Lecture 18 Towards general equilibrium Microeconomics 1000 Lecture 18 Towards general equilibrium

General equilibrium Partial equilibrium analysis focuses on a single market It is based on the ceteris paribus (i.e. all else equal) assumption But changes in one market may also affect several other markets A change in the price of a product affects the demand for complements and substitutes A change in the price of a factor of production affects the income of the owners of that factor, and hence their demand for goods Hence the need for general equilibrium analysis 6

Main problems Can a general equilibrium (i.e. a state where all markets are simultaneously in equilibrium) be reached? Is the general equilibrium efficient?

Figure 1 The Circular Flow Firms sell Households buy MARKETS FOR GOODS AND SERVICES Revenue Spending Goods and services sold Goods and services bought FIRMS Produce and sell goods and services Hire and use factors of production Buy and consume goods and services Own and sell factors of production HOUSEHOLDS Households sell Firms buy MARKETS FOR FACTORS OF PRODUCTION Factors of production Labor, land, and capital Wages, rent, and profit Income = Flow of inputs and outputs = Flow of dollars Copyright © 2004 South-Western

The Circular-Flow Diagram: agents Firms Produce and sell goods and services Hire and use factors of production Households Buy and consume goods and services Own and sell factors of production 7

The Circular-Flow Diagram: markets Markets for Goods and Services Firms sell Households buy Markets for Factors of Production (inputs, such as land, labor and capital, used to produce goods and services) Households sell Firms buy 7

Our First Model: One Good, One Input, One (Representative) Household Suppose there is only one good (corn) and only one input (labour) Hence, two markets Many identical households Many identical firms Perfect competition in both markets 7

Figure 2 The Production Function Quantity of Corn 3000 1000 Quantity of Labour Copyright©2003 Southwestern/Thomson Learning

Firm’s equilibrium We know that a perfectly competitive firm maximises its profit at a point where p = MC, or, equivalently, w = VMPL We can depict the profit-maximising choice of a point on the production function using iso-profit lines, i.e., lines where profit is constant

Iso-profit lines Dividing by p and re-arranging we get The slope of the iso-profit line is the real wage rate, i.e., the wage rate measured in units of corn

Figure 3 Equilibrium of the (representative) firm Quantity of Corn 3000 Supply of corn E Demand for labour 1000 Quantity of Labour Copyright©2003 Southwestern/Thomson Learning

Firm’s equilibrium The firm maximises its profit when it reaches the highest iso-profit line, given the production function. The slopes of the production function and the iso-profit line are equal at the optimum, i.e. This is the standard condition p = MC or w = VMPL

Household’s equilibrlium We have already analysed the household’s optimal choice of labour supply

Figure 4 Equilibrium of the (representative) household Quantity of Corn Demand for corn E Non-labour income Labour supply leisure 1000 Quantity of Leisure Copyright©2003 Southwestern/Thomson Learning

Important properties: relative prices Only relative prices matter (the real wage rate, i.e. the wage rate measured in units of corn) The real wage rate determines both the slope of the iso-profit lines (and hence the firm equilibrium) and the slope of the budget constraint (and hence the household equilibrium) Thus, with two goods we have in fact only one price to determine

The Production Possibilities Frontier The production possibilities frontier is a graph that shows the combinations of output that the economy can possibly produce given the available factors of production and the available production technology. 14

Figure 5 The Production Possibilities Frontier Quantity of Corn 3,000 D C 2,200 600 A 700 2,000 Production possibilities frontier 1,000 300 B 1,000 Quantity of Leisure Copyright©2003 Southwestern/Thomson Learning

Important properties: Walras’ law The two markets are interdependent When one market is in equilibrium, the other is necessarily in equilibrium Hence, with two goods we have in fact only one independent equilibrium condition And, indeed, we have only one (relative) price to determine

Figure 6 Disequilibrium: excess supply of labour Quantity of Corn H 3,000 Excess demand for corn K Excess supply of labour 1,000 Quantity of Leisure Copyright©2003 Southwestern/Thomson Learning

Figure 7 Disequilibrium: excess demand for labour Quantity of Corn 3,000 K Excess supply of corn H Excess demand for labour 1,000 Quantity of Leisure Copyright©2003 Southwestern/Thomson Learning

Figure 8 The General equilibrium Quantity of Corn 3,000 E 2,200 600 1,000 Quantity of Leisure Copyright©2003 Southwestern/Thomson Learning

Important properties: efficiency The general equilibrium of a perfectly competitive economy is efficient With homogeneous agents, efficiency is equivalent to the maximisation of the welfare (utility) of the representative agent

Figure 9 Efficiency of the General equilibrium Quantity of Corn 3,000 E 2,200 600 1,000 Quantity of Leisure Copyright©2003 Southwestern/Thomson Learning

Feedback Answers to Exercises are posted on the course web page Answers to Questions Sheets and mock exams will be posted TAs should mark the essays you hand in

Our Second Model: Two Goods, One Input, Constant Returns Suppose there are two goods (corn and bicycles) and again only one input (labour) Now, however, the marginal productivity of labour is constant Suppose that the supply of labour is fixed at 100 workers, and the productivity of labour is 10 bicycles or 20 tons of corn per worker 7

Constant marginal cost When marginal products and marginal costs are constant, prices are determined only by the supply side of the market Market demand affects only equilibrium quantities This simplified framework was used by classical economists (Adam Smith, David Ricardo)

Adam Smith (1723-1790)

David Ricardo (1772-1823)

Figure 10 The Ricardian Model Price of Corn Equilibrium price 450 1,000 Quantity of Corn Copyright©2003 Southwestern/Thomson Learning

Figure 11 The Production Possibilities Frontier in the Ricardian Model Quantity of Corn 2,000 C B Production possibilities frontier A 1,000 Quantity of Bicycles Copyright©2003 Southwestern/Thomson Learning

Equilibrium prices In terms of (tons of) corn, the wage rate is 20 and the price of a bicycle is 2 In terms of bicycles, the wage rate is 10 and the price of a ton of corn is ½

Figure 12 Equilibrium quantities Quantity of Corn 2,000 E 1,000 Quantity of Bicycles Copyright©2003 Southwestern/Thomson Learning