Question

1. Imagine a firm has the following short-run production function: q=f(L,K) = K L – L? Assume K = 25. a. Fill in the following table. (First, find the total output from the production function, then find the marginal product by dividing the change in total output by change in labor.) Capital MPL Labor 7 Total Output 126 APL 18 25 12 25 25 25 25 25 10 11 12 13 14 15 25 25 25 b. How many units of labor should the firm hire to maximize output? C. Draw the short-run TP, MP and AP, curves (You will probably want to use two diagrams)

Answer 1

Answer:

(a) Given, $q=f(L, \bar{K})=\bar{K}L-L^2$    or     $q=25L-L^2$

where K is constant and K=25 (Short run situation)

Thus, $MP_L=\frac{\partial q}{\partial L}(\bar{K}L-L^2)=\bar{K}-2L=25-2L$

and $AP_L=\frac{q}{L}=\frac{\bar{K}L-L^2}{L}=\bar{K}-L=25-L$

Now using the above formulas we get the following results,

Total Output q-25L-LA2 MPL-25-2L APL-25-L Capital (K) Labor (L) 126 25 7 11 18 25 8 136 9 17 25 9 144 7 16 25 10 150 15 25 11 154 3 14 13 25 12 156 1 156 25 13 -1 12 25 14 154 -3 11 150 25 15 -5 10 n

(b) To maximize output the firm should hire 12 units of labor as seen in the above table that when L=12 the total output q=156.

(c) Graphs

Short run Output Function 160 155 150 145 140 135 130 125 120 T 7 8 9 10 11 12 13 14 15 16 Labor (L) Total Output

Marginal Product and Average Product Curves 19 17 15 13 11 9 MPL 7 APL 5 1 -1 13 14 7 8 9 10 11 12 15 16 -3 -5 Labor (L) co Ov n MP and AP