ARE100B Lecture 2 Notes
ARE100B Lecture 2 Notes ARE 100B
Popular in Intermediate Microeconomics
Popular in Agricultural & Resource Econ
Miss Elton Cole
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This 5 page Class Notes was uploaded by Jessica Notetaker on Friday October 9, 2015. The Class Notes belongs to ARE 100B at University of California - Davis taught by Marilyn Whitney in Summer 2015. Since its upload, it has received 30 views. For similar materials see Intermediate Microeconomics in Agricultural & Resource Econ at University of California - Davis.
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Date Created: 10/09/15
Lecture 2 1 Pure Monopolv Continued A Whv Studv Monopolv We want to know the outcomes in markets of pure monopolies and near monopoly We want to maximize pro t B Monopoly To maximize pro t use the pro t function r P r r f x L V S J J quot wr quot a a 1 33 1 1 O Then nd the der1vat1ve L A u x D quotquot V I v Set MRMC i v m C Perfect Competition To maximize pro t use pro t function for little q and nd the derivative of total cost TunVDbOV TC CV F2 2 dry 11 Example Let s look at an example Suppose demand and cost of producing good Q is given Qd 2000 10P TCi 10000 80qi 06qu Consider the following two cases 1 A monopolist 2 5 competitive rms Find market price and quantity quantity per rm and pro t or loss per rm for each case First let s use the shortcut for Case 1 The rst step is to invert demand to get PQ Recall Qd abP and Pab1bQ r K 1quot q 3 LI 2 quota O o a letquot 03 i 39 393 6 Y quotmax nckul 74 C ckOu o quotN39 L JJGJE39 MR 3152 LA g C OU QGOQ2 New M EmNM 0 TC ux s h mum Q4005 NC gt dTC f 37539 62 Q NJ NM use mompok We max m e some in QeA HRML 8 100 1Q soHJQ Gquot n demand equow m 0 GM mm a Pace 39l TO QQ d Vk vquot and T9 an6 TC 8mm 1T TRquot TCF TR 9 Qquot LampltH 533 E thwsas I TC 900 seem 09mquot quot J OOO O 85 Ob 1 H03 Q TCQQ39B quotViv TC 9 o40555 b9213 E jttl 8to 9 VmECr J Now let s try the mglay to make sure we get the same values for Case 1 233 VQ 39Q quot TC d goo 193 Q L oomsoQ 10662 quot 2ch ACQZ39WOO KUQ 40 HQquot ch 9 AC G QTQ39 0 chx Qro 39quot7 loole O 1Q 20 a no 39Q 0 3 00 739 qQ e FQquot We get the same results here RUB m C 3 V 200 M Q 2m O 2533 93 av Cu L We also get the same results here F TR A TC 0 Cse39k quotNF 1 in VG 590 HEB 65 33 M Ta 000 goQ 439 0quot my lgllll olhc To TR 413 WGE B39 Cf Tug 4 t quot l A v39 39 g 1 mm demmcl aquarka 0 Dx39 p i a H 5 hm n quotL I I F gtV 1 Now consider Case 2 Where there is perfect competition in short run with 5 identical rms w race 0 A mi un om AQN CVQ kzgoov Trc gt39 60 ClOOO vOoOO4gtq2gt 39 0 0 and er x39L N39Vwrvk Rur quot 39 3 wr rv 3 3 1 393 g I C 3 PBC39 CL b quot EM WWW K Tr Be k Q R 39wlt l Cj39j W kkhi b j 31 ij 5 Chm cm 5 er na We AQ W YCA s P so 5 CCQ O Q 2 0is t k 3 quot39 f 1 0 5 d 3 NOUO use Q Q maker Clealt zyj Whig 0 Rod 3000 5 9 100040 2 5quot 3 i 7 7000 83 3 quot ogt g p ozquot Since Q Q5 use Whey exam Rina 00 0 009 000 k 5 0 C9 3 9 23013 3 627 3510 M 39 TO 36 x rm K39s nvd 3 I K ac Q MGM QnA 39Qm h Vim Gm QM We Q3 macaw R anicm s39qp39 zowmx omy lt5lt01c8amp5 Tkamxsm M39TK aim v88 i581339 H0 CL cco 80 q Cl002 mo Jr 80 20qu 0c aosco mam TC was s 034 mas t Liam 35 39 2 q c or Since rms are making pro t one Tr R 39 C quot U 01938 qu39qq M 8 could expect more rms to enter in the l t39l f t h qug 5 00 8an q mq39ss ong run un 1 pro 1 reac es zero III Monopoly Pricing vs Elasticity to Demand Let s prove a demand function QdAPAn has constant price elasticity of demand t 452 63 Vote Qckampcampj gt 3 Qa P dQ l P Reoxrcmoyb 0 9324 a x GA Acrwoenvsz a A qAVYH 75 25 lt l n n X quot391 Zz Let s try using real numbers iQ MC Q0 and quotLl wWQS V MC HQ 20 Pi 4 Z 75 l H A
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