第7章生産・費用・産業構造

We’ve explained that a firm’s total costs depend on the quantities of inputs the firm uses to produce its output and the cost of those inputs to the firm. The firm’s production function tells us how much output the firm will produce with given amounts of inputs. However, if we think about that backwards, it tells us how many inputs the firm needs to produce a given quantity of output, which is the first thing we need to determine total cost. Let’s move to the second factor we need to determine.

For every factor of production (or input), there is an associated factor payment. Factor payments are what the firm pays for the use of the factors of production. From the firm’s perspective, factor payments are costs. From the owner of each factor’s perspective, factor payments are income. Factor payments include:

We now have all the information necessary to determine a firm’s costs.

A cost function is a mathematical expression or equation that shows the cost of producing different levels of output.

What we observe is that the cost increases as the firm produces higher quantities of output. This is pretty intuitive, since producing more output requires greater quantities of inputs, which cost more dollars to acquire.

What is the origin of these cost figures? They come from the production function and the factor payments. The discussion of costs in the short run above, Costs in the Short Run, was based on the following production function, which is similar to Table 7.2 except for "widgets" instead of trees.

We can use the information from the production function to determine production costs. What we need to know is how many workers are required to produce any quantity of output. If we flip the order of the rows, we “invert” the production function so it shows $L=f\left(Q\right)$.

Now focus on the whole number quantities of output. We’ll eliminate the fractions from the table:

Suppose widget workers receive $10 per hour. Multiplying the Workers row by $10 (and eliminating the blanks) gives us the cost of producing different levels of output.

This is same cost function with which we began! (shown in Table 7.3)

Now that we have the basic idea of the cost origins and how they are related to production, let’s drill down into the details.

The cost of producing a firm’s output depends on how much labor and physical capital the firm uses. A list of the costs involved in producing cars will look very different from the costs involved in producing computer software or haircuts or fast-food meals.

We can measure costs in a variety of ways. Each way provides its own insight into costs. Sometimes firms need to look at their cost per unit of output, not just their total cost. There are two ways to measure per unit costs. The most intuitive way is average cost. Average cost is the cost on average of producing a given quantity. We define average cost as total cost divided by the quantity of output produced. $AC=TC/Q$ If producing two widgets costs a total of $44, the average cost per widget is $\mathrm{\$44}/2=\mathrm{\$22}$ per widget. The other way of measuring cost per unit is marginal cost. If average cost is the cost of the average unit of output produced, marginal cost is the cost of each individual unit produced. More formally, marginal cost is the cost of producing one more unit of output. Mathematically, marginal cost is the change in total cost divided by the change in output: $MC=\Delta TC/\Delta Q$. If the cost of the first widget is $32.50 and the cost of two widgets is $44, the marginal cost of the second widget is $\mathrm{\$44}-\mathrm{\$32.50}=\mathrm{\$11.50.}$ We can see the Widget Cost table redrawn below with average and marginal cost added.

Note that the marginal cost of the first unit of output is always the same as total cost.