Question 1: Farmers incorporated can produce 60 milk vats with 200 workers (L) and 10 machines (K). The firms production technology is such that the manager can always choose to replace 4 workers with 1 machine and vice versa.
a. Find the production function q = f (K,L)
b. Explain whether the production technology has increasing, decreasing, or constant returns to scale?
Question 2: John likes gangsta rap concerts (G) and gold watches (W). His utility function is U(G,W) = GW . John’s income is 12000 per year. The price of a gangsta rap concert is 600 and the price of a gold watch is 3000.
A. what is his budget constraint?
B. What will be John’s optimal consumption bundle?
C. What utility will he obtain at the optimal bundle?
D. John receives a discount so the Gangsta Rap concerts only cost 300 per concert (half price!). Determine the new consumption bundle and utility.
E. John wants to know how much income he would have needed to get his utility level from question
C but with the new price of a Gangsta Rap concert of 300 and the price of Gold watch of 3000.
F. Please use your answer in question E to calculate the income and substitution effects of this price decrease on Johns demand for rap concerts and show the effects in a graph and algebraically.