ps7_answers - Answers to Problem Set 7 1 Economic...

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Answers to Problem Set 7 1. Economic Development and the Wage Rate (4 points each part, 24 total) (a) and (b) The wage rate and interest rate functions are (the figure is for α >1) ( ) α α Ak L Y w = = 1 and 1 = = α α Ak K Y r r w , k α α 1 1 A α A ) 1 ( α ( ) A α α α α 1 Wage Function Interest Rate Function Figure 1a-b: Interest Rate and Wage as a Function of α for α >1. (c) The convergence of a country to its steady state involves an increase in the level of capital per capita (k). The wage will increase as the level of capital per capital increases. As the capital per capita increases, the marginal productivity of each worker increases and so does his wage. When the economy arrives to the steady state level of capital per capita, capital per capita stops changing and, hence, the wage stops growing. The interest rate is the marginal return to capital so it will be falling as the economy develops and will stop falling when we arrive to the steady state. (d) A sufficient answer for this part was to point out that even when population is growing all the time, the wage will stop increasing at the steady state and the interest rate will stop decreasing. A richer answer can be given by looking at the equations of the real wage and the interest rate at the steady state. Given a certain rate n of population growth, the steady state of this economy will achieved at: α δ + = 1 1 n sA k
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the wage (w ss ) and the interest rate (r ss ) at the steady state level are given by: ( ) α α δ α + = 1 1 n sA A w ss and s n r ss ) ( δ α + = So that it is clear that the wage and the interest rate have a steady state level that is different from the one that is achieved when there is no population growth. The new steady state level of capital per capita is lower, the reason is that population growth puts an additional demand on the economy’s capability of maintaining its capital per capita levels. The economy cannot afford to sustain the higher level of capital per capita that it had without population growth. Since capital per capita is lower, the marginal productivity of labor is lower and the marginal productivity of capital is higher. So, they are constant at the steady state but at a different level. (e) With productivity growth there will still be a steady state for this economy, only it will not be for capital per capita but rather for capital per productivity-weighted capita. However the wage per person will change. Because each person in the economy will become more and more productive. On the other hand, the interest rate will stop at the steady state since the accumulation of capital will reach a point at which savings will consider productivity growth.
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