13.1 Comparative Statics for a Competitive Firm

In the previous chapter we solved for the profit-maximizing output choice of different kinds of firms: some that faced a downward-sloping inverse demand curve, and others — “competitive” or “price taking” firms — that faced a horizontal inverse demand curve. In this chapter and the next we will analyze the comparative statics of a “competitive” or “price taking” firm: that is, we will examine how such a firm’s output and input decisions vary when the prices of output and inputs vary.

In this chapter we will be concerned with the short run: that is, the period of time in which some inputs are fixed. Following our convention, we will assume that capital is fixed and labor is flexible in the short run. We will therefore examine how the firm’s (joint) decision of how much to produce and how much labor to hire in the short run depends on the wage rate and the price at which the firm sells its output. In this chapter, we will continue to use our production function $q = f(L,K) = \sqrt{LK}$, with capital fixed at $\overline K = 32$. In the next chapter we will examine the decision made by the firm in the long run, when it can vary both labor and capital; and we’ll use a slightly different Cobb-Douglas production function.