General Equilibrium and Economic Welfare Perloff Chapter 10

General Equilibrium Partial equilibrium General equilibrium Changes in equilibrium are analysed in one (or a few) markets in isolation. Prices and quantities in ‘unrelated’ markets are held fixed. General equilibrium The study of how equilibrium is attained in all markets simultaneously.

GE in Corn and Soya Beans (a) Corn Market S c S c 3 e c Price, $ per bushel $2.15 D c e c $1.9171 1 e c 3 $1.9057 D c 1 8.227 8.2613 8.44 Corn, Billion bushels per year (b) Soybean Market S s e s $4. 12 Price, $ per bushel D s S s 2 S s 4 e s 2 $3.8325 $3.8180 e s 4 D s 2 D s 4 2.0505 2.0514 2.07 Soybeans, Billion bushels per year

Min. wages with incomplete coverage (a) Covered Sector (b) Uncovered Sector (c) Total Labor Market w, Wage per hour w, Wage per hour w, Wage per hour S w – S u w w w 1 1 1 Demand curve is the sum of individual demands in the two sectors. Interaction of S and D at aggregate level produces a wage of w1 and corresponding levels of employment in the 2 sectors. Min wage in in the covered sector causes employment to fall. Supply in the uncovered sector is effectively increased. Supply can be found as Market supply minus employment in the covered sector. This gives a new eq at w2. w 2 D c D u D L 2 L 1 L 1 L 2 L = L 1 + L 1 c c u u 1 c u L , Annual hours L , Annual hours L , Annual hours c u

Trade Between People: The Edgeworth Box (a) Jane ’ s Endowment (b) Denise ’ s Endowment Firewood, Cords e Firewood, Cords 30 j e 20 d I 1 I 1 d j j 20 Jane ’ s candy d 60 Denise ’ s candy Candy, Bars Candy, Bars (c) Edgeworth Box Jane ’ s candy Denise C A B 20 40 60 80 50 30 e a f j d I 1 Jane’s wood Denise’s wood

Obtaining the contract curve Denise ’ s candy 80 60 40 d 50 g Denise’s wood I Contract curve d d I 4 I 1 e j d 30 20 I 2 d c I 3 d f 20 30 B I 3 b I 2 j j I 1 j Jane’s wood a 50 20 40 80 j Jane ’ s candy

Four equivalent statements about points on the contract curve The indifference curves are tangential. The marginal rates of substitution are equal. No further mutually beneficial trades are possible. The allocation is Pareto efficient: One person cannot be made better off without making the other worse off.

Price that doesn’t lead to equilibrium (b) Prices That Do Not Lead to a Competitive Equilibrium Denise ’ s candy 80 60 43 d 50 45 Denise’s wood I 1 d e 30 20 I 2 d j 22 d 32 I 2 j 1.5 logs exchanged for 2 candy. Auctioneer recognises the existence of excess supply and demand and doesn’t allow trade. Calls out a new set of prices I 1 j Jane’s wood Price line a 50 j 20 30 60 80 Jane ’ s candy

Price that leads to equilibrium (a) Price Line That Leads to a Competitive Equilibrium Denise ’ s candy 80 60 40 d 50 Denise’s wood 40 I 1 d e 30 20 I 2 d f 20 30 I 2 j I 1 1 log is exchanged for 2 candy. j Jane’s wood Price line a 50 20 40 80 j Jane ’ s candy

Theorems of Welfare Economics The competitive equilibrium is Pareto efficient. Any efficient allocations can be achieved by competition. Any point on the contract curve can be achieved by trade along the appropriate price line. Achieving the desired point may involve some redistribution (value judgements required)

Production Possibilities 2 Firewood, Cords I 1 PPF a 50 Condition for efficient product mix. b 80 Candy, Bars

Competition Ensures Efficiency

The whole picture Price line Firewood, Cords 1 – – 2 1 PPF Jane s candy Jane’s wood 40 I j d Price line 1 – 2 20 30 f Denise ’ Denise’s wood a 50 j 80 Candy, Bars ’

Is efficiency enough? Many policies make somebody better off at the expense of somebody else. Producer surplus plus consumer surplus. As long as producers gain more than consumers lose, its efficient eg. first degree price discrimination. Weights producers and consumers equally.

Utility possibilities frontier Denise ’ s candy d Denise’s utility UPF Denise’s wood Jane’s wood j Jane s candy Jane ’ s utility

Welfare maximisation (a) (b) a Denise’s utility Denise’s utility UPF 3 The right hand picture shows the situation where we individuals welfare are weighted equally regardless of how much they have. Argue that the left is more realistic. W 1 W 2 c W 1 W 2 W 3 Jane ’ s utility Jane ’ s utility

How do we arrive at a social preference ranking Individuals rankings are transitive We need a rule which allows us to convert individual rankings into a social ranking. Majority voting 2 prefer a to b, 2 prefer b to c, transitivity would require 2 to prefer a to c. But 2 prefer c to a.

Voting with non-transitive prefrences With non-transitive preferences result depends on order the vote is taken in. a compared to b then compare winner to c a chosen in first vote c chosen in second vote c compared to a then compare winner to b c chosen in first vote b chosen in second vote

Arrow’s impossibility theorem Desirable properties of a social preference ordering. Complete If everyone prefers a to b, the social ranking should do the same Social ranking of a to b should not depend on the what other alternatives are available Dictatorship is not allowed No rule exists which produces a ranking that always satisfies these properties