No Such Thing as a Free Lunch: Principles of Economics (Part 36)

One of the most powerful insights in economics is this idea of a division of labor. You do the thing you're good at. Other people do something else that they're good at. The net effect is better for everybody.

Paul Romer

Short-Run Costs and Output Decisions

(Part C)

by

Charles Lamson

Total Costs

Having covered total fixed costs and total variable costs in the last two posts, we are now ready to complete the cost picture by adding total fixed costs to total variable costs. Recall that

TC = TFC + TVC

Total cost is graphed in Figure 7 where the same vertical distance (equal to TFC, which is constant) is simply added to TVC at every level of output. In Table 4 from last post and reintroduced below, column 6 adds the total fixed cost of $1,000 to total variable cost to arrive at total cost.

Average Total Cost (ATC) Average total cost (ATC) is total cost divided by the number of units of output (q):

ATC = TC / q

Column 8 in Table 4 shows the result of dividing the costs in column 6 by the quantities in column 1. For example, at 5 units of output, total cost is $1,042; average total cost is $1,042 / 5, or $208.40. The average total cost of producing 500 units of output is only $18 that is, $9,000 / 500.

Another, more revealing, way of deriving average total cost is to add average fixed cost and average variable cost together:

ATC = AFC + AVC

For example, column 8 in Table 4 is the sum of column 4 (AVC) and column seven (AFC).

Figure 8 derives average total cost graphically for a typical firm. The bottom part of the figure graphs average fixed cost. At 100 units of output, average fixed cost is TFC / q = $1,000 / 100 = $10. At 400 units of output, AFC = $1,000 / 400 = $2.50. The top part of Figure 8 shows the declining AFC added to AVC at each level of output. Because AFC gets smaller and smaller, ATC gets closer to AVC as output increases, but the two lines never meet.

The Relationship Between Average Total Cost and Marginal Cost The relationship between average total cost and marginal cost is exactly the same as the relationship between average variable cost and marginal cost. The average total cost curve follows the marginal cost curve, but lags behind because it is an average over all units of output. The average total cost curve lags behind the marginal cost curve even more than the average variable cost curve does, because the cost of each added unit of production is now averaged not only with the variable cost of all previous units produced, but also with fixed costs as well.

Fixed costs equal $1,000 and are incurred even when the output level is 0. Thus, the first unit of output in the example in Table 4 costs $10 in variable costs to produce. The second unit cost only $8 in variable cost to produce. The total cost of 2 units is $1,018; average total cost of the two is ($1,010 + $8) / 2, or $509. The marginal cost of the third unit is only $6. The total cost of the three units is thus $1,024, or $1,018 + $6, and the average total cost of three units is ($1,010 + $8 + $6) / 3, or $341. 

Marginal cost (MC) is what drives changes in average total cost.

An example using test scores should help you to understand the relationship between MC and AVC. Consider the following sequence of test scores: 95, 85, 92, 88. The average of these four is 90. Suppose you get an 80 on your 5th test. The score will drag down your average to 88. Now suppose that you get an 85 on your 6th test. The score is higher than 80 but it is still below your 88 average. As a result, your average continues to fall (from 88 to 87.5), even though your marginal test score rose. If instead of an 85 you got an 89---just one point over your average---you have turned your average around; it is now rising. 

If marginal cost is below average total cost, average total cost will decline toward marginal cost. If marginal cost is above average total cost, average total cost will increase. As a result, marginal cost intersects average total cost at ATC's minimum point, for the same reason that it intersects the average variable cost curve at its minimum point.

Short-Run Costs: A Review

Let us now pause to review what we learned about the behavior of firms. We know that firms make three basic choices: how much product or output to produce or supply, how to produce that output, and how much of each input to demand to produce what they intend to supply. We assume that these choices are made to maximize profits. Profits are equal to the difference between a firm's revenue from the sale of its products and the cost of producing that product: profit equals total revenue minus total cost.

So far, we have looked only at costs, but costs are only one part of the profit equation. To complete the picture, we must turn to the output market and see how these costs compare with the price that a product commands in the market. Before we do so, however, it is important to consolidate what we have said about costs.

Before a firm does anything else, it needs to know the different methods that it can use to produce its products. The technologies available determine the combinations of inputs that are needed to produce each level of output. Firms choose the technique that produces the desired level of output at least cost. The cost curves that result from the analysis of all this information show the cost of producing each level of output using the best available technology.

Remember that so far we have talked only about short-run costs. The curves we have drawn are therefore short-run cost curves. The shape of these curves is determined in large measure by the assumptions that we make about the short run, especially the assumptions that some fixed factor of production leads to diminishing returns. Given this assumption, marginal costs eventually rise, and average cost curves are likely to be U-shaped.

After gaining a complete knowledge of how to produce a product and how much it will cost to produce it at each level of output, the firm turns to the market to find out what it can sell its product for. It is to the output market that we turn our attention in the next post.

Table 5 summarizes the cost concepts that we have discussed. 

*MAIN SOURCE: CASE & FAIR, 2004, PRINCIPLES OF ECONOMICS, 7TH ED., PP. 159-162*

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