Problem 2

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Juan has just started a taco restaurant. In order to enter the business, he had to pay a sunk cost of 2, that is, the total value of the time he spent learning tacos recipes. In addition, he needs to pay for labor and capital. The wage rate he has to pay is ¹/₄, and the rental rate of each unit of capital is 1. Juan knows that his production function is given by q = K^1/3 L^1/3.

In the short run that units of capital that Juan has are fixed and equal to 3. Find the short run total cost function. (Exclude the sunk costs from this function.) To verify that you have found the correct short-run total cost function, comp7ute the short-run total cost of producing 30 tacos.

TC (30) =

Problem 3

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Now, let's consider a time horizon long enough such that producers like Juan can adjust the level of capital, although they still have to pay the sunk cost of 2 in order to learn the recipes. Assuming that they face the same price for labor (W=¹/₄) and for the rental rate of capital (r =1), find the long run total cost production function in this market. (Exclude the sunk costs in this function.) To verify that you have found the correct long-run total cost function, compute the long-run total cost of producing 30 tacos.

TC (30) =