Working harder: Calculating total factor productivity

94 Part II: Considering Which Side You’re On in the Decision-Making Process

indicates a linear relationship between both labor and output and capital and output. In this equation, for every one-unit increase in labor, the quantity of output produced increases by two units, while a one-unit increase in capital leads to a five-unit increase in output. Alternatively, the production function may take the form

This commonly used production function is called the Cobb-Douglas function. The Cobb-Douglas production function is widely used because it assumes some degree of substitutability between inputs, but not perfect substitutability. So, labor can be substituted for capital — dishes can be washed by hand at a restaurant or in a dishwasher — but labor is not a perfect substitute for capital.

Starting with Basics by Using Single Input Production Functions

Production functions typically have more than one input; however, in the case of a single input production function, you assume that the quantity employed of only one input can be varied. In other words, you have one variable input and all other inputs in the production process are fixed inputs — and you can’t change the quantity of the fixed inputs.

You’re a farmer trying to decide how much land you’re going to plant in corn and how much you’ll leave for hay. You’ve decided to treat the quantities of labor (you’re the only one working) and machinery employed constant. In this situation, labor and capital (the machinery) are fixed inputs and land is a variable input.

The following equation describes the relationship between the amount of land you use and the quantity of corn produced

Where q is the number of bushels of corn grown and N is the amount of land used.

I know, the 0.9 power looks strange, but trust me, your computer can handle it. Nevertheless, Table 6-1 presents some of the land, output combinations that are possible.