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Daniel l. Rubinfeld

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Price<br />

Dollars per 7 I<br />

Unit of<br />

Output 6<br />

o 1<br />

2<br />

,____ !"xerage Re\'enue (Demand)<br />

J>-<br />

5 6 7<br />

revenue are shown for the demand curve P = 6 - Q.<br />

reraae and marginal cost curves, AC and Me Marginal revenue and marginal<br />

8'V t a~e equal at quantity Q*. Then from the demand curve, we find the price P*<br />

COS d tl . . Q""<br />

that correspon s to lIS quantI~. ' . . " . .<br />

fIow can we be sure that Q' IS the profIt-maXllnIZmg quantity Suppose the<br />

onopolist produces a smaller quantity Q1 and receives the corresponding<br />

~gherprice Pl' As Fig~re 10.2 sho'ws,.marginal reven:le would then exceed marl'1nal<br />

cost. In that case, If the monopolIst produced a lIttle more than Qj! it would<br />

~ceive extra profit (MR - MC) and thereby increase its total profit. In fact, the<br />

monopolist could keep increasing output, adding more to its total profit until<br />

output Q*, at which point the incremental profit earned from producing one<br />

more unit is zero. So the smaller quantity Q1 is not profit maximizing, even<br />

though it allows the monopolist to charge a higher price. If the monopolist produced<br />

Ql instead of Q*, its total profit would be smaller by an amount equal to<br />

the shaded area below the MR curve and above the MC curve, between Q1 and Q*.<br />

In Figure 10.2, the larger quantity Q2 is likewise not profit maximizing. At this<br />

quantity, marginal cost exceeds marginal revenue. Therefore, if the monopolist<br />

produced a little less than Q2' it would increase its total profit (by MC - MR). It<br />

could increase its profit even more by reducing output all the way to Q*. The<br />

increased profit achieved by producing Q* instead of Q2 is given by the area<br />

below the MC curve and above the MR curve, betw'een Q* and Q2'<br />

We can also see algebraically that Q* maximizes profit. Profit 7T is the difference<br />

between revenue and cost, both of 'which depend on Q:<br />

7T(Q) = R(Q) - qQ)<br />

As Q is increased from zero, profit will increase lUltil it reaches a maximum and<br />

then begin to decrease. Thus the profit-maximizing Q is such that the incremental<br />

profit resulting from a small increase in Q is just zero (Le., j,,7T/~Q = 0). Then<br />

j"7T/j,,Q j"R/j"Q j"C/~Q = 0<br />

But ilR/j"Q is marginal revenue and ~C/~Q is marginal cost. Thus the profitmaximizing<br />

condition is that MR MC = 0, or MR = Me<br />

Chapter 10 Market Power: Monopoly and Monopsony 331<br />

Lost profit from producing<br />

too little (Q1) and selling at<br />

too high a price (P 1 )<br />

D=AR<br />

profit from producing<br />

too much (Qz) and selling at<br />

too Iowa price (Pz)<br />

To grasp this result more dearly, let's look at an example. Suppose the cost of<br />

production is<br />

qQ) = 50 + Q2<br />

In other words, there is a fixed cost of $50, and variable cost is Q2 Suppose<br />

demand is O'iven by<br />

o .<br />

P(Q) 40 - Q<br />

By s~t~ng marginal revenue equal to marginal cost, you can verify that profit is<br />

maXImIzed when Q = 10, an output level that corresponds to a price of $30.3<br />

Q* is the output level at which MR Me. If the finn produces a smaller output-say, Q1-it sacrifices some<br />

because the extra revenue that could be eamed from producing and selling the units between QJ and Q'" ..<br />

cost of producing them. Similarly, expanding output from Q* to Q2 would reduce profit because the additional<br />

would exceed the additional revenue.<br />

_ that average cost is c(Q)/Q 30/Q + Q and marginal cost is ~C/~Q = 2Q. Revenue is<br />

- P(Q)Q = JOQ - Q2, so marginal revenue is MR ~R/~Q 40 - 2Q. Setting marginal revequal<br />

to marginal cost gives ,10 2Q 2Q, or Q = 10.

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