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Unformatted text preview: 1 1 © 2008 by W. W. Norton & Company. Al rights reserved CHAPTER 4 A Model of Production Lecture 4 Chapter 4: A Model of Production Part 1 and 2 Ruxandra Prodan 2 © 2008 by W. W. Norton & Company. Al rights reserved CHAPTER 4 A Model of Production 4.1 Introduction In this chapter, we learn: how to set up and solve a macroeconomic model. how a production function can help us understand differences in per capita GDP across countries. the relative importance of capital per person versus total factor productivity in accounting for these differences. the relevance of “returns to scale” and “diminishing marginal products.” how to look at economic data through the lens of a macroeconomic model. 3 © 2008 by W. W. Norton & Company. Al rights reserved 4.1. Introduction A model is a mathematical representation of a hypothetical world that we use to study economic phenomena. It consists of equations and unknowns with real world interpretations. Macroeconomists document facts, build a model to understand the facts, and examine the model to see how effective it is at explaining the facts CHAPTER 4 A Model of Production 2 4 © 2008 by W. W. Norton & Company. Al rights reserved CHAPTER 4 A Model of Production 4.2 A Model of Production Vast oversimplifications of the real world in a model can still allow it to provide important insights. Consider a single , closed economy , with only one consumption good . A certain number of laborers (L) make the consumption good. A certain number of machines (K) are used to produce the good. Variables with a bar are parameters or variables being held constant in the model. A production function tells us 5 © 2008 by W. W. Norton & Company. Al rights reserved CHAPTER 4 A Model of Production Cobb-Douglas Production Function Assume that the production function is given by the Cobb- Douglas production function , a particular production function that takes the form of __________________________________________ is a productivity parameter called Total Factor Productivity (TFP) Positive constant A higher value of it means _________________________ We assume α = 1/3. This is because the data, historically, has revealed that capital’s share of income is fairly constant around 1/3. Thus, labor’s share of income is 2/3. We will see how these exponents represent these shares of income in a later slide! 6 © 2008 by W. W. Norton & Company. Al rights reserved CHAPTER 4 A Model of Production Returns to Scale A production function exhibits constant returns to scale if increasing each input in the same proportion causes output to rise by that same proportion. This is a desirable economic property....
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