Suppose that the capital (machines) in a particular plant is fixed in the short run and is equal to K = 2. Thus the only way to change the output level is by changing the number of workers (L). The technology of the firm (in the short run) is described in the following table.
K L Q MPL
2 0 0
2 1 100
2 2 220
2 3 340
2 4 450
2 5 550
2 6 640
2 7 720
2 8 790
2 9 850
2 10 900
a. Calculate the Marginal Product of Labor (MPL) in the above table and plot the graphs of output (Q) and MPL as functions of labor (L) on the same diagram.
b. Does the law of diminishing marginal product hold for this technology? Explain.
c. Complete the costs in the following table, assuming that = 30, =100 PK PL .
d. (Excel required). Plot the graphs of ATC, AVC, and MC on the same diagram.
e. Calculate the profit of the firm for the following market prices: = $1, = $1.25, = $2 PX PX PX .
f. Show the firm's profit when the price is $1.25 on the diagram in section d.
g. For each of the given above market prices, state whether the firm will operate in the short run? In the long run?