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Unformatted text preview: Disclaimer: These notes were prepared based on lectures of Prof Sala-i-Martin’s 2008 Fall Course of Intermediate Macro-W3213. Contents of these notes might not match completely with the current teachings in class. An updated version would be available later in the semester. 2.1 A simple model of Growth: The Solow-Swan Model In order to analyze the sources of growth we study some facts related to growth: a) One of the important empirical facts is that the capital stock (buildings, roads, machinery, computers, utensils, pencils, etc.) grows larger as the economy develops. So can capital accumulation ensure long run growth? b) Other important facts are (to be studied later) as an economy grows: technology improves, education level rises, size of the government increases, rate of population growth falls, there is structural transformation (from agriculture, miming, and exploitation of natural resources to industry to services). We will first look at the accumulation of capital as the driving force behind growth. QUESTION: CAN WE GROW FASTER FOREVER BY SIMPLY INVESTING IN PHYSICAL CAPITAL? We need a model in which by construction we shut down all other sources of growth. TONS OF ASSUMPTIONS TO BEGIN WITH: (A) ? = ? + + ¡ + ? ¢ [Basic Accounting Identity] The basic accounting identity tells us that output or cookies (Y) is equal to Consumption (C) plus Investment (I) plus Government expenditure (G) plus Net Exports (NX). For simplicity we are considering a closed economy without government, so there is no government expenditure or net export term. Thus ? = ? + 2.1 In this simple economy a family produces cookies (Y) and they EAT (C) them or they INVEST (I) them. (Think of wheat). First let us ask WHERE ARE THE COOKIES COMING FROM? (What is Y), and then we will ask what happens with C and I. This equation implies (B) Production Function: Each family has access to a production technology £ ¤ , ¥ , ¦ = ? Where Y is output, A is technology level, K is capital and L is labor. We can combine machinery (K) and labor (L) (and perhaps other inputs like intermediates) to produce cookies, wheat or pigs. The WAY to combine is some knowledge, a FORMULA that tells us how to do that. This is what we call technology. We will use a special form of production Function called the Cobb Douglas production function given by £ ¤ , ¥ , ¦ = ? = ¤ ¥ 1 − ≤≤ 1 2.A2.1 (For more on this production function check A2 in Appendix). Old societies had bad ways of combining inputs (A was low) so they were very poor. (C) For now we will assume that A is constant; there are NO improvements in A. We assume that L and K are homogeneous....
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- Spring '11
- per capita