Total Output, x “Stylized” view of production functions – long run and short run Long-run Production with 2 variable inputs (v 1, v 2 ): v1v1 v2v2 v11v11 v12v12 v21v21 v22v22 xAxA xBxB xCxC Labor Input, v 1 (with v 2 fixed) Total Output, Q Short-run Production with 1 fixed input (v 2 1 ) & 1 variable input (v 1 ): v11v11 v12v12 f(v1)f(v1) Production set

x 1 = f ( v 1, v 2 ) x1x1 v1v1 v1*v1* x1*x1* Isoprofit lines with slope Profit Maximization

Factors Affecting a Firm’s Cost Behavior Cost Function Technology Diminishing Returns Economies of Scale Economies of Scope  Factor Costs Purchasing Power Market Power of suppliers  Varian, (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(v 1, v 2 )

v1v1 Total Output, x Long-run production, factor intensity, and optimal input usage A “general rule” for efficient input usage: Isoquants v2v2 x0x0 x1x1 x2x2 x0x0 x1x1 x2x2 v1v1 v2v2

Long-run production, factor intensity, and factor substitution v1v1 v2v2 Elasticity of (factor) substitution: x0x0 x1x1 x2x2

v2v2 v1v1 v1*v1* v2*v2* Isocost lines with slope – w 1 /w 2 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 equations Prices 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  · The “Edgeworth Box”: a pure exchange economy x ·  ·

Assumptions: Pure exchange economy Two 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: Hence, we are seeking a set of prices,, that satisfies these equilibrium conditions. The Algebra of Equilibrium

A B ’’ · x’x’ ·  · 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 equations Prices 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. = and MRTS i,j 1 = MRTS i,j 2

Production x1x1 x2x2 x1x1 x2x2 x 1 = f ( v 1, v 2 ) = f ( v 1 ) = 10 v 1 1 x 2 = g ( v 1, v 2 ) = g ( v 1 ) = 20 v 1 2 Resource Constraint: v 1 = 10 (Hence, v v 1 2 = 10) x 1 /10 + x 2 /20 = 10 x 2 = x / x1x1 x2x2 300 x 1 = f ( v 1, v 2 ) = f ( v 1 ) = 20 v 1 1 x 2 = g ( v 1, v 2 ) = g ( v 1 ) = 10 v 1 2 Resource Constraint: v 1 = 10 (Hence, v v 1 2 = 10) x 1 /20 + x 2 /10 = 10 x 2 = /2 x 1 x1x1 x2x2 Add a 3 rd producer …

The Edgeworth Box used to illustrate a production economy [ ] Two goods,, produced with two inputs. [ ] Allocation of inputs to production: the amount of allocated to production of. Red: Isoquants for production of Blue: Isoquants for production of - MRTS

General Equilibrium: exchange and production [ ] Two consumers,, two goods,, produced with two inputs. [ ]

Producing Sectors: 1.Manufacturing 2.Mineral Extraction 3.Chemicals and Plastics 4.Agriculture 5.Transportation 6.Public Utilities 7.Communication 8.Services 9.Government Goods and Services: 1.Food 2.Apparel 3.Consumer Transport 4.Consumer Services 5.Business Services 6.Energy 7.Housing ProductionExchange Output Prices Input Prices Computable General Equilibrium (CGE) Models

Social Welfare Functions and Social Choice Theory  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? Utility Possibility Set Isowelfare Lines

A 10% 26% 30% B 15% 24% 36% C 25% Poor Middle Rich Preferences Poor: Middle: Rich: A B C B C A C 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 R.G. Lipsey and Kelvin Lancaster, “The General Theory of Second Best”, The Review of Economic Studies (1956).