GENERAL ECONOMY ASSIGNMENT – CONSIDER AN ECONOMY Problem Set 6 1. Consider an economy that is described by the production function = 025 075 . Moreover, the depreciation rate of capital is = 02. (a) What is the per-worker production function, that is = ? is the marginal product of capital, that is ? What (b) If the saving rate is = 02, find the steady state level of capital per worker ? . What is the steady state level of consumption per worker ? ? What is the steady state level of investment per worker ? ? What is the steady state level of output per worker ? ? (c) Find the golden rule level of capital per worker ? , i.e. the steady state level of capital per worker that yields the highest steady state consumption per worker. Find also the golden rule consumption per worker level ? that corresponds to this capital per worker and compare it to the one in question b. Is higher than ? ? (d) Find the savings rate that guarantees that we will reach the golden rule capital per worker ? . (e) If the government decides to implement policies that change the savings rate from = 02 to , what will be the immediate impact of this policy change on , and ? What will be the impact in the long run? (Provide numbers for both the immediate impact and the long run impact) 2. Assume a general savings rate and depreciation rate and a production per worker = , where 0 1. Draw two graphs. In the first graph, you should represent the steady state capital per worker ? . In the second graph, you should represent the golden rule capital per worker ? . a) Explain the di?erences between the two graphs. Be specific and give details: What is on the x-axis? What is on the y-axis? What does each line represent? What happens where the lines meet? (b) Suppose the savings rate increases. Using the graphs, explain what happens to the steady state ? . Does the golden rule capital per worker change? (c) Using the graphs, explain what happens to the steady state ? and to the golden rule capital if there is an increase in . (d) Now let us leave the graphs and use equations. Find an expression for the golden rule savings rate in terms of the parameters of the model ( and ). Does the golden rule savings rate depend on the depreciation rate ?
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