The production function for a firm isq=-0.6L3+18L2K+10L,q=-0.6L3+18L2K+10L,
where q is the amount of output, L is the number of labor hours per week, and K is the amount of capital. The wage is $100 and the rental rate is $800 per time period.
- Using Excel, calculate the total short-run output, q(L), for L=0, 1, 2, ..., 20,L=0, 1, 2, ..., 20, [&L|=|0, 1, 2, |altelip|, 20,&] given that capital is fixed in the short run at ¯¯¯¯K=1.K¯=1. [&*obar*{K}|=|1.&] Also, calculate the average product of labor, APL,APL, [&AP_{L},&] and the marginal product of labor, MPL.MPL. [&MP_{L}.&] (You can estimate the MPLMPL [&MP_{L}&] for L=2L=2 [&L|=|2&] as q(2)-q(1),q(2)-q(1), [&q(2)|-|q(1),&] and so on for other levels of L.)
- For each quantity of labor in (a), calculate the variable cost, VC; the total cost, C; the average variable cost, AVC; the average cost, AC; and the marginal cost, MC. Using Excel, draw the AVC, AC, and MC curves in a diagram.
- For each quantity of labor in (a), calculate w/APLw/APL [&w/AP_{L}&] and w/MPLw/MPL [&w/MP_{L}&] and show that they equal AVC and MC, respectively. Explain why these relationships hold.