Objectives of this Chapter

In this chapter, we study the behavior of firms, specifically the production of output and optimal use of inputs. We use this theory of firm behavior to understand the sources and causes of growth in developed and developing countries.

We model the output of an average or “representative” firm as the outcome of a Cobb–Douglas production function with technology, capital, and labor as inputs. Technology is assumed to be freely available, but capital and labor are costly inputs. We derive two important properties of this production function: constant returns to scale and declining marginal products. Next, we solve for a firm's profit-maximizing choices of labor and capital where the firm takes as outside of its control the market prices for labor (wage rates) and capital (rental rates). We show that when a firm maximizes its profits, it sets the marginal product of labor equal to the wage rate for labor and sets the marginal product of capital equal to the rental rate on capital.

When all firms in the economy produce output according to a Cobb–Douglas production, we can derive average rates of growth of output and capital in a developed economy with a stable population. Specifically, we show that when the rate of return on capital is constant, output of an economy cannot increase solely by the accumulation of capital. Rather, the level of technology must increase for sustained growth to occur, and further the rate of growth of technology determines the rate of growth of both output and capital.