Lecture Microeconomics (5th edition): Chapter 16 - General equilibrium theory. This chapter presents the following content: General equilibrium – Analysis I, efficiency and perfect competition, general equilibrium – Analysis II.
Chapter 16 Copyright (c)2014 John General Equilibrium Theory Chapter Sixteen Overview General Equilibrium – Analysis I • Partial Equilibrium Bias Efficiency and Perfect Competition General Equilibrium – Analysis II • The Efficiency if Competition • The Edgeworth Box • Analysis of Allocation: A Pure Exchange Economy • Analysis of Production Chapter Sixteen Copyright (c)2014 John Partial vs. General Equilibrium Chapter Sixteen Copyright (c)2014 John If there are spillover effects from one market to another, then the effects of a change in one market on the economy must be analyzed by examining its effect on all markets Partial vs. General Equilibrium Copyright (c)2014 John Further, many exogenous events (or policy changes) affect many markets simultaneously (example: discovery of a major oil deposit that raises the income of all citizens in an economy and so affects equilibrium in all markets) If we do not take into account all markets in our equilibrium calculation, we induce a bias in our analysis Chapter Sixteen Partial vs. General Equilibrium Definition: Partial Equilibrium analysis is the study of how equilibrium is determined in only a single market (e.g. a single product market) Chapter Sixteen Copyright (c)2014 John Definition: General Equilibrium analysis is the study of how equilibrium is determined in all markets simultaneously (e.g. product markets and labor markets) Partial vs. General Equilibrium Example: Equilibrium in two markets Q1D = 12 – 3p1 + p2 Q1s = 2 + p1 Q2D = 4 – 2p2 + p1 Q2s = 1 + p2 Copyright (c)2014 John What is the general equilibrium level of prices and output in this economy? Market 1 equilibrium: • 12 – 3p1 + p2 = 2 + p1 • p1 = 10/4 + p2/4 Market 2 equilibrium: • 4 – 2p2 + p1 = 1 + p2 • p2 = 1 + p1/3 Chapter Sixteen Partial vs. General Equilibrium Substituting condition 1 into condition 2: • • • • Copyright (c)2014 John 4 – 2p2 + 10/4 + p2/4 = 1 + p2 2 = p2e 3 = p1e Q1e = 5 Q2e = 3 Chapter Sixteen Equilibrium in Two Markets P1 4.67 P1 = 4 + P2/3 – QD1/3 Q1 14 Chapter Sixteen Copyright (c)2014 John Market Equilibrium in Two Markets P1 P1 = Q1s 2 4.67 Q1 2 14 Chapter Sixteen Copyright (c)2014 John Market Equilibrium in Two Markets P1 P1 = Q1s 2 4.67 e1 • P1 = 4 + P2/3 Q1D/3 Q1 2 5 14 Chapter Sixteen 10 Copyright (c)2014 John Market The Producers’ Problem Max = pXQX + pYQY – C*QX,QY Where: we will suppose that the cost of production is fixed whatever the optimal output mix (e.g., we just want to know how to employ the labor we have contracted) Chapter Sixteen 73 Copyright (c)2014 John Suppose that the producers produce goods X and Y and choose the product mix so as to maximize profits given the prices pX and pY: Isoprofit Copyright (c)2014 John Definition: an isoprofit line shows the output combinations that result in a given level of profit, 0 or QY = ( 0 + C*)/pY – pXQX/pY Chapter Sixteen 74 The Profit Maximizing Product Mix Copyright (c)2014 John Y PPFJ X Chapter Sixteen 75 The Profit Maximizing Product Mix Y ( 0+C*)/PY Copyright (c)2014 John • pX/pY PPFJ X Chapter Sixteen 76 The Profit Maximizing Product Mix Y ( 0+C*)/PY • Profit maximising product mix pX/pY PPFJ X Chapter Sixteen 77 Copyright (c)2014 John Direction of increasing profits Hence, If the firm maximizes profits, then, it chooses the product mix that shifts out the isoprofit line as much as possible while remaining feasible. This is a tangency point such that for all producers: MRTX,Y = pX/pY Chapter Sixteen 78 Copyright (c)2014 John The Profit Maximizing Product Mix The Profit Maximizing Product Mix In other words, in equilibrium, the price ratio will measure the opportunity cost of production of one good in terms of production of the other good Because competition ensures that both the MRS and the MRT equal the (same) price ratio for all producers and all consumers, a competitive equilibrium achieves an efficient product mix for all producers and all consumers Earlier allocative efficiency results still hold with production Chapter Sixteen 79 Copyright (c)2014 John Therefore General Equilibrium PPF Chapter Sixteen X 80 Copyright (c)2014 John Y General Equilibrium Ys XeB • YeB Xs PPF Chapter Sixteen X 81 Copyright (c)2014 John Y General Equilibrium Ys XeB • • Slope = p1e/p2e YeB PPF XeA Xs Chapter Sixteen X 82 Copyright (c)2014 John Y General Equilibrium Ys YeA XeB • XeA • Slope = p1e/p2e YeB Xs PPF Chapter Sixteen X 83 Copyright (c)2014 John Y General Equilibrium Ys and Xs are the amounts of X produced in the economy; (XeA,YeA) is the amount of X and Y consumed by person A and (XeB,YeB) is the amount of X and Y consumed by person B • • • Efficiency in exchange (on contract curve) Efficiency in use of inputs (on PPF) Efficiency in product mix (tangency with PPF) Chapter Sixteen Consider 84 Copyright (c)2014 John Where: 1. The allocation of goods and inputs that arises in a general competitive equilibrium is economically efficient. That is, given the resources available to the economy, there is no other feasible allocation of goods and inputs that could simultaneously make all consumers better off 2. Any economically efficient allocation of goods and inputs can be attained as a general competitive equilibrium through a judicious allocation of the economy’s scarce supplies of resources Chapter Sixteen 85 Copyright (c)2014 John Fundamental Theorems of Welfare Economics 1. If there are spillover effects among markets in the economy, we need to calculate equilibrium by determining equilibrium in all markets simultaneously. Otherwise, our results for equilibrium prices and quantities will be biased. This bias can be large 2. In partial equilibrium analysis, a perfectly competitive and allocates goods in a way market produces a Pareto efficient amount of output that is Pareto efficient Chapter Sixteen 86 Copyright (c)2014 John Summary 3. We can make a similar statement about perfect competition in a general equilibrium analysis. In other words, taking into account that income is determined endogenously and costs are determined endogenously was well, we can still state that perfect competition produces a Pareto efficient amount of output and allocates it in a Pareto efficient way 4. More specifically, competitive allocations are efficient in exchange, efficient in the use of inputs in production, and efficient in the mix of outputs Chapter Sixteen 87 Copyright (c)2014 John Summary ... underestimate the true price for good 1 Chapter? ?Sixteen 15 Equilibrium in Many Markets Copyright (c)2014 John Consider an economy with: types of households – white-collar households and blue-collar households purchasing... of which is produced with input services – labor and capital Chapter? ?Sixteen 16 Copyright (c)2014 John Equilibrium in Many Markets Chapter? ?Sixteen 17 The law that states that in a general competitive... of each good Chapter? ?Sixteen 22 Copyright (c)2014 John Edgeworth Box Copyright (c)2014 John Edgeworth Box Diagram Chapter? ?Sixteen 23 Copyright (c)2014 John Edgeworth Box Diagram Chapter? ?Sixteen