Intermediate Microeconomics: A Modern Approach, Seventh Edition

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Unformatted text preview: Suggested Solution to Final Exam A for ECON 301 Jennifer Wissink Cornell University PartI 1. P=-1/2X+150, Pxx=-1/2X2+150X9 MR=-X+150 TC=10+V2X19MC=X from profit maximizing condition MC = MR, x = - X+ 150 9 x* = 75 P=—1/2x+150 9P"'=112.5 n= I dx/dpxp/x I = I-2 x112.5+75 I = 3, thus demand is elastic. 2. ( long-run totalcost function) Min 6K +7 2L s.t. Min (2K, 2L) = x fromconstraint,2K= 2L = x 9 K=1/2 X, L=1/2X Thus, C=6 x1/2X+ 2x1/2x:> C=4 X ( short-run total cost function ) Min 6x8 + 2L s.t. Min (16, 2L) = x . from constraint, 2L = X 9 L = 1/2 x, 0 S X S 16 Thus, C=48+ 2 x1/2X:> C=48+x,(0$xs16) 3. (DMRS Abe = MRS Betty, 4. MinC1+C2 =Mi112x12+90+6x22 +40 5.1: X1 + X2: 36 - by plugging constraint into objective function, Min 2X12 + 90 + 6(36 — )(1)2+ 40 then FOC is 4 x1 —12(36— x1) = ‘0 9 x:* = 27, x2*= 9 5. Disagree Income increase 9 demand curve shifts to right (D—>D’)-) price increase (Po—+P1)9 new private firms enter 9 short-run supply curve shifts to right(SSu~>'SS’) 9 price decrease (P.—>P0) 9 new equilibrium (QB—>Q.). There is only change of short-run supply curve, because long—run supply curve is I horrizontal in competitive market. 18 Part II 1. a. (.1) Reaction function for firm 1 Px x1 =20x1 —x;2 —x1x2* -) MR=20 —2x1 —-X2*, MC=8 from MC=MR, 20 — 2X1 ~ X2* = 8 @(2) Reaction function for firm 2‘ PxX2=20X2—X22 —x1*x2 —) MR=20d2x2—x1*, MC= 2 from MC=MR, 20 — '2x2 — x1* = 2 from (1) and (2), X? = 2, x2*= 8, x=*= 10 P = 20 — X" = 10 then, “1* = 10x2 —8><2 = 4, “22* = 10x8 — 2x8 = 64, in?” = 4+64 = 68 ‘ b. Since MC of firm 2 is lower than that of firm 1, we don’t have to produce in firm 1. P=20—X2,PxX2=20X2—-X229MR=20—-2X2, ' fromMR=MC,20—2x2 = 2 9 x? = 9, Xg” =0, X*= 9 P = 20 n X* = 11 then, in“ = 0, Iliz" =11><9 ~2><9 = 81, it" = 0+81 = 81 To maintain cartel, firm 2 has to subsidize firm 1 some money(M*). "‘ 4 < M" < 17 c. Like part b, we don’t have to produce in firm 1, because MC of firm 2 is lower than that of firm 1 Competitive solution means MC = P 9. P* = 2 from P = 20 —X2, Xi" = 18, Xfi '-= 0, X*= 18 then,m* = 0, It? = 2x18 — 2x18 = 0, 1t* = 0 19 . a mg mo Not Develop 0, 100 b. There is no dominant strategy equilibria to this game. Boeing's best response is if Airbus chooses develop 9 Choose “not develop” if Airbus chooses not develop -) choose "develop" Airbus’ best response is if Boeing chooses develop-7" choose “not. develop" if Boeing chooses not develop -) choose “develop” c. (Boeing, Airbus) =I (Develop, Not Develop), (Not Develop, Develop) d. dominant strategy : none for Boeing, Develop for Airbus Nash equilibria : (Boeing, Airbus) = (Not Develop, Develop) 'e. If there is no subsidy, Airbus never chooses develop strategy if Boeing develops. By the subsidy, Airbus always chooses develoP strategy regardless of Boeing’s strategy. Also, Europe never pays the subsidy, because the equilibrium is now Airbus develops and Boeing doesn’t. f. (Boeing, Airbus) = (Develop, Not Develop) Because Boeing moves first, Boeing gets 100, compared to the Nash equilibrium With its "not develop” strategy. .a. < Abe > ' < Betty > utility increase uIih'ty increase Clothing Clothing 20 b, c. d. 100 4—— Betty‘s food 0 B clothi . 5 Initial endowment 0A 100 Abe’s food 21 ...
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