Profit Maximizing Production in the Short Run

The goal of an individual firm is to maximize its profit, i.e. the difference be-tween revenues and costs. In the short run, it does that under the restriction that it cannot change the amount of capital.

We will now study the short-run production in a diagram. In the upper part of the diagram in Figure 9.1, we have drawn the total cost, TC, total revenue, TR, and the profit, S = TR - TC. Since the firm cannot influence the price in a perfectly competitive market, TR will simply be a straight line with a slope equal to p (the price). This is since each additional unit of the good it sells will yield an income of p. The shape of TC is often more complicated (see Sec-tion 8.1).

The goal is to maximize the profit, which in the graph occurs at a quantity of q = 78 units, where the profit is 41. (This is the point where S reaches its max-imum.) As profit is the difference between revenues and costs, the difference between TR and TC is at a maximum here: 172 - 131 = 41.

Total cost: The total cost of producing a certain quantity of a good.

Total revenue: The total income from selling a certain quantity of a good.

Profit: The difference between revenue and cost.

Please click the advert

Download free ebooks at bookboon.com 70

Figure 9.1: Profit Maximization under Perfect Competition

In the lower part of the diagram, we have drawn the marginal revenue, MR, the price, p, the marginal cost, MC, and the average variable cost, AVC. MR corresponds to the slope of TR, which we argued must be equal to p. In other words, if we sell one more unit of the good, we receive an additional income equal to the price, p. Therefore, MR is equal to p.

In point a, the MC curve intersects the MR curve. This is a condition for profit maximization. To see why, think about what would happen if we sold one unit more or one unit less than 78. If we had produced and sold one unit more, we would have incurred a cost of MC, but we had only received an income of MR.

And MR < MC, so we had reduced profit. Conversely, if we had produced one unit less, we would have saved the production cost of that unit, MC, but we would also have lost the revenue from selling it. Moreover, to the left of 78, MR > MC, so we had reduced profit that way as well. Therefore, 78 is indeed the best choice we can make. The condition for profit maximization is:

*

* MC q

q MR

TC

q C, R

0 41 131 172

q AC, MC

12 78

2,20

MC

a TR

S

MR = p AVC

72

Marginal revenue: The additional income a firm receives if it sells one more unit.

Marginal cost: The addi-tional cost a firm incurs if it produces one more unit.

Download free ebooks at bookboon.com Microeconomics

71

Perfect Competition

The firm, consequently, chooses the quantity, q^*, that makes MR = MC. Note that, at the quantity 78 in the figure, TR and TC have the same slope. That is the same thing as MR = MC.

9.3.1 Strategy to Find the Optimal Short-Run Quantity We can summarize the strategy for finding the point where the firm maximizes its short-run profit in a few steps:

x Find the point where MC = MR and where the MC curve is increas-ing.

x Is that point above (or equal to) AVC, i.e. is p = MR • AVC? In that case, choose to produce the corresponding quantity.

x In the opposite case, i.e. if p = MR < AVC, choose to produce nothing at all; q = 0. The condition p = MR < AVC is called the shut down condition.

Note that (as in the first bullet point) the MC curve must be increasing. In Fig-ure 9.1, we can see that the MC curve also intersects the MR curve at the quan-tity q = 12, but there the MC curve is decreasing. That point instead maximizes the loss!

Also, note for bullet points 2 and 3, the reasoning behind the condition MR • AVC: Since we are looking at the short run, the fixed cost, FC, cannot be changed. The firm can always choose to produce nothing. If it does so, it rece-ives no revenues and incurs no variable costs, but it will still incur the total fixed cost, FC. Total profit will then be a loss of -FC. This means that the firm will choose to produce as long as it can at least recover some of that loss.

Moreover, the firm will do so as long as the price, and therefore MR, is larger than or as large as AVC.

In the short run, the firm can consequently accept to produce at a (small) loss, since the loss will be smaller than if one chooses to shut down production completely. If instead MR < AVC, the revenues from additional units sold can-not even cover the average variable cost of producing them. Then it is better to shut down.

9.3.2 The Firm’s Short-Run Supply Curve

What happens if the market price changes? Then MR changes, and the point of intersection between MR and MC also changes. The firm will then choose to produce the quantity that corresponds to the new point of intersection, so the quantity supplied follows the MC curve as the price changes.

However, this is only true as long as the price is higher than AVC. To see why, look at the shut down condition above again. Suppose the market price falls to the point where the MC curve intersects the AVC curve, i.e. at the quantity q = 72 in the figure. At that point, MR = p = MC = AVC and the profit becomes q^*(p - AVC) - FC = 72*0 - FC = -FC. Note that p – AVC is what the firm gets paid in excess of average variable cost for each unit it sells; q^*(p - AVC) is then what it gets paid in excess of average variable cost for all units it sells; finally, subtracting FC yields what it gets paid in excess of all costs (= profit).

The loss is consequently as large as if we choose to produce nothing at all. If the price falls even more, the losses increase and it is better to produce nothing.

The conclusion of this is that, the firm’s short-run supply curve is the part of

Shut down condition: The condition under which it is better to produce nothing rather than produce some-thing: MR < AVC.

Download free ebooks at bookboon.com 72

the MC curve that lies above AVC, i.e. the part that is drawn with a full line in the lower part of Figure 9.1.

9.3.3 The Market’s Short-Run Supply Curve

The market is the sum of all individual firms. We get the market’s supply curve by summing all individual firms’ supply curves horizontally. Compare to the method used in Section 4.2.