Production Possibilities FrontierOutput Market EfficiencyGeneral equilibrium in the output marketCite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 1 1 Production Possibilities Frontier 14.01 Principles of Microeconomics, Fall 2007 Chia-Hui Chen October 31, 2007 Lecture 20 Produc tion Possibilities Frontier and Output Market Efficiency Outline 1. Chap 16: Production Possibilities Frontier 2. Chap 16: Output Market Efficiency 1 Produc tion Possibilities Frontier Marginal rate o f transformation (MRT ): • How much clothing must be given up to produce one additional unit of fo od. • The absolute value of the slope of the production possibilities frontier. • If MRT increases in fo od, then the production possibilities frontier is concave. • M CFM RT = . M CC Proof. Reducing $1 input from clothing, C decreases by 1 ; adding $1 M CC input to food, F increases by 1 . Thus, M CF 1ΔC M CC M CFM RT = = = . ΔF 1 M CCM CF 2 Output M arket Efficiency Suppose we have two industries, clo thing and food, in the market. Consumers have demand for the two goods. They have a representative utility U (C, F ). A Pareto efficient result occ urs w hen the production possibilities frontier is tangent to the indifference curve (see Figure 3). That is to say, M RT = M RS.10 9 OC8 7 6 5 4 3 2 OF1 0 0 1 2 3 4 5 6 7 8 9 10 C 10 9 8 7 6 5 4 3 2 1 0 Clothing Production Possibilities Frontier Food 0 1 2 3 4 5 6 7 8 9 10 F Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 2 2 Output Market Efficiency Figure 1: Production Contract Curve. Figure 2: Production Possibilities Fro ntier.1 2 3 4 5 6 7 8 9 C Production Possibilities Frontier Indifference Curve 10 0 0 1 2 3 4 5 6 7 8 9 10 F 10 0 1 2 3 4 5 6 7 8 9 C Production Possibilities Frontier Indifference Curve 0 1 2 3 4 5 6 7 8 9 10 F Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 3 2 Output Market Efficiency Figure 3: Production Possibilities Fro ntier and Indifference Curve.Figure 4: Equilibrium in the Output Market.Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 2.1 General equili bri um in the output market 4 The prices are PF for food, and PC for clothing. When the market reaches its equilibrium, industries are maximizing their profits, so M CF (q) = PF ; M CC (q) = PC . Thus, M CF PFM RT = = . M CC PC Consumers maximize their utility, so PFM RS = . PC Combining the equations toge ther, we obtain (see Figure 4) PFM RT = = M RS. PC ′ ′Consider non-equilibrium prices PF and PC , ′ PF PF < . ′ PC PC Given the prices, food has a shortage and clothing has an excess (see Figur e 5). ′The prices will change to adjust to the equilibrium state, namely, PF increases ′and PC decreases. 2.1 General equilibrium in the out put market Example (Gains from Free Trade). Assume that Holland a nd Italy both produce cheese a nd wine, unit of labor requir ed is provided in Ta ble 2.1). If these Cheese Wine Holland 1 2 Italy 6 3 Table 1: Unit of Labor Required in Cheese and Wine Pr oduction. two countries cannot trade cheese or wine, we consider the domestic markets separately. The price ratio is not the same: P H P I W W< . P H P I C C Consumer utility levels are UH and UI , respectively. However, if they can trade, Holland exports cheese and imports wine, and Italy exports wine and imports cheese. T he prices ratio will adjust to agree, and people in both countries are better off because both indifference curves move upwards (see Figure 6). The ′ ′new utility levels are UH and UI .10 9 8 7 0 1 2 3 4 5 6 7 8 9 10 F 0 1 2 3 4 5 6 CSupply Demand Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 2.1 General equili bri um in the output market 5 Figure 5: Non-equilibrium Consumption and Production.14 0 2 4 6 8 10 12 UH UH ’ Holland 0 1 2 3 4 5 6 7 8 9 10 Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 2.1 General equili bri um in the output market 6 (a) Trade in Holland. 0 1 2 3 4 5 6 7 8 9 10 W (b) Trade in Italy. Figure 6: Gains from Free Trade. 0 1 2 3 4 5 6 7 8 9 10 C Italy UI UI