A firm discovers that when it uses K units of capital and L units of labor, it is able to produce √K L units of output.
a. Draw the isoquants corresponding to 1, 2, 3, and 4 units of output.
b. Suppose that the firm produces 10 units of output using 20 units of capital and 5 units of labor. Compute the MRTSLK. Compute the MPL. Compute the MPK.
c. On the basis of your answers to part (b), is the equation MRTSLK = MPL/MPK approximately true? (It would become closer to being true if we measured inputs in smaller units.)
d. Suppose that capital and labor can each be hired at $1 per unit and that the firm uses 20 units of capital in the short run. What is the short-run total cost to produce 10 units of output?
e. Continue to assume that capital and labor can each be hired at $1 per unit. Show that in the long run, if the firm produces 10 units of output, it will employ 10 units of capital and 10 units of labor.
f. Does this production function exhibit constant, increasing, or decreasing returns to scale?