R pQ g(Q) (A BQ) Q AQ BQ2R pQ g(Q) Q (252 14 Q)Q 252 Q 14Q2MR change in revenuechange in output∆ R(Q, p)∆ Q∆ TR(Q, p)∆ QmaxypQ C(Q, w)< maxQg(Q)Q C(Q, w)< maxQ(252 14 Q) Q C(Q, w)< maxQ252Q 14 Q2 C(Q, w)April 2, 2001MonopolyHandout 1A firm is a monopoly if it is the only supplier of a product for which there is no close substitute. A monopoly sets the priceof its product without concern that the price might be undercut by rivals. A monopoly faces a downward sloping demandcurve.The demand function for a monopolist is written as where Q is the quantity demanded at the price p. The inverseQ D(p)demand function is given by where g denotes the inverse of the function D. For example ifp D1(Q) g(Q) then .Q 18 114pp 252 14QRevenue for a monopolist - The revenue of a firm (R) is given by pQ, where p is the price of the product and Q is the levelof output. In market equilibrium, the price depends on the amount consumed and produced. The monopolists’ revenue istherefore . If the inverse demand function is linear and given by , then revenue is given byR pQ g(Q) Qp A BQFor example if the inverse demand function is then revenue is given byp 252 14QMarginal revenue is the increment, or addition, to revenue that results from producing one more unit of output. Marginalrevenue is the change in total revenue from producing one more unit of output. In discrete or average terms marginal revenueis given bywhere ∆ denotes change, R and TR both denote revenue, and Q denotes output. For a linear inverse demand function, it iseasy to compute marginal revenue. If the inverse demand function is given by then marginal revenue is givenp A BQby . So marginal revenue has the same intercept and a slope twice as steep as inverse demand. One way toMR A 2 BQdraw this is to find the intercept on the Q axis for the demand function and then use ½ of that value as the Q intercept for themarginal revenue function.Once the firm has determined the least costly way to produce each output level, it chooses the level of output whichmaximizes profits. Specifically, it has the following maximization problemCost Curves, Marginal Revenue and Optimal Price0501001502002503003504000.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00Output$DemandMRMCP OptQ OptQ FC VC C AFC AVC ATC MC ∆ MC Demand/PriceTR MR ∆ MR Profit0 100 0 100 252 0 252 -100120 2381 100 120 220 100.00 120.00 220.00 109 238 238 224 18100 2102 100 220 320 50.00 110.00 160.00 92 224 448 196 12886 1823 100 306 406 33.33 102.00 135.33 81 210 630 168 22478 1544 100 384 484 25.00 96.00 121.00 76 196 784 140 30076 1265 100 460 560 20.00 92.00 112.00 77 182 910 112 35080 986 100 540 640 16.67 90.00 106.67 84 168 1008 84 36890 707 100 630 730 14.29 90.00 104.29 97 154 1078 56 348106 428 100 736 836 12.50 92.00 104.50 116 140 1120 28 284128 149 100 864 964 11.11 96.00 107.11 141 126 1134 0 170156 -1410 100 1020 1120 10.00 102.00 112.00 172 112 1120 -28 0190 -4211 100 1210 1310 9.09 110.00 119.09 209 98 1078 -56 -232230 -7012 100 1440 1540 8.33 120.00 128.33 252 84 1008 -84 -532Cost Curves, Marginal Revenue and Loss0501001502002503000 2 4 6 8 1012141618Output$DemandMRMCATCQ OptP OptATC OptAVCATC OptNow let inverse demand be given by .p 165 14 QQ FC VC C AFC AVC ATC MC ∆ MC Demand/PriceTR MR ∆ MR Profit0 100 0 100 165 0 165 -100120 1511 100 120 220 100.00 120.00 220.00 109 151 151 137 -69100 1232 100 220 320 50.00 110.00 160.00 92 137 274 109 -4686 953 100 306 406 33.33 102.00 135.33 81 123 369 81 -3778 674 100 384 484 25.00 96.00 121.00 76 109 436 53 -4876 395 100 460 560 20.00 92.00 112.00 77 95 475 25 -8580 116 100 540 640 16.67 90.00 106.67 84 81 486 -3 -15490 -177 100 630 730 14.29 90.00 104.29 97 67 469 -31 -261106 -458 100 736 836 12.50 92.00 104.50 116 53 424 -59 -412128 -739 100 864 964 11.11 96.00 107.11 141 39 351 -87 -613156 -10110 100 1020 1120 10.00 102.00 112.00 172 25 250 -115 -870190 -12911 100 1210 1310 9.09 110.00 119.09 209 11 121 -143
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