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46 Fig. II The Gains & Losses        ::::x::::t\   1 I [C> \ 1 N.    < 1 N    Q Q+1  
Recall from Section V that AR = (TR)/Q = (PQ)/Q = P. Therefore price along a demand curve is an average fimcdon. But we also know from Secdon V that when any average funcdon such as price falls, the associated marginal funcdon (marginal revenue) must lie below it. Therefore, MR < AR = P or MR < P. Put differendy, when price is falling along a demand curve, marginal revenue is always below it. To have a closer look at whats happening, consider the graph in Figure II. Initially, the monopolist is selling Q units at a price of P. His total revenue (PQ) is given by area A plus area B. Now in order to sell an added unit, he must decrease his price from P to P. But this is a price cut on all units, notjust on the added unit. This means that he will now 1 a total revenue of only PQ on those first Q units instead of PQ By cutung price, he therefore loses the revenue in area A. On the other hand, he gains the sale of one unit at the new price, P, which equals area in Figure II. The total change in revenue (MR) is what he gahis less what he loses, or P  area A. Since area A is not zero, MR must be less than the new price P. In Figure III the loss from a price cut exceeds the gains so that MR is negative at Q. Of course, the shaded area is captured at either price. If, on the other hand, the loss was less than the gain, MR would be positive. For further insight into why MR is less than price, consider die numerical demand schedule in Table I. Suppose that die monopolist is selling three units at a price of $8. If he sells a 4di unit, he gains its sale price of $7. On the other hand, he could have sold the first three units at a price of $8. After his price cut, he will only get $7 per unit for them. Therefore, on each of diese three units, he will lose a dollar (S8 $7) that he could have had were diere no price cut, for a total loss of $3 [ (3) ($1) ]. His total change in revenue (MR) from selling the 4th unit equals the sale of one more unit at the new price, $7, less the loss of 51 per unit on each of the first three units, for a total loss of $3. Hence MR = ($7  $3) = $4. As predicted by the marginal/average rules, this is less than the price of the 4th unit, $7. To cement your understanding, we recommend that you calculate MR on the 5th unit by this method (gain = $6; loss = $4). However, the above procedure is not a computadonally efficient method for calculadng marginal revenue. In Table II, we present a portion of the demand for coconuts in the first two columns. Total Revenue (PQ) is in the 3rd. Since MR is the change in Table i Fig. Ill P, MR
total revenue, MR for the 5th coconut is $3 ($35  $32); for the 6th, it is $1 ($36  $35). We recommend that you make this procedure your roudne method for calculating MR and that you verify that MR is negative after six coconuts. ELASTICITY AND MARGINAL REVENUE Now consider the downvirard sloping demand curve in Figure IV. If the firm cuts its price to P, it vwll continue to capture the shaded area in its total revenue. The loss in revenue stemming from a price cut is offset by an equal gain, so that toul revenue (TR) must be constant. If total revenue is constant, we know two things: first, MR must be zero since the change in total revenue is zero; second, from Section IV, the elasticity of demand must be equal to 1.0. Figure V illustrates that MR = 0 at Q where the elasticity ofdemand is 1.0. At levels of output Q, demand is inelastic and at levels of output below Q, demand is elasdc. In other words, the firms total re\enue increases by expanding output up to Q and decreases after that. But MR is precisely the gain in total revenue obuined by expanding output by 1 unit. Therefore, out to Q,, MR must be positive. Similarly, since the firm loses total revenue by expanding beyond Q, the change in total revenue (MR) must be negative in this range. Consequendy total revenue is maximued where MR = 0, i.e., when = 1 . Figure VI graphs total revenue as a function of output. Since toul revenue (PQ) will be zero whenever P or Q is zero, the total revenue curve rises from zero at Q = 0 and returns to zero when P = 0. Total revenue is maximized at Q where MR = 0 and = 1 . From the discussion above alone we know that no profit maximizing firm  whether a monopolist or not  ever sells in the inelasdc portion of its demand curve. To see this, consider the profit formula below: Jt = [TR]  [TC] Suppose a pricesearcher is currendy selling in the inelastic pordon. Then if he cuts output by one unit, price will rise. F«)mSectio«D4\\:hendemand is inelasdc, an increase in price raises total revenue (TR) in the profit formula. Moreover, the reduction in output also reduces total cost (TC) in the formula. Therefore, since total revenue increases and total cost decreases after this output reducdon, profit must cerUinly increase. Addidonal reductions in output will
Fig. V MR & Elasticity  P, MR     \ e (irrelevant)    TR ,  Fig. VI TR & Output 1 / 1 \    / 1 \ / \ / \ / \ f t \     
continue to raise profit so long as the firm remains in the inelastic portion. Once the elastic portion is reached, however, total revenue will start to fall with further output reducdons. As such, we can no longer predict the impact on profit. Since profit maximizing firms do not sell in the inelasdc region of their demand curVes, we have marked the entire inelasdc portion of Figure V as irrelevant. MONOPOLY OUTPUT PRICE AND PROFIT To determine the profit maximizing output, cost curves must be considered. Figure VII appends some cost cur\es to the demand information in Figure v. Equilibrium output will be Qm, where marginal cost equals marginal revenue because all aliernadve outputs reduce total profit. Consider an output like Q which falls short of the profit maximizing output Qn,. At Q the increase in total revenue from selluig an addidonal unit, MR, exceeds the addidonal cost, MC, so it pays to produce more. A similar analysis applies at all other points to the left of Qm . Now consider a point like Q*, which exceeds the profit maximizing output Qm. Here, one unit reduction in output lowers totjd cost more than it lowers total revenue (MC* > MR*). As such, profits rise. Therefore, the firm will uant to cut back producdon at Q*. A similar analysis applies to every other output lo the right of Qm • It fol lows that Qm is the profit maximizing output. In other words, die firm will produce Qm units, where MC = MR, if it produces at all. Naturally, monopolists must still cover their average variable or average total costs, whichever is appropriate. For example, a monopolist will shut down if price is less than average variable cost in the short run and if it is less than average total cost in the long run. For the determinadon of profit and price, consider Figure VIII containing the cost and demand informadon of Figure VII. Output is Qm as we have seen. Price will be Pm, ie., the highest price at which all Qm units can be sold. Note that Pm is a market clearing price. Profit is given by n = (TR  TC) = [PQ(ATC)Q3 = [P  (ATC)]Q= Area 2. To be sure you see diis, consider diat TR = (PmQm ) = Area I + 2, while TC = (ATC)Qm = Area 1. In contrast to pure compeddon, the monopoly output implies price exceeding the marginal cost of the equilibrium output This will be important. Further note that the compedtive output occurs where the MC curve strikes the demand curve at Qc Hence, the compeddve price, PC, is lower than the monopoly price and the competidve output of Qc is greater. In summary, in monopoly: 1. Entry to the industry is blocked in one way or another. The monopolist faces the demand curve of the enure industry. MR is less than P. The monopolist never sells in the inelasdc pordon of his demand curve, where MR is negadve. If the monopolist produces, he picks the output at which MR = MC. P is greater than MC at the monopoly profit maximizing output. Monopoly output is less than that of the compeddve industry. Profits can exist in the long run because entry is blocked. The monopolist will shut down in the short run if P is less than AVC and in the long run if P is less than . 3. 4. EFFICIENCY Recall from Section II that the price along a demand curve represents a measure of marginal benefit, i.e., the subjective value to the demander of having another unit to consume. Thus, if you are willing to pay $12 to consume a second unit of a good, the
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