question set 8 - Microeconomic Theory Jeffrey Carpenter...

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Unformatted text preview: Microeconomic Theory Jeffrey Carpenter Econ 255 ' Warner 305F {Problem set number 8 . jpc©middlebury.edu Due: Monday April 30til (in class) X3241 CHAPTER 24 — MONOPOLY Monopoly Theory — Say the inverse market demand for a good is p(y) = a-Zby and all the firms s producing in this market have the same cost structure, C(y) = c+dy2. (a) If there is one firm producing in the market, find the monopolist’s profit maximizing output level and price. (b) Graph the monopolist’s choice on a regular supply and demand graph, including the amount of profit that the monopolist makes. (0) If a210, b=2, c=0 and d=1, what is the value of the deadweight loss associated with monopoly? CHAPTER 27 — OLIGOPOLY 2) Stockelberg Theory — Now let’s say that there are two firms in the market, call them one and two (we are still using the cost functions from (1)). This means that the inverse market demand is now p(y) = ar2b(y,+y2). If firm one takes on the leader’s role how much does it produce? How much does the follower, firm two, produce? How does this compare to the monopoly situation? Are consumers better or worse off? (Remember that this problem differs from your notes because the firms have costs now. Also, at the end you should piug in the numbers from (10) to make the algebra easier) Cournot Theory — Now let’s say there is no clear leader (but we are still using C(y) = c+dy2). Find the best response functions for two Conmot duopolésts. What are the production levels of the two Cournot firms. (Remember that this problem differs from your notes because the firms have costs now. Also you should plug in the numbers from (1c) to make the algebra easier) ’7’ ~_;'\ A ‘1? -~ / U ', , 1:! .1 ’4' ’r Iva-{J N4, is .1; f. x .a ~__%_‘__~_~_ ' 334° #23 a fit? at} if H. ‘7 —.n_.‘-_ ‘ 7 u C)" (K; fir!) .5; We...“ ." L.“ ~~——~—— _H- ‘_ E2 :5» f~ {f f 4V¢k¢a¢4 (cf? 3 / \«9/ i 1 1 MW, 3; 1 2 19; 2 30:2: ' ‘ (“I 23), If“ ‘37, / : 23:10_?1 :irj'é I ELM; R35 3 ‘12: WE: ~ ,2» N \_V./ 7% .4 S A f ' "3-1-2 1’! - f ’3 § 7‘ ’ Wv’z- = '1*:’ aaa’fi’vu &Lz:‘a5;21w. T Jr? J ,I J \ ' .- n ‘ ‘1 M L<é ma 1.; J5": ,3 _.. g ’34 J ”V; M 12 :M/ 5:; I" ,J ‘ I 474 C a are???“ ”-7" V ‘ z ’ “4..” —.—...<--..———»-- -~———~ w“ “:1. If } Rm." f O 75V, g: 135.3% 2'23 ’3 I ....... WM“ _ _- 7L : 6,3: I 5.9%,: t ‘ (’5') \« x , " fr 6’ v" WED-{aux}? Inf if? 5. M i J . , ‘3 “3 2 «d w ; fig’é’pafggyé fig)" 8, v, {I ’1'" 1 37’” O(? m ”‘ '2“ 3 \\ W I ; “x \ ._ g \ \\\ /J ...
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