As you may recall from the chapter on cost functions, Irma’s handicrafts has the production function f(x1, x2) = (min{x1, 2x2})1/2, where x1 is the amount of plastic used, x2 is the amount of labor used, and f(x1, x2) is the number of lawn ornaments produced. Let w1 be the price per unit of plastic and w2 be the wage per unit of labor.
(a) Irma’s cost function is c(w1, w2, y) = _________.
(b) If w1 = w2 = 1, then Irma’s marginal cost of producing y units of output is MC(y) = _________. The number of units of output that she would supply at price p is S(p) = _________. At these factor prices, her average cost per unit of output would be AC(y) = _________.
(c) If the competitive price of the lawn ornaments she sells is p = 48, and w1 = w2 = 1, how many will she produce? _________. How much profit will she make? _________.
(d) More generally, at factor prices w1 and w2, her marginal cost is a function MC(w1, w2, y) = _________. At these factor prices and an output price of p, the number of units she will choose to supply is S(p,w1, w2) = _________.