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##### Economics 360: Microeconomic Theory Spring, 2014 Problem Set #4

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Question;Economics;360: Microeconomic Theory;Spring, 2014. Assigned;Mar 27. Due Thurs Apr 3 in lecture.;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 Roy?s 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 whether?and why?the;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.

Paper#55737 | Written in 18-Jul-2015

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