Ch31 - Chapter 31 Production In the previous chapter we...

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Unformatted text preview: Chapter 31 Production In the previous chapter we looked at the general equilibrium model of a pure exchange economy where people have fixed endowments of goods and examined how they might trade those goods themselves. In this chapter we describe how production fits into the general equilibrium framework. 31.1 The Robinson Crusoe Economy Robinson Crusoe stranded on an island is both a consumer and a producer. He can spend his time consuming labor and getting a suntan, or spend his time gathering coconuts. Robinson’s preferences for coconuts and leisure are depicted in Fig- ure 31.1 below. Also drawn into the figure is the production function , which shows the relationship between how much Robinson works and how many coconuts he gets. Note that due to diminishing returns to labor, the marginal product of labor declines. Robinson’s decision on how much to work and consume is illustrated at the point where the highest indifference curve just touches the production possibilities frontier. At this point, the slope of the indifference curve is equal to the slope of the production function. If they crossed, there would some other feasible point that was preferred. This means that the marginal 1 2 CHAPTER 31. PRODUCTION product of an extra hour of labor must equal the marginal rate of substi- tution between leisure and coconuts. 31.2 Crusoe, Inc. Robinson Crusoe decides to set up a firm, Crusoe, Inc. and becomes its sole shareholder. The firm looks at prices for labor and coconuts and decides how much labor to hire and how many coconuts to produce. Robinson collects a wage as a worker and profit as the shareholder, and as a consumer decides how much of the the firm’s coconuts he will purchase. In order to keep track of his transactions, Robinson invents a currency called “dollars” and chooses arbitrary to set the price of coconuts at one dollar apiece. So, coconuts are the numeraire good for this economy, and we need only determine the wage rate. What should the wage rate be in 31.3. THE FIRM 3 order to make this market work? Let’s look at the choices made by the firm and then the consumer. 31.3 The Firm Given the price of coconuts is 1 and wage is w , the firm’s profit maximiza- tion problem is given in Figure 31.2. Let’s consider all combinations of coconuts and labor that yie;d a con- stant level of profits, π . This means that π = C- wL Solving for C gives C = π + wL 4 CHAPTER 31. PRODUCTION This formula describes the isoprofit lines - all combinations of labor co- conuts that yield profits of π . That is, Crusoe, Inc. chooses a point that maximizes profits. This implies the usual tangency condition: the slope of the production function (the marginal product of labor) must equal w as illustrated in Figure 31.2. Note, the vertical intercept of the isoprofit line measures the maximal level of profits measured in units of coconuts: if Robinson generates π * dollars in profits, this money can buy π * coconuts, since the price of coconuts has been set at 1. Anyway, Crusoe, Inc. givessince the price of coconuts has been set at 1....
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This note was uploaded on 03/14/2010 for the course ECON microecono taught by Professor Yy during the Spring '10 term at Seoul National.

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Ch31 - Chapter 31 Production In the previous chapter we...

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