Juan has just started a taco restaurant. In order to enter the business he had to pay a sunk cost of2, 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 is1/4, and the rental rate of each unit of capital is1. Juan knows that his production function is given byq=K1/3L1/3. In the short run the units of capital that Juan has are fixed and equal to3. 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, compute the short-run total cost of producing 30 tacos.

E1)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 of2in 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)=?