1) Futons Inc. produces futons using only two inputs – capital (wood, nails, and hammers) and labor (measured in worker hours) – with a technology characterized by the following function:q = 2ln(K + 3L)Futons Inc. spent $100 on 100 units of capital at the beginning of the period. They can neither purchase nor sell units of wood, nails, and hammers until the end of the period, but the material does not lose any value over time.
a) Solve for the average product of labor and the marginal product of labor.
b) Assuming that futon makers earn a wage of $9 per hour and the prevailing interest rate in the economy is 10 percent, solve for short run costs as a function of the numbers of futons produced.
2) Suppose the recent recession led to a drop in wages such that the price of labor fell by 25 percent. Economists predict that this drop will be sustained in the long run. Furthermore, the user cost of capital has not changed, nor is it predicted to. How does this change in relative prices affect a firm’s long run expansion path? Please explain using both words (i.e., economic intuition) and a graph.