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Economics 360: Microeconomic Theory




Economics 360: Microeconomic Theory;Spring, 2014. Assigned Mar 27. Due Thurs Apr 3 in lecture.;Prof. Andreas Pape;Problem Set #4;1. Roy is the manager of a hot dog stand that uses only labor and capital to produce hot;dogs. The firm usually produces 1,000 hot dogs a day with 5 workers and 4 grills.;One day a worker is absent but the stand still produces 1,000 hot dogs. What does this;imply about the 1,000 hot dog isoquant? Draw this part of the isoquant. What does;this imply about Roys management skills?;2. The production function for puffed rice is given by;q = 100(KL)1/2;where q is the number of boxes produced per hour, K is the number of puffing guns;used each hour, and L is the number of workers hired each hour.;a.;Calculate q = 1,000 isoquant for this production function and show it on a;graph.;b.;If K = 10, how many workers are required to produce q = 1,000? What is;the average productivity of puffed-rice workers?;c.;Suppose technical progress shifts the production function to q = 200(KL)1/2;answer part a and b for this case.;3. A firm purchases capital and labor in competitive markets at prices of r = 6 and w = 4;respectively. With the firm's current input mix, the marginal product of capital is 12;and the marginal product of labor is 18. Is this firm minimizing its costs? If so;explain how you know. If not, say whetherand whythe firm ought to;replace some labor with capital, or;replace some capital with labor.;4. Suppose that hamburger-based fast-food production is a well-understood technology.;Moreover, suppose it has standard cost curves. Consider the market for hamburgers;along highways.;a. Suppose that, after historically high gas prices, gas prices fall. Show what;happens to the price and quantity of hamburgers produced in the short run;using both a graph of the market AND a graph for the generic firm.;b. Show what happens to price and quantity in the long run in this market AND;on the graph for the generic firm. Compare this price and quantity to both the;original and short run values.;1;5. Consider this production function;f(K,L) = min(2K.5, 3L.5);a. What are the returns to scale of this production function? Explain.;b. What is the optimal ratio of capital to labor, as a function of input prices r and;w? What other type of production function is this one most similar to?;Explain.;6. Consider this production function;f(K,L) = 10 K.4 L.4;a. What are the returns to scale of this production function?;b. What are the optimal quantities of K and L, as a function of input prices r, w;and the output price p?;c. What is the cost function which corresponds to this production function, when;r=1 and w=2?


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