higher
8
Malthus’s model: production
• Production function
Y = A Kα L1-α
Y/L = A (K/L)α
• Questions
– What is α?
– What happens to Y/L as we increase L?
9
Malthus’s model: production
• To keep things simple
– Everyone works (L=POP)
– Capital K =1000 is constant (land)
– Productivity A = 79.37 also constant (don’t ask)
– Initial population L0 arbitrary (millions)
• See spreadsheet
10
Malthus’s model: production
11
Malthus’s model: production
12
3
Malthus’s model: population
• Things that change population
– Births (B) increase population (L)
– Deaths (D) decrease population (L)
• Population
Lt+1 = Lt + Bt − Dt
13
Malthus’s model: population
• To keep things simple
– Birth rate constant
– Death rate declines with income (increases with population)
• Birth and death rates
Bt /Lt = b
Dt/Lt = d0 + d1 (1000 − Lt)
• Numbers: b = 0.05, d0 = 0.05, d1 = 0.0001
14
Malthus’s model: population
15
Malthus’s model: population
• Questions for the figure
– On the left (right), is population high or low
– Is population increasing or decreasing?
– Is income per person increasing or decreasing?
– Which way are we moving in the figure?
– Where do we end up?
16
Experiments
What if we start with low population?
• Where is that on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
18
4
Malthus’s model: population
19
Malthus’s model: production
20
What if we reduce mortality?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
21
Malthus’s model: population
22
What if we increase productivity?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
23
Malthus’s model: production
24
5
Malthus’s model: population
25
Bottom line
• None of these things raise long-term living standards
• If there’s a lot to eat, more people will arrive to eat it [“If you grow it, they will come”]
• Biologists have similar models for flies, rabbits, etc
26
Assessment
What happened?
• In the UK
– Population increased by a factor of 5
– Income per person increased by a factor of 20!
– Agriculture became less important
• Oops!
• Where did we go wrong?
28
Where did Malthus go wrong?
• Incomes rose (massive increases in productivity) [unprecedented]
• Demographics changed: as people became richer, they had fewer children [also unprecedented – see Gapminder]
• Something to think about
– How important was China’s one-child policy to its rapid growth?
29
Takeaways
• Malthus had a nice theory for the period before 1800
• Since then, not so much
– Enormous productivity growth
– Dramatic change in demographics
• How should we think about that?
Y/L = A (K/L)α
30
6
For next class
• Should we save more?
– As individuals or as countries?
– Why? Or why not?
– Examples?
31
1
Macroeconomics
Malthus’s Model of Growth
Practice Problems #0
• Questions?
2
“Guard your manhood”
• https://www.depend.com/guard-your-manhood/#home
3
Malthus & his model
Malthus
• English “philosopher” and “political economist”
• Lived 1766-1834
• Ordained minister
– Concerned with the poor
– England had lots of poor
• Original “dismal scientist”
• Dead wrong – afterwards
5
Models
• Model = a specific implementation of a theory
– A way of organizing our thoughts
– Uses equations to be precise
– Simplicity is good: strip away details [we can always add them back in later]
– A laboratory for asking “what if?”
6
2
What Malthus knew
• J Hatcher:
– Between Domesday [1086] and the Black Death, the population of England rose from just under 2 million to about 4 million. Land was scarce, wages and the standard of living were low. Then in 1348-1349 the Black Death reduced the population by about 60%. [In the century that followed] wage levels rose to previously unknown heights, as did the general standard of living.
• What’s going on? Why did living standards rise?
7
Malthus’s growth model
• Picture of the world
– Everyone’s a farmer
– Growing food to eat
• Ingredient 1: production function
– Relate output to labor input
– Larger population => more workers => higher output => lower income per person
• Ingredient 2: population dynamics
– Population adds births, subtracts deaths
– Death rate lower if incomes are higher
8
Malthus’s model: production
• Production function
Y = A Kα L1-α
Y/L = A (K/L)α
• Questions
– What is α?
– What happens to Y/L as we increase L?
9
Malthus’s model: production
• To keep things simple
– Everyone works (L=POP)
– Capital K =1000 is constant (land)
– Productivity A = 79.37 also constant (don’t ask)
– Initial population L0 arbitrary (millions)
• See spreadsheet
10
Malthus’s model: production
11
Malthus’s model: production
12
3
Malthus’s model: population
• Things that change population
– Births (B) increase population (L)
– Deaths (D) decrease population (L)
• Population
Lt+1 = Lt + Bt − Dt
13
Malthus’s model: population
• To keep things simple
– Birth rate constant
– Death rate declines with income (increases with population)
• Birth and death rates
Bt /Lt = b
Dt/Lt = d0 + d1 (1000 − Lt)
• Numbers: b = 0.05, d0 = 0.05, d1 = 0.0001
14
Malthus’s model: population
15
Malthus’s model: population
• Questions for the figure
– On the left (right), is population high or low
– Is population increasing or decreasing?
– Is income per person increasing or decreasing?
– Which way are we moving in the figure?
– Where do we end up?
16
Experiments
What if we start with low population?
• Where is that on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
18
4
Malthus’s model: population
19
Malthus’s model: production
20
What if we reduce mortality?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
21
Malthus’s model: population
22
What if we increase productivity?
• How does that show up on the graph that follows?
• What do you think happens?
– To population?
– To income?
– To income per person?
• Think about how the model works
23
Malthus’s model: production
24
5
Malthus’s model: population
25
Bottom line
• None of these things raise long-term living standards
• If there’s a lot to eat, more people will arrive to eat it [“If you grow it, they will come”]
• Biologists have similar models for flies, rabbits, etc
26
Assessment
What happened?
• In the UK
– Population increased by a factor of 5
– Income per person increased by a factor of 20!
– Agriculture became less important
• Oops!
• Where did we go wrong?
28
Where did Malthus go wrong?
• Incomes rose (massive increases in productivity) [unprecedented]
• Demographics changed: as people became richer, they had fewer children [also unprecedented – see Gapminder]
• Something to think about
– How important was China’s one-child policy to its rapid growth?
29
Takeaways
• Malthus had a nice theory for the period before 1800
• Since then, not so much
– Enormous productivity growth
– Dramatic change in demographics
• How should we think about that?
Y/L = A (K/L)α
30
6
For next class
• Should we save more?
– As individuals or as countries?
– Why? Or why not?
– Examples?
31