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Econ102SQ3Spring2007 - UCLA ECONOMICS 102 E McDEVITT SQ...

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UCLA ECONOMICS 102 E. McDEVITT SQ set #3: SOLOW GROWTH MODEL 1. What is a steady state? What is investment in a steady state? What is the intuition behind this equation? Assume the following initial values: K t = 500 , L t =100, δ = 8%, and n = 2%. The capital-to-worker ratio is k = 500/100 = 5. What would happen to the capital-to-labor ratio if actual investment was 20? How much investment is required to maintain the capital-to-labor ratio at 5? Verify by calculating the levels of K & L and the ratio k. 2. Convert the following production function into the per-worker production function: Y = AK 0.1 L 0.9 . Find k gold . Show steps. Assume that the population growth rate is 5%, the depreciation rate is 5%, and that A = 100. Show outcome on a graph. 3. True or false? The higher the steady-state capital-labor ratio (k) is, the more consumption each worker can enjoy in the long run. Explain. 4. What equation do we use to determine the steady state level of k? How do you interpret each side of the equation? Explain why k increases when its initial level is below the steady state level. ...when its initial level is above the steady state level. Write out the equation that gives us the change in k. Show these cases on graphs. Label each curve. Suppose an economy initially in a steady-state experiences an event (such as a war) that moves k below the steady-state level. What is the impact of this event on y? What is the impact on MPK (relate this to the graph)?...impact on MPL? 5. a. Using the information from question (2) find the steady state level of k when the savings rate is 5%. Show all steps. b. What is output per worker and consumption per worker in this steady state? c. What savings rate is required to bring about k gold ? 6. Using the short-cut formula, indicate how a change in A, s, or n affects the steady-state value of k in the Solow growth model. Shows these results on graphs and also show the impact on steady state y and c. 7. Assume s = 10%, δ = 3%, n = 2%, Y t = A*K t 1/3 L t 2/3 and A is constant at 1. a. Find k steady-sstate , y steady-state and c steady-state using the “short cut” formulas. b. Suppose the initial value of k was k 0 = 9. What is required investment per worker at this initial value? In what sense, do we mean “required investment”? What is actual investment per worker at this initial value? What is k in the next period? 8. Suppose the current savings rate is below the savings rate that brings about k gold . Does it follow that policies designed to increase the savings rate are desirable? Explain.
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