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Unformatted text preview: 1 Chapter Seven CHAPTER 7 Economic Growth II ® A PowerPoint Tutorial To Accompany MACROECONOMICS, 6th. ed. N. Gregory Mankiw By Mannig J. Simidian 2 Chapter Seven The Solow Growth Model is designed to show how growth in the capital stock, growth in the labor force, and advances in technology interact in an economy, and how they affect a nation’s total output of goods and services. Let’s now examine how the model treats the accumulation of capital. 3 Chapter Seven 4 Chapter Seven The production function represents the transformation of inputs (labor ( L ), capital ( K ), production technology) into outputs (final goods and services for a certain time period). The algebraic representation is: Y = F ( K , L ) The Production Function Income Income is is some function of some function of our given inputs our given inputs Let’s analyze the supply and demand for goods, and see how much output is produced at any given time and how this output is allocated among alternative uses. Key Assumption: The Production Function has constant returns to scale. z z z 5 Chapter Seven This assumption lets us analyze all quantities relative to the size of the labor force. Set z = 1/ L . Y / L = F ( K / L , 1 ) Output Output Per worker Per worker is is some function of some function of the amount of the amount of capital per worker capital per worker Constant returns to scale imply that the size of the economy as measured by the number of workers does not affect the relationship between output per worker and capital per worker. So, from now on, let’s denote all quantities in per worker terms in lower case letters. Here is our production function: , where f ( k ) = F ( k, 1) . y = f ( k ) This is a constant This is a constant that can be that can be ignored. ignored. 6 Chapter Seven MPK = f( k + 1) – f ( k ) y y k k f ( k ) The production function shows how the amount of capital per worker k determines the amount of output per worker y = f ( k ). The slope of the production function is the marginal product of capital: if k increases by 1 unit, y increases by MPK units. 1 MPK 7 Chapter Seven consumption consumption per worker per worker depends depends on on savings savings rate rate (between 0 and 1) (between 0 and 1) Output Output per worker per worker consumption consumption per worker per worker investment investment per worker per worker y = c + i 1) c = c = (1 (1 s s ) ) y y 2) y y = (1 = (1 s s ) ) y y + i + i 3) 4) i = i = s s y y Investment = savings . The rate of saving s is the fraction of output devoted to investment. 8...
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This note was uploaded on 04/29/2009 for the course ECO 3302 taught by Professor Avdjiev during the Spring '08 term at SMU.
 Spring '08
 AVDJIEV
 Macroeconomics

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