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Matthias Doepke - Marcroeconomics - Chapter 2

Chapter 2 Work Effort, Production, and Consumption Robinson Crusoe is alone on an island, so he is an economy unto himself. He has preferences over consumption and leisure and can produce consumption goods by using labor and capital. | Chapter 2 Work Effort Production and Consumption Robinson Crusoe is alone on an island so he is an economy unto himself. He has preferences over consumption and leisure and can produce consumption goods by using labor and capital. We examine production first. Then we turn to preferences. Putting these two pieces together yields Crusoe s optimal choices of labor leisure and consumption. 2.1 CsusoeP Production Possibiiities Crusoe uses factors of production in order to make output y. We can think of this output as being coconuts. Two common factors of production and those we consider here are capital k and labor I. Capital might be coconut trees and labor is the amount of time Crusoe works measured as a fraction of a day. How much Crusoe produces with given resources depends on the type of technology A that he employs. We formalize this production process via a production function. We often simplify our problems by assuming that the production function takes some particular functional form. As a first step we often assume that it can be written y A fc Z for some function . This means that as technology A increases Crusoe can get more output for any given inputs. It is reasonable to require the function to be increasing in each argument. This implies that increasing either input or I will increase production. Another common assumption is that output is zero if either input is zero 01 0 and f k 0 0 for all and I. One functional form that has these properties is the Cobb-Douglas function for example 10 Work Effort Production and Consumption y Ak ala for som i between zero and one. This particular Cobb-Douglas function exhibits constant returns to scale since 1 a a 1. Figure 2.1 is a three-dimensional rendering of this function for particular values of A and a. capital k F0.8 0.6 0.4 0.2 0 Figure 2.1 Cobb-Douglas Production labor l 1 We will not be dealing with capital until Chapter 9 so for now we assume that capital is fixed say at k 1. This simplifies the production .