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Consider the following production function:Y = AK^αL^(1-α) where Y is units of output, K is units of capital, and L is units of labor. Both Aand are constant parameters characterizing the production technology.
(a) Derive the function for the marginal product of K.
(b) Derive the function for the marginal product of L.
(c) If 0 < α < 1, does diminishing marginal returns apply to K? To L?
(d) Does the function exhibit increasing, constant, or decreasing returns to scale?
(e) Derive the expression for the marginal rate of technical substitution for thisproduction function.(f ) If α = 0.3, the price of capital is $10 per unit and price of labor is $15 perunit, what is the cost-minimizing ratio of capital to labor.
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Compute the discount factor 1/(1+r)^t for r=1, 5, or 10 perent interest rates and t=30 and 50 years. remember that 1 percent is .01. based on your computation, is teh choice of discount factor important for deciding whether to do somehtinga bout..
Calculate the optimal amount of pretzels and soft drinks that minimizes this firm's costs and how many frames do you provide each month?
It can be shown that the marginal return to schooling investments is MW(s) = k0 = ps. What condition governs the optimal choice of education, s*? If r= 5% and ifk 0 = 5.25, what is the optimal schooling level? Suppose that the wage-schooling sc..
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In the boom years of the late 1990s, it was often said that rapidly increasing stock prices were responsible for much of the rapid growth of real GDP. Explain how this could be true, using aggregate demand and aggregate supply analysis.
The following statement was released through FOMC following recent meeting on March 21. The Group, although hopeful for a future of moderate growth with moderating inflation,
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Maximum possible combinations of food and clothing that can be produced in a given period of time: Units of food (millions) Units of clothing (millions)Draw a PPF for this economy. b. What is the opportunity cost of moving from producing 4 mi..
Assume the players are monopolists, but the teams are competitive in the labor market. Calculate the marginal revenue product of labor (MRPL) and find the equilibrium wage and quantity of labor.Find the equilibrium wage and quantity of labor.
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