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1、1,CHAPTER 7 Economic Growth II,MANKIWS MACROECONOMICS MODULES,A PowerPointTutorial To Accompany MACROECONOMICS, 6th. ed. N. Gregory Mankiw By Mannig J. Simidian,2,The Solow Growth Model,The Solow Growth Model is designed to show how growth in the capital stock, growth in the labor force, and advance
2、s in technology interact in an economy, and how they affect a nations total output of goods and services. Lets now examine how the model treats the accumulation of capital.,3,The Accumulation of Capital,4,The production function represents the transformation of inputs (labor (L), capital (K), produc
3、tion technology) into outputs (final goods and services for a certain time period). The algebraic representation is: Y = F ( K , L ),The Production Function,Lets 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 alte
4、rnative uses.,5,Constant Returns to Scale,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 ),Constant returns to scale imply that the size of the economy as measured by the number of workers does not affect the relationship bet
5、ween output per worker and capital per worker. So, from now on, lets 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 ),6,Marginal Product of Capital (MPK): The Slope of the Production Function,MPK = f(k + 1) f (k),The
6、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.,Diminishing Marginal Product of Capital,7,The Demand for
7、Goods and the Consumption Function,Investment = savings. The rate of saving s is the fraction of output devoted to investment.,8,Growth in the Capital Stock and the Steady State,Here are two forces that influence the capital stock: Investment: expenditure on plant and equipment. Depreciation: wearin
8、g out of old capital; causes capital stock to fall.,This equation relates the existing stock of capital k to the accumulation of new capital i.,9,Output, Consumption and Investment,The saving rate s determines the allocation of output between consumption and investment. For any level of k, output is
9、 f(k), investment is s f(k), and consumption is f(k) sf(k).,10,Depreciation,Impact of investment and depreciation on the capital stock: Dk = i dk,Remember investment equals savings so, it can be written: Dk = s f(k) dk,Depreciation is therefore proportional to the capital stock.,11,The long-run equi
10、librium of the economy,Investment and depreciation,Capital per worker, k,i* = dk*,k*,k1,k2,At k*, investment equals depreciation and capital will not change over time.,Below k*, investment exceeds depreciation, so the capital stock grows.,Investment, s f(k),Depreciation, dk,The Steady State, k*,Abov
11、e k*, depreciation exceeds investment, so the capital stock shrinks.,12,How Saving Affects Growth,Investment and depreciation,Capital per worker, k,i* = dk*,k1*,k2*,Depreciation, dk,Investment, s1 f(k),Investment, s2f(k),The Solow Model shows that if the saving rate is high, the economy will have a
12、large capital stock and high level of output. If the saving rate is low, the economy will have a small capital stock and a low level of output.,An increase in the saving rate causes the capital stock to grow to a new steady state.,13,The Golden Rule Level of Capital,14,c*= f (k*) - dk*.,According to
13、 this equation, steady-state consumption is whats left of steady-state output after paying for steady-state depreciation. It further shows that an increase in steady-state capital has two opposing effects on steady-state consumption. On the one hand, more capital means more output. On the other hand
14、, more capital also means that more output must be used to replace capital that is wearing out.,Steady-state Consumption,The economys output is used for consumption or investment. In the steady state, investment equals depreciation. Therefore, steady-state consumption is the difference between outpu
15、t f (k*) and depreciation dk*. Steady-state consumption is maximized at the Golden Rule steady state. The Golden Rule capital stock is denoted k*gold, and the Golden Rule consumption is c*gold.,15,16,Population Growth,The basic Solow model shows that capital accumulation, alone, cannot explain susta
16、ined economic growth: high rates of saving lead to high growth temporarily, but the economy eventually approaches a steady state in which capital and output are constant. To explain the sustained economic growth, we must expand the Solow model to incorporate the other two sources of economic growth. So, lets add population growth to the model. Well assume that the population and labor force grow at a constant rate n.,17,The Steady State
