opportunity cost and production possibilities overheads

Opportunity Cost and Production Possibilities

Overheads

Opportunity CostOpportunity Cost

The The opportunity costopportunity cost of any choice of any choice

is what we give up when we makeis what we give up when we make

that choicethat choice

The The opportunity costopportunity cost of any good or of any good or serviceservice

is its value in its next best alternative useis its value in its next best alternative use ..

For example, the For example, the opportunity costopportunity cost of the of the

service of an service of an inputinput used in the production used in the production

of any particular commodity is the of any particular commodity is the

maximum maximum amount that the input would amount that the input would

produceproduce of any other commodity. of any other commodity.

Examples of Opportunity CostExamples of Opportunity Cost

1.1. Farmer who raises hogs and considers Farmer who raises hogs and considers using his own corn to feed the hogsusing his own corn to feed the hogs

2.2. Recent college graduate who chooses Recent college graduate who chooses a high paying job in Chicago when his a high paying job in Chicago when his family all live in Iowa and he plans to family all live in Iowa and he plans to visit them once or twice a monthvisit them once or twice a month

3.3. Businessman who hires a maid to clean his Businessman who hires a maid to clean his house so he has time to do more consulting house so he has time to do more consulting in the eveningin the evening

4.4. Woman who is considering whether to Woman who is considering whether to stay home and take care of her childrenstay home and take care of her childrenor work at a job paying $9.50 per houror work at a job paying $9.50 per hourand hire a baby sitterand hire a baby sitter

Examples of Opportunity CostExamples of Opportunity Cost

5.5. Seamstress who chooses to make blue Seamstress who chooses to make blue shirts instead of striped shirtsshirts instead of striped shirts

66.. A landowner decides to farm his A landowner decides to farm his own land instead of renting it to a own land instead of renting it to a neighborneighbor

Examples of Opportunity CostExamples of Opportunity Cost

Individuals who have a high value of time - Individuals who have a high value of time -

either due to high income, either due to high income, or personal preferenceor personal preference

- have a high opportunity cost for- have a high opportunity cost foralternative activitiesalternative activities

All economic decisions taken by individuals All economic decisions taken by individuals or society are costly or society are costly

Principle of Opportunity CostPrinciple of Opportunity Cost

The correct way to measure the cost of a The correct way to measure the cost of a

choice is its opportunity cost — choice is its opportunity cost —

that which is that which is given upgiven up to make the choice to make the choice

The Process of Production

Uses Inputs

Produces Outputs

An input is a good or service that An input is a good or service that

is employed in the production is employed in the production

processprocess

Inputs are denoted by x or byInputs are denoted by x or byxx11, x, x22, … , x, … , xnn

An output is a good or serviceAn output is a good or service

that is the outputthat is the output

of a particular production process of a particular production process

Outputs are denoted by y or byOutputs are denoted by y or byyy11, y, y22, … , y, … , ymm

Production TechnologiesProduction Technologies

The The technology settechnology set (technology for short) (technology for short)

for a given production process is defined for a given production process is defined

as the set of as the set of all input and output all input and output

combinationscombinationssuch that the such that the set of outputs yset of outputs y

can be produced fromcan be produced from

the given set of the given set of inputs xinputs x

The technology set is the set of The technology set is the set of

feasible input and output feasible input and output

combinationscombinations

Inputs Used for Producing Holes in the GroundInputs Used for Producing Holes in the Ground

shovel semi skilled labor

Output for the Digging TechnologyOutput for the Digging Technology

Some number of postholes or trenchesSome number of postholes or trenches

1 shovel 1 hour semi skilled labor

4 postholes 0 trenches

Elements of the Digging Technology SetElements of the Digging Technology Set

1 shovel 1 hour semi skilled labor

0 postholes 2 trenches

1 shovel 1 hour semi skilled labor

2 postholes 1 trenches

Elements of the Digging Technology SetElements of the Digging Technology Set

powdered milk water eggs oil

flour baking powder salt bowl

whip measuring set cup spatula

small griddle camp stove white gas matches

semi skilled labor butter maple syrup

plate knife fork

Inputs Used for Producing PancakesInputs Used for Producing Pancakes

The Output (single) for the Pancake TechnologyThe Output (single) for the Pancake Technology

Some number of pancakes served Some number of pancakes served on a plate with butter and syrup on a plate with butter and syrup along with a knife and forkalong with a knife and fork

One Element of the Pancake Technology SetOne Element of the Pancake Technology Set

1/3c powdered milk 15/16c water 1egg 2Toil

1c flour 2t baking powder 1/4t salt 1bowl

1whip 1measuring set 1 cup 1 spatula

1small griddle 1camp stove 1/4c white gas 2matches

1/4 h semi skilled labor 3Tbutter 1/2c maple syrup

1plate 1knife 1fork

10 pancakes

The Producible Output Set P(x)The Producible Output Set P(x)

The producible output set P(x)

is the set of all combinations of outputs,

that are obtainable from a fixed level of inputs.

Construction of the Producible Output SetConstruction of the Producible Output Set

Fix all inputs at a specific level

x ( x1, x2, x3, , xn)

For that level of y1, list all feasible

levels of y2 , then repeat this for all other

levels of y1.

Fix the level of y1 at some level, say y1

pancakes

crepes

P(x)

Producible Output Set for Pancakes and CrepesProducible Output Set for Pancakes and Crepes

5

12 14

10

00

Law of Increasing Opportunity CostLaw of Increasing Opportunity Cost

The more of something we produce,The more of something we produce,

the greater is the opportunity costthe greater is the opportunity costof producing still more.of producing still more.

200 acres land 20,000 lbs nitrogen 1 combine 1 grain head 1 corn head

15 hrs labor per month 1 tractor 1 disk 1 planter 1 rotary hoe

400 gallons diesel 1 row cultivator 1 wagon 1 hand hoe 1 butterfly net

60 bags corn seed 120 bags soybean seed

Vector of Inputs for Corn and SoybeansVector of Inputs for Corn and Soybeans

Possible Output Combinations for Corn and SoybeansPossible Output Combinations for Corn and Soybeans

CornCorn SoybeansSoybeans

16,00016,000 0 0 00 4,000 4,000

9,6009,600 3,000 3,000

soybeans

corn

P(x)

Producible Output Set for Corn and SoybeansProducible Output Set for Corn and Soybeans

16,000

4,000

9,600

3,000

0

The Boundary of the Set is Concave

0

Why concavity of the boundary?

Some inputs are better suited to some uses

Some allocated inputs may be shared(between uses)

New Digging Technology SetNew Digging Technology Set

2 identical semi-skilled workers

1 shovel 1 post hole digger

Input-Output CoefficientsInput-Output Coefficients

Shovel

Post Holes/Hour Trenches/Hour

4 2

Post Hole Digger

6 1/2

Some Efficient Sample PointsSome Efficient Sample Points

Each worker can only use one tool

10 post holes - No trenches

6 post holes - 2 trenches

0 post holes - 2.5 trenches

8 post holes - 1 trench

3 post holes - 2.25 trenches

0

2

4

6

8

10

12

0 0.5 1 1.5 2 2.5 3

Trenches

Po

sth

ole

sPostholes and Trenches

(2,6)

(1,8)

(2.25, 3)

(1.25,7.5)(0.5, 9)

Some Inefficient Sample PointsSome Inefficient Sample Points

5 post holes - 1.25 trenches

3 post holes - 1 trench

4 post holes - 0.5 trenches

(1/2 time on each)

(“wrong” tasks)

(rest 1/2 time)

Wrong Tasks

¼ holes

0

2

4

6

8

10

12

0 0.5 1 1.5 2 2.5 3

Trenches

Po

sth

ole

sPostholes and Trenches

(2,6)

(1,8)

(2.25, 3)

(1, 3)

(1.25, 5)½ each1 7/8, 2.5

(0.5, 4)Shirk

(1.25,7.5)(0.5, 9)

Buttons on right

Buttons on left

Shirts with buttons on the left and on the rightShirts with buttons on the left and on the right

P(x)

Linear Producible Output Set12

12

Production Possibility FrontierProduction Possibility Frontier

The boundary of the producible output set is calledThe boundary of the producible output set is calledthe production possibility frontierthe production possibility frontier

P(x)

y1

y2

PPF

Efficient and Inefficient PointsEfficient and Inefficient Points

Points in P(x) that are on the frontier are called efficient pointsPoints in P(x) that are on the frontier are called efficient points

Points in the interior of the set P(x) are called inefficient pointsPoints in the interior of the set P(x) are called inefficient points

We say that an input-output combination is We say that an input-output combination is technically efficienttechnically efficient if the maximum possible output is being produced given the inputs.if the maximum possible output is being produced given the inputs.

We say that an input-output combination is We say that an input-output combination is technically efficienttechnically efficientif it is on the production possibility frontier.if it is on the production possibility frontier.

P(x)

y1

y2

PPF

Inefficient Production PointsInefficient Production Points

0

2

4

6

8

10

12

0 0.5 1 1.5 2 2.5 3

Trenches

Po

sth

ole

sPostholes and Trenches

(2,6)

(1,8)

(2.25, 3)Wrong Tasks

Shirk

(1.25,7.5)

Wrong Division

Once we are on the production possibility frontier, Once we are on the production possibility frontier,

No Free LunchNo Free Lunch

we cannot produce more of one output,we cannot produce more of one output,

without producing less of another outputwithout producing less of another output

0

2

4

6

8

10

12

0 0.5 1 1.5 2 2.5 3

Trenches

Po

sth

ole

sPostholes and Trenches

0

2

4

6

8

10

12

0 0.5 1 1.5 2 2.5 3

Trenches

Po

sth

ole

sPostholes and Trenches

A Free LunchA Free Lunch

If we are at a point in the producible output setIf we are at a point in the producible output setthat is not on the boundary,that is not on the boundary,

then we can get more output from the then we can get more output from the same input bundle and thus there is a “free same input bundle and thus there is a “free lunch.”lunch.”

0

2

4

6

8

10

12

0 0.5 1 1.5 2 2.5 3

Trenches

Po

sth

ole

sPostholes and Trenches

(2,6)

(1,8)

(2.25, 3)Wrong Tasks

Shirk

(1.25,7.5)

Wrong Division

(0.5, 9)

The End