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Problem 7.4 and 7.7

7.4 Suppose that the hourly output of chili at a barbecue (q, measured in pounds) is characterized by where K is the number of large pots used each hour and L is the number of worker hours employed. Graph the q=2,000 pounds per hour isoquant.

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Problem 7.4 and 7.7

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  1. 7.4 Suppose that the hourly output of chili at a barbecue (q, measured in pounds) is characterized by where K is the number of large pots used each hour and L is the number of worker hours employed. • Graph the q=2,000 pounds per hour isoquant. • The point K=100, L=100 is one point on the q=2,000 isoquant. What value of K corresponds to L=101 on that isoquant? What is the approximate value for the RTS at K=100, L=100? • The point K=25, L=400 also lies on the q=2,000 isoquant. If L=401, what must K be for this input combination to lie on the q=2,000 isoquant? What is the approximate value of the RTS at K=25, L=400? • For this production function, the RTS is RTS=K/L. Compare the results from applying this formula to those you calculated in part b and part c. To convince yourself further, perform a similar calculation for the point K=200, L=50.

  2. 7.7 The production function where , is called a Cobb-Douglas production function. This function is widely used in economic research. Using the function, show that • The chili production in problem 7.4 is a special case of the Cobb-Douglas. • If , a doubling of K and L will double q. • If , a doubling of K and L will less than double q. • If , a doubling of K and L will more than double q. • Using the results from part b through part d, what can you say about the returns to scale exhibited by the Cobb-Douglas function?

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