Chapter 6,Economic Growth: Malthus and Solow,The Malthusian Model of Economic Growth,Malthus argued: advances in the technology for producing food increased population growth no increase in the standard of living unless there were some limits on population growth A dynamic model with many periods Confine attention to what happens in the current period and the future period,Aggregate production function with constant returns to scale: (1) where is current aggregate output is current fixed supply of land is current labor There is no investment and no government spending Assume each person is willing to work at any wage and has one unit of labor to supply (a normalization), so that in Equation (1), is both the population and the labor input,Suppose population growth depends on the quantity of consumption per worker (2) where is the population in the future (next) period is an increasing function is aggregate consumption so that is current consumption per worker , mainly due to the fact that higher food consumption per worker reduces death rates through better nutrition,All goods produced are consumed, so C = Y. Hence, (3) Then use Equation (3) to substitute for C in Equation (2): (4) The constant-returns-to-scale property of the production function implies that After multiplying each side by N, Equation (4) can be rewritten as (5),Population growth depends on consumption per worker in the Malthusian model is the steady state for the population If then population increases If then population decreases,Steady State Analysis of the Malthusian Model,Recall Letting , and Then from Equation (2): In the steady state, so then can be determined,In panel (b), is determined In panel (a), is determined from the per-worker production function Steady state population is given by,The Steady State Effects of an Increase in z,Suppose the economy is initially in a steady state, with , which then increases once and for all time to unchanged falls Steady state population increases,Population increases over time to its steady state value increases at time T consumption per worker increases then decline to its steady state value Another example: population control both c* and l* increase.,How Useful is the Malthusian Model of Economic Growth?,Before the Industrial Revolution in about 1800: economic growth consistent with the Malthusian Model From the perspective of the early 21st century: Malthus was wrong Why? - Did not allow for the effect of increases in the capital stock on production, and - Did not account for all the effects of economic forces on population growth,The Solow Model: Exogenous Growth,Consumers: The population grows over time: where is the population in the future period is the rate of growth in the population Assume that consumers consume a constant fraction of income in each period: where is current consumption is the aggregate savings rate,The Representative Firm: Constant returns production function with capital and labor inputs: where is output per worker is capital per worker where is constant depreciation rate and,Competitive Equilibrium: Equilibrium condition:,Quantity of capital per worker converges to a constant, quantity of output per worker converges to a constant, If s, n and z are constant, real income per worker cannot grow no betterment in living standards,Steady State Analysis,In the long run, when the economy converges to the steady state quantity of capital per worker, k*, all aggregate quantities (K, Y, I and C) grow at the rate n.,Analysis of the Steady State,In the steady state, by rearranging,Comparative Statics: An Increase in the Savings Rate,The curve, , shifts up levels of capital per worker and output per worker are higher BUT there is no effect on the growth rates of aggregate variables,Before time T, aggregate output is growing at the constant rate, Savings rate increases at time T After time T, output then converges in the long run to a new higher steady state growth path,Consumption per Worker and Golden Rule Capital Accumulation,Consumption per worker in the steady state is (golden rule quantity of capital per worker) gives the maximum consumption per worker, Property of the golden rule:,Comparative Statics: An Increase in Labor Force Growth,An increase in the labor force growth rate (n) causes a decrease in the quantity of capital per worker and output per worker Growth rates in aggregate output, aggregate consumption and aggregate investment increase,Comparative Statics: An Increase in Total Factor Productivity,The Solow Model predicts that a countrys standard of living can continue to increase in the long run only if there are continu