# LEC6 - Macroeconomic Policy Class Notes Long run growth 2...

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Macroeconomic Policy Class Notes Long run growth 2: The Solow model Revised: October 10, 2011 Latest version available at www.fperri.net/teaching/macropolicyf11.htm Why do we see such large diﬀerences in level of income across countries and in their growth rate performance? To answer this question we introduce one of the leading models in economics, introduced by Robert Solow (economist at MIT, winner of the Nobel prize in economics in 1987) in the 50s. This is a pretty simple theory but quite powerful in the sense that it can be used to analyze a whole variety of issues. The key point of the theory is that sustained growth and high levels of income per capita in a country can be achieved through saving and capital accumulation. Limits to capital accumulation are posed by the fact that returns to capital are decreasing. Decreasing returns simply means that the beneﬁt of any additional unit of capital are declining with the stock of capital per worker. Suppose I am a weaver and I weave by hands. My output will be quite low. If I purchase a loom I will increase my output a lot. If I buy a second loom I will increase my output but not as much as the ﬁrst increase because now I have to divide my time between the two looms. If I have 10 looms and I add an 11th loom my output will not really increase by much because I don’t have really the time to operate it. The basic model For now we will consider the total number of worker in a country constant and equal to L . We will also assume that everybody in this economy work so GDP per capita is also equal to GDP per worker ( L is also equal to population). The theory is built around two simple equations. The ﬁrst equation is the aggregate production function of a country that is assumed to be of a particular form called Cobb-Douglas Y = AF ( K,L ) = AK α L 1 - α Y here represents output produced, K is the capital stock in place, L is the amount of labor employed and A is a parameter that determines the eﬃciency of the factors

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The Solow Model 2 of production. A sometimes is also called “Total Factor Productivity”. Note the the particular functional form display “Constant Return To Scale” that is a doubling of both inputs of production (labor and capital) lead to a doubling of output. The second equation follows from the fact that national income is split it between consumption C and investment I Y = C + I For now we are assuming that the economy is closed (no link with the rest of the world) and we do not model the government separately from the private sector. Also for now let’s assume that consumers consume a ﬁxed fraction of their income and let’s call this fraction (1 - s ) so C = (1 - s ) Y. Using this assumption and the division of national income we obtain Y = C + I = (1 - s ) Y + I I = sY this implies that investment is a ﬁxed fraction of income. Dividing everything by the total number of workers L and denoting with lower case letters the per-worker variables we get i = sy where i = I L y = Y L dividing by L both sides of the production function we also get y = AK
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## This note was uploaded on 12/21/2011 for the course ECON 3014 taught by Professor Michaelshaw during the Spring '11 term at HKU.

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LEC6 - Macroeconomic Policy Class Notes Long run growth 2...

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