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37

jrves. This must be so: to the left of the inter-„ the two average curves are falling because MC jW them. To the right thev are rising because MC jove them. Since the average curves are falling to .e left and rising to tlie right of the intersecdon, it follows that tbe intersection is a minimum.

Tbe short run average total, average variable, average fixed, and marginal cost curves of Figure \ 1 are characteristic of almost all the market structures considered in this book, notjust those considered in the present section. Consequendy, a mastery of this figure is cmcial for understanding most of the remainder of this book.

To summarize these short run cost curves:

1 . Total cost (TC) and total \-ariable cost (TVC) curves rise first at a decreasing rate (become flatter) and then at an increasing rate (become steeper).

2. The output at which these two curves begin to increase at an increasing rate is known as the point of diminishing returns.

3. Average total cost ( ) and average variable cost (AVC) can be derived from their corresponding total curves by drawing rays from the origin to the curves. The slope of these rays gives and AVC.

4. Multiplying average total, average variable, and average fixed cost by quantity will give back total, total variable, and total fixed cost respectively

5. Marginal cost (MC), the change in total

 Fig. VII The Marginal & Average Cost Curves /

cost from producing one more unit, is derived from the total cost curve by taking tangents to the total cost curve.

6. Marginal cost falls as the slope of the total cost curve becomes flatter and then rises once diminishing returns set in.

7. The marginal cost curve passes through the minimums of both the average total ( ) and the average variable cost (AVC) curves.

8. The distance between average total and average variable cost is average fixed cost, which declines continuously.

9. Average total, average variable, and marginal cost curves are all roughly "U" shaped.

INDUSTRY AND DEMAND

Figure VIII shows the industry supply and demand curves as well as the demand curve faced by the compedtive firm. This could be either the short run or the long run situation, but for now consider it to be the short run. As one of the industrys many sellers, the compedtive firm can effectively do nothing to affect the going market price, as we saw in Secdon III. Consequendy, the demand curve faced by the price-taking firm is perfectly elastic at the price P so that the firm can sell as much as it likes vnthout cutting price.

We can define average revenue (AR) as total revenue divided by output, (TR)/q. Substituting for total revenue and cancelhng gives AR = (Pq)/q = P-Hence, average revenue equals price. Marginal revenue (MR), is the change in total revenue (ATR) from selling an addidonal unit. For price-taking firms with their perfecdy elastic demand curves, MR also equals P. This follows because the average funcdon, AR, is constant for the price-taking firm; therefore from the marginal/average rules, the marginal funcdon, MR, must be equal lo it Hence, MR = AR = P for price-taking firms. As a numerical example, assume price is \$4 and the output ofa price-taking firm is 6 units, so that TR = \$24. If the firm steps up output to 7 units, the new total revenue will be \$28, so that the change in total revenue, ATR, obtained from selling the 7th unit will be \$28 - \$24 = \$4. Thus marginal revenue and price both equal \$4 as claimed. Figure IX shows how we can geometrically get back tolal revenue from the related functions. Geometrically total revenue (Pq) is the shaded area. Note that muldplying average revenue or marginal revenue by quantity gives the same

lie

""/"iilive

Fig. vm

Fig. IX

INDUSTRY

PRICE-TAKING FIRMS DEMAND CURVE

result. As a numerical example, if price were \$2 per unit and output 3 units, the total revenue of \$6 would be geometrically represented by the shaded area back in Figure IX.

THE MEANING AND MEASUREMENT OF PROFIT

The theory of the firm assumes that firms seek to maximize their profits, ir, which are, of course, the difference between total re\enue (TR) and total cost (TC). With a bit of high school algebra we can substitute to get:

(1) =TR-TC

= Pq-(ATC)q -[P-(ATC)]q

Whether firms in fact do try to maximize profiu or pursue some other goal has been debated without resolution for some dme. Nonetheless, at the very least, firms in very competidve enrironments must achie\e something like profit maximizadon just in order to survive. Otherwise they will go bankrupt and disappear. Therefore the profit maximizing assumption has validity even if real world firms blindly stumble into their pricing and output decisions. In other words, even though real world firms do not m fact know any of the models we are about to present, they must to some extent conform to them in order to surxive. Moreover, the more knowledgeable and energedc real world firms happen to be, the greater the extent to which they conform to the profit maximizing model.2

However, before deriving the profit maximizing output, its best to spend a moment on the meaning of profit. Recall from Secdon I that all costs are opportunit) costs in economics. Therefore the pres-

ence of profit implies the firm is doing better tl any alternative use of its resources. For example,! ing the firm earns a profit of \$500 means its ea \$500 more than it could in its next most profit opportunit). In such situations, we say the firm is i ing super-normal profits, economic profits, orl plain profits. On the other hand, when total re just equals total cost, economists say the firm is ma normal profits or zero economic profits, or just i profiL The expression means the firm is doing asj as it could in its next best alternative and better I in all other ones.

Do not confuse economic profit with thel ventional accounting meaning of profit. AccounJ do not include all opportunit) costs in calcul: profit In other words, what the firm could getl where is excluded from cost. As a result, accout] profits exceed economic profits. Thvis. in many! tions in which an accountant would report profit] economist would see a loss. Throughout this 1 costs are opportunity costs and all profits are ic profits. The following analysis examines the cfl quences of profit maximization under these cc tions.

THE PROFIT MAXIMIZING OUTPUT

There is one central rule for profit maxir tion throughout economics: Provided the firm she operate at all, it should continue to increase ouB undl the marginal revenue (MR) from a funher put increase just equals maiginal cost MC). This! is so crucial that we present it three ways: intuH mathematical!), and graphically.

Intuitively, so long as producing another] adds more to revenue than to cost, the firm will

duce it. For example, if at some output q, the gain in total revenue (MR) from producing and selling an additional unit is \$7 and the increase in the firms total cost (MC) is \$5, the firm can pick up \$2 (\$7 - \$5) in profit by expanding output by a unit, and will do so. Suppose it now costs the producer \$6 to produce the next unit (MC = \$6) and he still can gain another \$7 from selling this unit (MR = \$7), then it will pay to produce this unit as well because the firm can pick up another \$1 (\$7 - \$6) in profit. On the other hand, suppose producing another unit costs him \$10 (MC = \$10) but he could only sell that unit for \$7 (MR = \$7), then surely the firm would not want to do so. It would lose \$3. Thus, weve established that the firm should expand output so long as marginal revenue is greater than marginal cost and that it should cut back output vienever marginal cost is greater than marginal revenue. It follows that the firm should neither expand nor contract output when marginal revenue just equals marginal cost At that point, it has maximized its profit. It. We can summarize all this in Table I below.

The profit maximizing rule given below allows

us to derive the firms supply curve. Consider Figure XV displaying the marginal cost curve for a price-taking firm. Suppose that the price is \$5, then marginal revenue will also be \$5 and the firm will want lo produce 8 units. At P = \$6, MR =6 so the firm will want to produce 9 units. At P = \$7, the fum equates marginal revenue and marginal cost by producing 10 units. Since for any possible price we know the output of the firm, weve consequendy derived the supply curve of the price-taking firm: provided the firm should produce at all, its supply curve is its marginal cost curve.

Looking at profit maximization mathematically.

recall that profits are given by:

(2) -71 = TR - TC

It follows that the change in profit, , from increasing output by just one unit is;

(3) -1 = ATR -

where ATR is the change in total revenue and is the change in total cost. But the change in total revenue, ATR, is marginal revenue, MR, and die change in total cost, , is marginal cost, MC. Therefore

(4) = MR - MC

Now if the firm wants to maximize its total profits, it should continue expanding output until it can gain no additional profits by further expansion, i.e., undl the gain in profit, , from expanding any further just exacdy equals zero. At that point total profit is maximized. For example, suppose expanding output from 5 units to 6 increases total profit by \$8 (Air = \$8). Clearly the firm should expand, because it gains \$8 in profit. Now suppose that expanding from 6 units to 7 increases profit by +\$4 ( , = \$4). Clearly the firm would expand to gain the \$4. Now imagine that expanding still further from 7 to 8 does not change profit (Air = 0). In this case the firm would be indif fercnt to producing the eighth unit because it neither gains nor loses total profit from doing so.

If the firm were to press on to produce a ninth unit. Air might be -\$4 so that the firms profits would fall by \$4. Consequendy, the firm should continue to expand only up to the output at which the change in profit, , just equals zero. But from (4) = 0 when

Table I

Fig. XV

Reactions of the Profit Maximizing Firm*

If Firm Should (& Will)

MR>MC MR<MC MR=MC

Assuming it should operate at ail

Expand Production Contract Production Make No Changes

P, MR, AR

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