1. A jolly elf runs a toy factory that employs only labor (L) to manufacture toys (Q). The factory has a production function given by Q = (L 1) 1 2 Suppose the cost of labor is w = 1.

(a) Show that the elf's cost function is C(Q) = Q 2 + 1

(b) Given this cost function, show that the marginal and average cost of production are MC(Q) = 2Q AC(Q) = Q + 1 Q (You can use these expressions henceforth even if you didn't complete these parts.)