At Albert’s Pretzel Company, MPL = 1/L, and MPK = 1/K. The isoquant fo

At Albert’s Pretzel Company, MPL = 1/L, and MPK = 1/K. The isoquant for 100 pounds of pretzels daily is shown in the above figure.

Albert minimizes the cost of producing 100 pounds of pretzels daily by hiring 5 units of labor and 10 units of capital when w = 50 and r = 25. When r rises to 100, what is the minimum cost of producing 100 pounds of pretzels daily in the short run? in the long run?

ANSWER

In the short run, the input mix cannot change. The short-run cost is (5 ∗ 50 ) + (10 ∗ 100 ) = 1250. In the long run, Albert will change the input mix. From the graph, the new mix will be L = 10 and K = 5. To check, the MRTS = K/L and costs are minimized when MRTS = w/r which equals 1/2. As a result, the long-run cost of 100 pretzels is (10 ∗ 50 ) + (5 ∗ 100 ) = 1000.