Total Output, x

“Stylized” view of production functions – long run and short run

Long-runProduction with 2 variable inputs (v1, v2):

v1

v2

v11 v1

2

v21

v22

xA

xB

xC

LaborInput, v1

(with v2 fixed)

Total Output, Q

Short-runProduction with 1 fixed input (v2

1)& 1 variable input (v1):

v11 v1

2

f(v1)

Production set

x1=f(v1, v2)

x1

v1

v1*

x1*

Isoprofit lines with slope

Profit Maximization

Factors Affecting a Firm’s Cost Behavior

( )xCCost Function

Technology

Diminishing Returns

Economies of Scale

Economies of Scope

Factor Costs

Purchasing Power

Market Powerof suppliers

Varian, 19.12 (p. 360):If a firm is maximizing profits and if it chooses to supply some output y, then it must be minimizing the cost of producing y. If this were not so, then there would be some cheaper way of producing y units of output, which would mean that the firm was not maximizing profits in the first place.This simple observation turns out to be quite useful in examining firm behavior. It turns out to be convenient to break the profit-maximization problem into two states: first we figure out how to minimize the costs of producing any desired level of output y, then we figure out which level of output is indeed a profit-maximizing level of output…

The Production Function:

x = f(v1, v2)

v1

Total Output, x

Long-run production, factor intensity, and optimal input usage

n

n

w

mp

w

mp

w

mp

2

2

1

1

A “general rule” for efficient input usage:

Isoquants

v2 x0x1

x2

x0

x1

x2

v1

v2

Long-run production, factor intensity, and factor substitution

v1

v2

Elasticity of (factor) substitution:

x0

x1

x2

v2

v1v1

*

v2* Isocost lines with slope – w1/w2

Isoquant associated with chosen output

Cost Minimization

General Equilibrium Theory

A General Economy

• m consumers• n producers

(n goods)• Resources

• m X n demand equations

• n supply equationsPrices

A Pure Exchange Economy An economy in which there is no production. A special case of a general economy in which economic activities consist only of trading and consuming.

The simplest form of a pure exchange economy is the two-agent, two-good exchange economy, which may be illustrated graphically using the Edgeworth – Bowley Box.

A

B

1A

2A

1x

1x

2x

2x

1B

2B

·

The “Edgeworth Box”: a pure exchange economy

0AU

0BU

x

·1AU

1BU

2

1P

P

·

Assumptions:Pure exchange economyTwo goods: and Two agents, A and B, with …

Identical preferences:

Arbitrarily determined, but different, endowments:

Equilibrium is defined as a consumption bundle Where aggregate excess demands are zero in both markets:

2121 ,;, BBAA xxxxx

0,

0,

212

211

ppz

ppz

1x 2x

10 ,

,12121

12121

xxxxU

xxxxU

B

A

2121 , ,

,

BBBAAA

BA

Hence, we are seeking a setof prices, , thatsatisfies these equilibrium conditions.

21, pp

The Algebra of Equilibrium

1AU

0AU

1BU

0BU

A

B

31 A

221 A ’ ·

1x

1x

2x

2x

61 B

62 B

51 Ax

215 Ax

41 Bx

122 Bxx’

·

21

A

71

B

25.13 Ax 5.132

Bx

5.41

Ax

5.41

Bx

·

x ·

Pure Exchange and Redistribution – Example from class

General Equilibrium Theory

A General Economy

• m consumers• n producers

(n goods)• Resources

• m X n demand equations

• n supply equationsPrices

A Pure Exchange Economy An economy in which there is no production. A special case of a general economy in which economic activities consist only of trading and consuming.

The simplest form of a pure exchange economy is the two-agent, two-good exchange economy, which may be illustrated graphically using the Edgeworth – Bowley Box.

A Production and Exchange Economy To achieve a general equilibrium, an production and exchange economy must simultaneously achieve efficiency in production and efficiency in exchange.

By,x

Ay,x

y

x MRSMRSp

p==y,xMRT =

and MRTSi,j

1 = MRTSi,j2

Production

x1

x2

x1

x2

x1 = f(v1, v2) = f(v1) = 10v11

x2 = g(v1, v2) = g(v1) = 20v12

Resource Constraint: v1 = 10(Hence, v1

1 + v12 = 10)

x1/10 + x2/20 = 10x2 = 200 - 2x1

200

-2 -1/2

200

100

100x1

x2

300

300

x1 = f(v1, v2) = f(v1) = 20v11

x2 = g(v1, v2) = g(v1) = 10v12

Resource Constraint: v1 = 10(Hence, v1

1 + v12 = 10)

x1/20 + x2/10 = 10x2 = 100 - 1/2x1

x1

x2

Add a 3rd producer …

11v

12v

1x

1v 2x

2v

21v

22v

The Edgeworth Box used to illustrate a production economy

1v2v

2

1

x

x[ ]Two goods, , produced with two inputs .[ ]2

1

v

vAllocation of inputs to production: the amount of allocated to production of .1v 2x≡21v

Red: Isoquants for production of

Blue: Isoquants for production of

1x

2x

-MRTS

1x

2x

0=1Z

General Equilibrium: exchange and production

1AU

1BU

2

1

x

x[ ]Two consumers, , two goods, , produced with two inputs .[ ]2

1

v

v

B

A[ ]

0=2Z

Producing Sectors:1.Manufacturing2.Mineral Extraction3.Chemicals and Plastics4.Agriculture5.Transportation6.Public Utilities7.Communication8.Services9.Government

Goods and Services:1.Food2.Apparel3.Consumer Transport4.Consumer Services5.Business Services6.Energy7.Housing

Production Exchange

Output PricesInput Prices

Computable General Equilibrium (CGE) Models

Social Welfare Functions and Social Choice Theory

AU

BU

The “Utilities Possibilities Set”

Any Pareto efficient allocation can be a welfare maximum for some welfare function.

Types of social welfare functions:

- Classical utilitarian- Rawlsian Is it possible to aggregate

individual preferences into a coherent social welfare function?

UtilityPossibility

Set

Isowelfare Lines

A

10% 26% 30%

B

15% 24% 36%

C

25% 25% 25%

PoorMiddleRich

PreferencesPoor:Middle:Rich:

A B CB C AC A B

Social Choice Theory: Voting and Aggregation of Preferences

Social Choice Theory: Arrow’s General Possibility Theorem

Condition 1: Given a set of consistent and transitive individual preferences, a social welfare function should exhibit similar rationality. [Unrestricted scope.]

Condition 2: If each individual prefers x to y, then the social welfare function should rank x ahead of y. [Positive association of individual and social values.]

Condition 3: The social welfare function’s ordering of x and y should not be altered by the introduction of a third option, z. [Independence of irrelevant alternatives.]Condition 4: The social welfare function is not imposed on society. [Citizens’ sovereignty.] Condition 5: The social welfare function is not a dictatorship.

General Possibility Theorem: Given at least three alternative which the members of a society are free to order in any way, every social welfare function that satisfies conditions 1 through 3 is either imposed or dictatorial.

Kenneth Arrow, Social Choice and Individual Values (1951)

It is impossible to construct an acceptable social welfare function out of individual preference functions.

The “General Theory of the Second Best”

Maximization of the objective function U, subject to the blue constraint (a production possibilities frontier) would result in selection of point B, which is technically efficient.

Imposition of the second constraint (red) would lead to selection of point A which is preferable to point C even though point C is technically efficient while point A is technically inefficient.The General Theory of the Second Best: If certain constraints

within an economic system prevent some efficiency conditions from holding, then, given these secondary constraints, it generally will not be desirable to have the optimum conditions hold elsewhere in the system.

A

B

C

Quantity of x

Quantity of y

1U

2U

3U

4U

R.G. Lipsey and Kelvin Lancaster, “The General Theory of Second Best”, The Review of Economic Studies (1956).