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1. For each of the following production functions, state and show whether it is Constant/Increasing/or Decreasing Returns to Scale: [Hint: to show Constant/Increasing/or Decreasing Returns to Scale, see how production changes when all inputs increase by a factor of α where α > 1. ] (a) F(K,L) = K^1/3 L^2/3 + K + L has___________returns to scale. (b) F(K,L) = 5(K^1/2)*3(L^1/2) has__________ returns to scale. (c) F(K,L) = K^1/3 L^2/3 + 2 has _________returns to scale. (d) F(K,L) = (K^1/3 + L^1/3)^2 has________returns to scale. 2. Using the same production function from question 1d, and given wages w = 3 and rental rate of capital r = 6: (a) solve for the cost function in terms of q when the firm is free to choose both labor and capital. (You will need to solve the cost minimization problem and find the optimal K,L in terms of q in order to find cost in terms of q). (b) Solve for the marginal cost function using your result from part a). (c) Suppose p = 30 and that the firm is a price taker. What is the optimal amount of output the firm should produce? 3. Suppose there is a fixed amount of capital K¯ = 10. Find the short run cost function CFK(q) when the wage is 6 and the rental rate of capital is 3 for a firm whose production function is F(K,L) = K^3/5L^2/5. What does this say about the marginal return to labor as you increase the amount of labor used? 4. Using the production function: F(K,L) = K^1/3L^2/3: (a) Solve for the firm's maximum profit in terms of w, r and p. (b) Suppose w=2, r=4 and p=10. How much labor and capital will the firm use? How much output will the firm produce? What will the firm's profit be?
(c) Suppose w=5, r=5 and p=8. How much labor and capital will the firm use? How much output will the firm produce? What will the firm's profit be?
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suppose the hotel in the lecture example raised its price from 30 to 30.50. with the new price the hotel expects 96
calculations Definition and explanation of the indices Discussion about what the specific indices mean in relationship to the overall article and how they impact each other Appropriate evaluation, decisions and forecasts that could be made from th..
Consumer Buying Behavior
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george dundee operates a lumber mill outside of oklahoma city. dundee has a contract to deliver 15 truckloads of cut
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