Suppose that a semiconductor plant's production function is q = 5LK, where q is its output rate, L is the amount of labor it uses per period of time, and K is the amount of capital it uses per period of time. Suppose that the price of labor is $1 a unit and the price of capital is $2 a unit.
a. The firm's vice president for manufacturing hires you to figure out what combination of inputs the plant should use to produce 20 units of output per period. What advice would you give? Explain.
b. The same as in (a), but the plant needs to produce 40 units of output. Explain.
c. Compare your answers to part (a) and (b) and explain the scale effect. Explain.
d. The same as in (a) but the price of labor has risen to $2 a unit. Explain.