Sample_Problems_for_the_Final_Exam_2008[1]

Sample_Problems_for_the_Final_Exam_2008[1] - Sample...

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Sample Problems for the Final Exam NOTE: This is not the format of the final – the final exam will have two parts. Part One will consist of 4 required questions and Part II will consist of 2 questions and you will have to select one of them. 1. Suppose that the following production function represents a firm’s ability to manufacture pencils: f(L,K) = 3 1/2 K 1/4 L 1/4 . a) Show that this production function exhibits decreasing returns to scale. b) Assume that the wage rate is equal to 9 and the rental rate on capital is equal to 4. In addition assume that the firm has a fixed cost of production equal to 16. Find the compensated factor demands for labor and capital. Find the cost of the cost minimizing input bundle (ie find the variable cost curve) and the total cost curve. c) Find the marginal cost function and the average cost function. Graph the marginal cost function and the average cost function in a single diagram. Show that the optimal size of the firm is 2. What is the minimum value of the average cost curve? d) If this firm is a price taker then what is the firm's supply curve? e) Suppose that there is a second firm in the pencil business, which has an identical total cost function and that these two firms are the only two firms in the industry then what is the industry supply curve? f) If the demand for pencils is given by the inverse market demand curve P = 100 – Q then what is the market clearing price and quantity for the pencil market? g) Do you expect that there will be entry or exit in the long run? What will be the long run price of pencils? How many units will be traded in the long run? 2. The bolt industry currently consists of 20 producers, all of whom operate with identical total cost functions given by TC(Q) = 16 + Q 2 . Quantity is measured in tons of bolts. a) What is the marginal cost curve associated with this total cost curve? What is the average cost curve? What is the optimal size of the firm? What is the minimum value of the average cost curve? Illustrate your answer in a diagram. b) What is the individual firm’s supply curve? What is the market supply curve? Suppose that demand for bolts is given by Q D = 132 – P. Price is measured in dollars per ton. c) What will be the market clearing price and quantity traded in the short-run? How many units will each firm supply to the market? Will firms be earning normal, super-normal or sub-normal profits? Briefly explain your answer without calculating the firm’s level of profits. d) What is the long-run price of bolts? Do you predict that there will be entry or exit from this industry? e) What is the long-run quantity traded in this market? How many units will each firm produce in the long-run? How many firms will there be in the long-run? 3.
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Sample_Problems_for_the_Final_Exam_2008[1] - Sample...

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