Cost Minimization for Cobb-Douglas, Microeconomics

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3.Cost Minimization for Cobb-Douglas. Suppose the Acme Gumball Company has the produc-

tion function of q=LK. Given that the MPL=K, MPK=L and MRT S=MPL/MPK.

Part a-b, we are analyzing the impact of output on input choices.

a. Suppose wage rate is w= $5 and rental rate is r= $5. What is the cost-minimizing combina-

tion of L and K to produce 100 gumballs? How much is the cost?

b. Given the same wage and rental rate as part a. What is the cost-minimizing combination of

L and K to produce 200 gumballs? How much is the cost?

c. The production function for Acme Gumball Company exhibits _________ (increasing,

constant, or decreasing) return to scale. The total cost increases _________ (faster than, slower

than, or at the same rate as) the output increases.
Part d-e we are analyzing the impact of input prices on its choices. Suppose the firm targets to produce 100 gumballs.
d. Suppose wage rate is w=$5 and rental rate is r=$10. What is the cost-minimizing combination of L and K? How much is the total cost?
e. Suppose wage rate is w=$5 and rental rate is r=$15. What is the cost-minimizing combination of L and K? How much is the total cost?

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