Michael is the owner of a fast-food restaurant in Portland. Each week his restau
ID: 1111580 • Letter: M
Question
Michael is the owner of a fast-food restaurant in Portland. Each week his restaurant produces cheese- burgers c using workers L (measured in worker-hours per week) and kitchen machines K (toasters, grills, fryers, etc), measured similarly. The number of cheeseburgers that can be produced is constrained by the technology function
c = 5K^(1/3)L^(1/2.)
Michael employs mostly high school students and is able to pay them the minimum wage of w = $9.25 per hour. The rate at which his kitchen equipment depreciates is r = $3.00 per hour, which is his rental rate of capital. Cheeseburgers sell for $8.00 each.
(e) The State of Oregon has instituted a new minimum wage of $14.75 in Portland. Suppose that his new wage rate is adopted immediately. In the short run, Michael’s capital stock is fixed at the previous level of capital. How much labor will he now use? How many cheeseburgers are produced? What is the total profit?
(f) Now suppose that the state decides to implement the minimum wage slowly, over the period of many years (as is actually the case). Now Michael’s decision is in the long run, so he is able to choose labor and capital optimally. How much labor will he choose in the long run? How many cheeseburgers are produced? What is the total profit?
(g) Given you answers above, should the state implement the new minimum wage immediately or phase it in slowly? Explain.
Please help me. I am not sure how to find the fixed K for the question 2E!! All of the existing questions that have been answered don't make sense to me.
Explanation / Answer
(e) In this the fixed capital is at the point where r = P*MPK. In short run, the capital stays at this level only given that the rental rate is fixed. This is the capital level that you found in other parts. Take this level of capital fixed. use that.