Daniel l. Rubinfeld
Daniel l. Rubinfeld
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.