1. Suppose that the production function of an economy is characterized by the followingCobb-Douglas production technology Y = Ka L*1, where Y is the aggregate output, Kis the capital stock, L is the labor and 0< a <1.a Assuming dosed economy with no govemment, labor growth rate being constant(gs) and depreciation rate is positive ô > 0, show the step-by-step derivation ofthe fundamental equation of growth (using per worker capital, k). Hint: Firstderive per worker production function.b. Find the steady-state values of capital per labor (k), output per labor(), and consumption per labor (c). Hint: use the fact: k= 0.What would be the effect of changes in s, gs and a on kf2. Recall that general form of fundamental equation of growth in Solow model isdescribed as follows:k = s - f(k.) – (gs + 6)kaNoting that at steady-state kss = 0 and hencea Using the fact kes= 0, show the steady-state graphically and provide economicinterpretation of the steady-state condition s- f(k s) = (gs + 6)k *b Using the same graph you draw in part (a) explain the transitional dynamics ofthe Solow. Hint: Defime what happens if k. k s-3. Assume that production fumction takes the form Y = (K'0.5) + L'as)E, Show ifthis production function obeys neoclassical assumptions.4. Lets assume that the time derivative of a continuous variable Xa is defmed asX = M+Nwhere, M: and N: are also continuous variables defined by following functions:N: = ekt & M, = et and k is a constant. Find the grow th rate of x at the steady statein terms of k.

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1. Suppose that the production fumction of an economy is characterized by the foll owing Cobb-Douglas production technology Y = Ka L*•i, where Y is the aggregate output, K is the capital stock, Lis the labor and 0 0, show the step-by-step derivation of the fundamental equation of growth (using per worker capital, k). Hint: First derive per worker production function. a Find the steady-state values of capital per labor (k), output per labor (). and consumption per labor (c). Hint: use the fact k= 0. c What would be the effect of changes in s, g; and a on kf

1. Suppose that the production fumction of an economy is characterized by the foll owing Cobb-Douglas production technology Y = Ka L*•i, where Y is the aggregate output, K is the capital stock, Lis the labor and 0 0, show the step-by-step derivation of the fundamental equation of growth (using per worker capital, k). Hint: First derive per worker production function. a Find the steady-state values of capital per labor (k), output per labor (). and consumption per labor (c). Hint: use the fact k= 0. c What would be the effect of changes in s, g; and a on kf

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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3. Consider a dynamic (two-period) representative firm's problem. This representative firm is given K unit of capital to produce in the current period. Firm can choose (current-period and future-period) labor demands and investment (to adjust future- period's capital stock) to maximize its present-value lifetime profit. Given that the market interest rate is r and the capital depreciation rate is & after production in each period. Let's further assume that this firm sells all the capital after future-period production. (a) Clearly definite the profit functions for both periods and write down this repre- sentative firm's problem. (b) Write down the optimal condition on investment. Intuitively explain the optimal condition. (c) Suppose K increases, graph the change of investment curve. Intuitively explain the changes on the graph you just drew.