Chapter 16 General Equilibrium Theory Chapter Sixteen Overview 1.General Equilibrium – Analysis I • Partial Equilibrium Bias 3.Efficiency and Perfect Competition 5.General Equilibrium – Analysis II • The Efficiency if Competition • The Edgeworth Box • Analysis of Allocation: A Pure Exchange Economy • Analysis of Production Chapter Sixteen Partial vs General Equilibrium 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 Chapter Sixteen Partial vs General Equilibrium 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 not take into account all markets in our equilibrium calculation, we induce a bias in our analysis Chapter Sixteen Partial vs General Equilibrium Definition: General Equilibrium analysis is the study of how equilibrium is determined in all markets simultaneously (e.g product markets and labor markets) 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 Partial vs General Equilibrium Example: Equilibrium in two markets Q1D = 12 – 3p1 + p2 Q2D = – 2p2 + p1 Q1s = + p1 Q2s = + p2 What is the general equilibrium level of prices and output in this economy? Market equilibrium: • 12 – 3p1 + p2 = + p1 • p1 = 10/4 + p2/4 Market equilibrium: • – 2p2 + p1 = + p2 • p2 = + p1/3 Chapter Sixteen Partial vs General Equilibrium Substituting condition into condition 2: – 2p2 + 10/4 + p2/4 = + p2 • = p2e • = p1e • Q1e = • Q2e = Chapter Sixteen Equilibrium in Two Markets P1 Market 4.67 P1 = + P2/3 – QD1/3 14 Chapter Sixteen Q1 Equilibrium in Two Markets P1 P1 = Q1s - Market 4.67 14 Chapter Sixteen Q1 Equilibrium in Two Markets P1 P1 = Q1s - Market 4.67 e1 • P1 = + P2/3 - Q1D/3 14 Chapter Sixteen Q1 The Producers’ Problem 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: Max Π = 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 Isoprofit Definition: an isoprofit line shows the output combinations that result in a given level of profit, Π0 or QY = (Π0 + C*)/pY – pXQX/pY Chapter Sixteen The Profit Maximizing Product Mix Y PPFJ X Chapter Sixteen The Profit Maximizing Product Mix Y Isoprofit Lines (Π0+C*)/PY • -pX/pY PPFJ X Chapter Sixteen The Profit Maximizing Product Mix Y Isoprofit Lines (Π0+C*)/PY Direction of increasing profits • Profit maximising product mix -pX/pY PPFJ X Chapter Sixteen The Profit Maximizing Product Mix 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 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 Therefore 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 General Equilibrium Y PPF X Chapter Sixteen General Equilibrium Y Ys XeB • YeB PPF Xs X Chapter Sixteen General Equilibrium Y Ys XeB • • Slope = -p1e/p2e YeB PPF XeA X Xs Chapter Sixteen General Equilibrium Y Ys YeA XeB • • Slope = -p1e/p2e YeB PPF XeA Xs X Chapter Sixteen General Equilibrium Where: 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 Consider • Efficiency in exchange (on contract curve) • Efficiency in use of inputs (on PPF) • Efficiency in product mix (tangency with PPF) Chapter Sixteen Fundamental Theorems of Welfare Economics 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 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 Summary 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 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 Summary 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 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 ... in equilibrium Chapter Sixteen Edgeworth Box – Infeasible Allocation Chapter Sixteen Edgeworth Box – Infeasible Allocation Chapter Sixteen Edgeworth Box – Infeasible Allocation Chapter Sixteen... Chapter Sixteen Equilibrium in Two Markets P2 P2 = Q2s - Market 5.5 P2 = + P1/2 - Q2D/2 11 Chapter Sixteen Q2 Equilibrium in Two Markets P2 P2 = Q2s - Market 5.5 e2 • P2 = + P1/2 - Q2D/2 11 Chapter. .. supply of each good Chapter Sixteen Edgeworth Box Diagram Chapter Sixteen Edgeworth Box Diagram Chapter Sixteen Edgeworth Box Diagram Chapter Sixteen Edgeworth Box Diagram The length of the side