2) (50 points) For this problem, you will work with a rm that has a production function such as y = f (L, K) = J: + W, where y, L, and K are output, labor, and capital, respectively. The prices of labor and capital are w and r, which are not revealed to you and should be taken as parameters. (20 points) If the price of the output is p (also an unknown parameter), nd the factor demands and the optimal level of output. Show your work, including the optimization problem you are solving. (10 points) Does this firm present constant, increasing or decreasing returns to scale? Show it mathematically. (20 points) Now, assume we want to nd the long-run cost curve for this rm. Find the conditional factor demands for labor and capital. Compute the total cost curve for this rm. Is the functional form of the cost curve you found here consistent with your answer in b)? Explain