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AGEC 603
Derived Demand for Land
Individual Demand Individual Demand
• Based on consumer choice • Utility theory and budget constraint
• Utility theory • Utility is the satisfaction one gets from
consuming a good or service
• Budget constraint – how much you have to spend
Marginal Utility Marginal Utility
• Change in utility derived from a change in consumption of a particular good holding other goods constant
• Law of Diminishing Marginal Utility - as consumption per unit of time increases, marginal utility decreases
• Examples
– M&Ms
– Texan Steak - Amarillo
2
Indifference / Isoutility Curves Indifference / Isoutility Curves
L1 L2
Land units
Bundle of goods
B1
B2
Negative slope
Nonintersecting
Everywhere dense
Convex to the origin
Consuming B1L1 provides the same utility
as consuming B2L2
Indifference Curves Indifference Curves
Which bundle would you
prefer … bundle M or
bundle B?
Which bundle would you
prefer … bundle M or
bundle B? M
B
1 2 3 4 5 6 7 8
Land Units
Bu
nd
les
of
go
od
s
1 2
3
4 5
6
7 8
The answer is that this we
would be indifferent
because they give us the
same utility. The ultimate
choice will depend on the
prices of these two
products.
The answer is that this we
would be indifferent
because they give us the
same utility. The ultimate
choice will depend on the
prices of these two
products.
Indifference Curves Indifference Curves
1 2 3 4 5 6 7 8
Land Units
B
un
dle
of
go
od
s
1 2
3
4 5
6
7 8
Which bundle would you
prefer more…bundle C or
bundle N?
Which bundle would you
prefer more…bundle C or
bundle N?
C N We would prefer bundle N
over bundle C because it
gives us more utility or
satisfaction. The question
is whether we can afford
to buy bundle N!
We would prefer bundle N
over bundle C because it
gives us more utility or
satisfaction. The question
is whether we can afford
to buy bundle N!
3
Marginal Rate of Substitution Marginal Rate of Substitution
• The rate at which the consumer is willing to substitute one good for another and maintain a constant utility level
• MRS of land for bundle with utility constant
• Notice - rise over run = the slope for a specific segment for a nonlinear curves
land
bundle
Marginal Rate of Substitution Marginal Rate of Substitution
• MRSland for bundle
going from 2 to 3
land units
1 2 3 4 5 6 7 8
1
Land Units
Bu
nd
le o
f g
oo
ds
1 2
3 4
5
6 7
8
-
1
This means the consumer
is willing to give up 1
bundle unit in exchange
for one land unit!
This means the consumer
is willing to give up 1
bundle unit in exchange
for one land unit!
11
1
_
land
bundle
Marginal Rate of Substitution Marginal Rate of Substitution
• MRSbundle for land
going from 2 to 3
bundle units
1 2 3 4 5 6 7 8
-2
Land Units
Bu
nd
le o
f g
oo
ds
1 2
3 4
5
6 7
8
1
502
1.-
-land
bundle
This means the consumer
is willing to give up 2 land
units for one additional
unit of bundle of goods!
This means the consumer
is willing to give up 2 land
units for one additional
unit of bundle of goods!
4
Marginal Rate of Substitution Marginal Rate of Substitution
• Why? – Utility must be constant
– What you give up with one, you must gain with the other!
bundle
land
MU
MU
land
bundleMRS
Budget Constraint Budget Constraint
• Represents the amount of income available for spending on the consumption bundles
• Example land / bundle budget
Pland x Qland + Pbundle x Qbundle Budget
where Pland and Pbundle represent the price of land and the bundle of goods
while Qland and Qbunlde represent the quantities you purchase during the
time period.
Budget Constraint – Graph
1 2 3 4 5 6 7 8 9 10 11
Land
B
un
dle
of
go
od
s
1 2
3
4 5
6
7 8
Apply all income to bundle
Apply all income to land Budget Constraint
Income = $200
Prices = $40 / unit bundle and $20 / unit land
5
Bundle Price Decreases by 1/2 Bundle Price Decreases by 1/2
1 2 3 4 5 6 7 8 9 10 11
Land
Bu
nd
le o
f g
oo
ds
1 2
3
4 5
6
7 8
9
1
0 Bundle price decreases by 1/2
Apply all income to land
Original price budget
constraint
After price change budget
constraint
Bundle Price Increases by 2 Bundle Price Increases by 2
1 2 3 4 5 6 7 8 9 10 11
Land
B
un
dle
of
go
od
s
1 2
3
4 5
6
7 8
9
1
0
Original price budget
constraint
Bundle price decreases by
1/2 budget constraint
Bundle price doubles budget
constraint
Land Price Changes Land Price Changes
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Land
B
un
dle
of
go
od
s
1 2
3
4 5
6
7 8
9
1
0
Original price budget
constraint
Land price doubles
Land price decreases by 1/2
6
Income Changes Income Changes
1 2 3 4 5 6 7 8 9 10 11
Dozen corn ears consumed per week
Ste
ak
s (l
bs)
co
nsu
med
per
week
1 2
3
4 5
6
7 8
Budget Line at increased
income
Original Budget
Line
Budget Line
at ½ income
Note: parallel shifts
Objective - Maximize Utility
1 2 3 4 5 6 7 8 9 10 11
Land Units
B
un
dle
of
go
od
s
1 2
3 4
5
6 7
8
Indifference Curve – below budget constraint
Can increase utility by moving outward
Not Optimal
Indifference Curves and
points above the budget
Constraint exceeds your
budget - not feasible
Point Indifference Curve is Tangent
to Budget Constraint
Feasible – spends all budget
Maximizes Utility – highest curve obtainable
Slope Budget Constraint
1 2 3 4 5 6 7 8 9 10 11
Land Units
B
un
dle
of
go
od
1 2
3 4
5
6 7
8
Using x and y intercept points to calculate slope
land = 0, bundle = 5 and land = 10 and bundle = 0
Slope = rise / run = (5-0)/(0-10) = -0.5
These points obtained
Income / price of bundle = 5 and
Income / price of land = 10
bundle
land
land
bundle
land
bunlde
P
P
P
I
P
I
P
I
P
I
)0(
)0(
7
• Slope of indifference curve = slope of budget constraint
• Slope of indifference curve = MRS = - MUland / MUbundle
• Slope of budget constraint = -Pland / Pbundle
• Therefore,
Tangency Conditions
bundle
bundle
land
land
bundle
land
bundle
land
P
MU
P
MU
P
P
MU
MUMRS
• Point where utility is maximized subject to the budget constraint occurs at
MUland MUbundle
Pland Pbundle
• In other words, the marginal utility derived from the last dollar spent on each good is identical. This can be expanded to include all goods and services purchased by the consumer.
Consumer Equilibrium
=
Individual Demand Curve
1 2 3 4 5 6 7 8 9 10 11
Land units
B
un
dle
of
go
od
s
1 2
3 4
5
6 7
8
Original Price = $20 / unit
Consumption bundle
2.5 bundle units and
5 units land
What if price decreases to $15?
What happens to budget constraint?
8
Land Price Decreases
New x-intercept
Same Why
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Land Units
B
un
dle
of
go
od
s
1 2
3 4
5
6 7
8
9
1
0 1
1
New equilibrium
= 2.75 bundle and 6 land
Why an increase in bundle
and increase in land?
Land Price Increases
New y-intercept same
Why?
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Land Units
Bu
nd
le o
f g
oo
ds
1 2
3 4
5
6 7
8
9
1
0 1
1
New equilibrium
= 3.125 bundle and 1.5 land
Why an decrease in land
and increase in bundle?
Individual Demand Curve - Land
Demand Schedule
Price Quantity
Pincrease 1.5
Po 5
Pdecrease 6
9
Market Demand Curve - Land
+ =
The market demand curve is the horizontal
summation of the demand schedules
for all the consumers in the market.
The market demand curve is the horizontal
summation of the demand schedules
for all the consumers in the market.
Demand Curve Jargon - Review
• Specific terms to distinguish between
movement along a demand curve and a shift
in a demand curve
• Change in the quantity demanded is a
movement along a demand curve - Cause
• Change in demand is a shift in the demand
curve - Causes
World Population and Demand World Population and Demand
• Population one of the most important factors in
determining demand for land
• Trends
• Changing characteristics
• Future outlook
• Density
D
L1 L2 L3
Land Quantity
Price
P3
P2
P1
S
Increasing population leads to
1) increasing price and
2) increasing land use
assuming no change in supply curve
10
World Population World Population
Source: http://one-simple-idea.com/Environment1.htm
World Population World Population
Year Population Change
1 AD 200 million
1650 500 million
1804 1 billion Doubled in 313 years
1927 2 billion Doubled in 118 years
1960 3 billion Increased by 1 billion in
38 years
1999 6 billion Doubled in 39 years
2013 7.1 billion
2015 7.2 billion Source U.S. Census Bureau
http://geography.about.com/od/obtainpopulationdata/a/worldpopulation.htm
http://en.wikipedia.org/wiki/File:World_population_distribution.svg
World Population Distribution World Population Distribution
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http://www.nationsonline.org/oneworld/world_population.htm
World Population by Country World Population by Country
http://en.wikipedia.org/wiki/World_population
Urban Areas >= million
inhabitants in 2006
Urban Areas >= million
inhabitants in 2006
http://www.worldometers.info/world-population/#region
•
World Population Density
(people/km2)
World Population Density
(people/km2)
12
http://www.census.gov/population/international/data/idb/worldgrgraph.php
© 2009 Population Reference Bureau. All rights reserved. www.prb.org
Source: United Nations Population Division, World Population Prospects, The 2008 Revision.
World Population Growth Is Almost Entirely
Concentrated in the World's Poorer Countries.
World Population (in Billions): 1950-2050
13
Year Population Area (sq. km.)
Density
(persons per
sq. km.)
Acres /
person
1950 2,557,628,654 132,061,547 19.4 14.10
1960 3,042,828,380 132,061,547 23.0 12.16
1970 3,712,338,708 132,061,547 28.1 9.86
1980 4,450,929,761 132,061,547 33.7 8.20
1990 5,287,869,228 132,061,547 40.0 6.88
2000 6,090,319,399 132,061,547 46.1 5.98
2010 6,866,054,281 132,061,547 52.0 5.31
2020 7,631,071,690 132,061,547 57.8 4.80
2030 8,315,758,309 132,061,547 63.0 4.40
2040 8,896,844,579 132,061,547 67. 4.10
2050 9,376,416,975 132,061,547 71.0 3.80
Population Density Projections
• http://www.census.gov/population/international/data/idb/informationGateway.php
Global Hunger Index
• The 2013 (GHI) ranks 88 countries using
three indicators: – The proportion of people who are calorie
deficient, or undernourished
– The prevalence of underweight in children
under the age of five
– The under-five mortality rate
• Takes into account the special vulnerability
of children to nutritional deprivation
• Ratings from 0 (best) to 100 (worst).
Global Hunger Index
• Countries are rated from 0 (best) to 100
(worst).
• Overall GHI scores improved from 18.7 in
the 1990 to 15.2 in the 2008.
• Sub-Saharan Africa and South Asia have
the worst scores on the 2008 GHI.
Policy Research Institute, http://www.ifpri.org
14
2008 Global Hunger Index
GHI-Winners and Losers 1990 - 2008
Global Hunger Index http://www.ifpri.org/ghi/2013
Policy Research Institute, http://www.ifpri.org
16
U.S. Population
U.S. Population
One birth every 8 seconds
One death every 12 seconds
One international migrant (net) every 40 seconds
Net gain of one person every 17 seconds
Components of Population Change
http://www.census.gov/popclock/embed.php?component=counter
State Population,
2013
Pop. per sq. mi.,
2013 2030 Poplation
California 38,332,521 246.1 46,444,861
Texas 26,448,193 101.2 33,317,744
New York 19,651,127 417.0 28,685,769
Florida 19,552,860 364.6 19,477,429
Illinois 12,882,135 232.0 13,432,892
Pennsylvania 12,773,801 285.5 12,768,184
Ohio 11,570,808 283.2 12,227,739
Georgia 9,992,167 173.7 10,712,397
Michigan 9,895,622 175.0 12,017,838
North Carolina 9,848,060 202.0 10,694,172
http://www.census.gov/popclock/#populous-counties
10 Most Populous States
17
Fastest Growing Cities 2010- 2011
http://www.census.gov/newsroom/releases/archives/population/cb12-117.html
Percent
Increase
2011 Total
Population
1. New Orleans 4.9 360,740
2. Round Rock,
Texas 4.8 104,664
3. Austin, Texas 3.8 820,611
4. Plano, Texas 3.8 269,776
5. McKinney, Texas 3.8 136,067
6. Frisco, Texas 3.8 121,387
7. Denton, Texas 3.4 117,187
8. Denver 3.3 619,968
9. Cary, N.C. 3.2 139,633
10. Raleigh, N.C. 3.1 416,468
11. Alexandria, Va. 3.1 144,301
12. Tampa, Fla. 3.1 346,037
13. McAllen, Texas 3.0 133,742
14. Carrollton, Texas 3.0 122,640
15. Atlanta 3.0 432,427
http://www.census.gov/newsroom/releases/archives/population/cb11-215.html
The 10 Fastest Growing States from April
1, 2010, to July 1, 2011
Percent
change
1. District of Columbia 2.70
2. Texas 2.10
3. Utah 1.93
4. Alaska 1.76
5. Colorado 1.74
6. North Dakota 1.69
7. Washington 1.57
8. Arizona 1.42
9. Florida 1.36
10. Georgia 1.32
The 10 States with the Largest Numeric
Increase from April 1, 2010, to July 1, 2011
Numeric
change
1. Texas 529,000
2. California 438,000
3. Florida 256,000
4. Georgia 128,000
5. North Carolina 121,000
6. Washington 105,000
7. Virginia 96,000
8. Arizona 90,000
9. Colorado 88,000
10. New York 87,000
Fastest Growing States 2010- 2011
http://www.census.gov/dataviz/visualizations/051
U.S. Population Movement
18
Births Deaths
2015 321,363 2,471 0.77 1,677 4,290 2,613 794
2020 333,896 2,521 0.76 1,612 4,380 2,768 909
2025 346,407 2,478 0.72 1,453 4,413 2,959 1,024
2030 358,471 2,364 0.66 1,225 4,433 3,208 1,139
2035 369,662 2,159 0.59 1,002 4,505 3,503 1,156
2040 380,016 2,022 0.53 848 4,612 3,765 1,174
2045 389,934 1,969 0.51 778 4,729 3,951 1,191
2050 399,803 1,985 0.50 781 4,820 4,038 1,204
Vital eventsNet
international
migration1
Table 1. Projections of the Population and Components of Change for the United States: 2015 to 2060
Year PopulationNumeric
change
Percent
change
Natural
increase
http://www.census.gov/population/projections/data/national/2012/summarytables.html
U.S. Population Projections
thousands
29.2
7.6 9.5
42.9
45.8
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
50.0
United States Northeast Midwest South West
Interim Projections: Percent Change in Population by Region of the United States, 2000 to 2030
Source: U.S. Census Bureau, Population Division, Interim State Population Projections, 2005
Texas Population Projections
Low – zero migration
High – 2000-2010
migration rate
http://txsdc.utsa.edu/
19
Texas Population Projections
http://txsdc.utsa.edu/
Growth
rates vary
by year
and area
Changing Demographics
Aging Population
20
Changing Race Make-up
Changing Demographics Changing Demographics
Mean Commute travel
times
Year Minutes
1980 21.7
1990 22.4
2000 25.5
2009 25.1
Back to Demand Theory
• How does above fit into our simple
theoretical aggregated demand
– Changing demographic
• Aging – usually lower disposable income
• Work at home – lower travel expenses – increase
income to spend elsewhere
– Change in taste and preferences
• Change in indifference curve
• Only time will tell?
21
Changing Income and Utility Max
Land Units
B
un
dle
of
go
od
s
Increase in income
increase budget
constraint
Increase in budget
constraint move
equilibrium
Changing Income
Land Units
L
an
d P
rice
Increase in demand
D new
D original
World GDP – Increase - Projected
22
U.S. & Texas Income
Non Ag Land Resource Needs
• Increasing Population – mineral and energy
needs increasing
• Urbanization
• Increased incomes – increase demand for land
• Increased incomes – increase in recreational /
leisure activities
• All increasing demand for land
• Changing taste and preferences
Competition between Land Uses
• Highest and best use
• Conflicts of interest arise
– Many land uses are not compatible with each
other
– Owners have different objectives
– Conflicts of interest between owners and
society
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