c wl now robinson the consumer will try to achieve

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Unformatted text preview: optimally how much he wants to work and how many coconuts he wants to consume. At this optimal choice, the marginal rate of substitution between consumption and leisure must equal the wage rate, just as in the standard consumer choice problem. PUTTING THE SPLIT PERSONALITY TOGETHER AGAIN Now if we superimpose the Bobby C's Inc. profit maximization picture onto the Robinson the Consumer picture we get... Indifference Curve Coconuts Budget Line / Isoprofit Line Production Function C* Consumption Optimum Production Optimum Profit = * Labour L* It turns out that the schizophrenic Robinson did exactly what the "sane" Robinson did. This optimal solution is the same one as we started with before when Robinson made all the decisions at once. Using the market system results in the same outcome as choosing the consumption and production plans directly. This is directly due to the fact that the MRS between consumption and leisure and the MPL are equal to w. This assures us that the MRS = the MPL and thus, the slope of the indifference curve and the slope of the production function are equal. 149 Let's do a simple example... Suppose Robinson Crusoe has a utility function and a production function defined as: URC = URC (C , ) = C1/2(24 - L)1/2 C = f(L) = L We can find Robinson's optimal consumption-leisure choice by equating his MRS between consumption and leisure with his MP of leisure... First, let (24 L) = , where represents leisure MRS = C-1/21/2 = L C1/2-1/2 C MPL = 1 So, (24 - L) = 1 C (24 - L) = C (24 - C) = C 2C = 24 (24 - L) C C = 12 = L and = (24 - L) = 12 Now let's do one that is a little more challenging. Suppose Robinson Crusoe has a utility function and a production function defined as: URC = URC (C , ) = C1/2(18 - L)1/2 C = f(L) = 4 L1/2 Now remember Robinson wants to maximize his leisure subject to his maximum profit First, let (18 ) = L or alternatively, (18 L) = (meaning that Robinson sleeps 6 hours per night and this sleep time is counted as neither labour nor leisure). 150 Max PC C + w since w = the opportunity cost for Robinson. Max 4 PC (L1/2...
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This note was uploaded on 05/25/2010 for the course ECON 301 taught by Professor Sning during the Spring '10 term at University of Warsaw.

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