Consider the production function Q = f( K, L) = KL.

a). What kind of production function is this? What is the firm's output when it uses 9 units of labor and 4 units of capital?

b). Roughly graph the isoquants for Q = 10 and Q = 20.

c). Does this production function exhibit increasing, decreasing, or constant returns to scale? Explain.

d). What is the equation for the MPL when K is held constant at 16 units? Graph it. (Remember, the MPL is just the partial derivative of the production function with respect to labor.)

e). Suppose the firm has decided that the optimal level of output is 100. Also, the firm faces a wage rate w = $9 per hour, and a rental rate of capital v = $25 per hour of capital use. Calculate the precise amount of capital and labor that this firm should use. Lastly calculate the Total variable costs to produce these 100 units. TVC = w*L +v*K The demand curves found by the Lagrangian Technique turn out to be:

K = Q(w/v)1/2 and L = Q(v/w)1/2 with Q = quantity, w = wage v = price of capital/hour