PracticeProblems-2_Solutions - Practice Problems 2...

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Practice Problems 2 Solutions :: 8.10 fl.otten Kid Theorem In the second stage, the parent chooses I to maximize U 2(Y2(r) - L) + aU 1(\(r) + L) yielding first-order condition -U2(2Q)- L)+aui(1(r) +I) = s. Even though the preceding equation cannot be solved explicitly for t 1r7, we can still use the implicit function rule to find the derivative df =uLYi?)-auiYie) dr -Ui +uU{ In the first state, the child maximizes f\Yt1r; - fJ 1r;, yielding hrst-order condition uilri<,>.41 I d') :( --!i --=)f",'frX-u i + aufi +uiy2e)- auffie)l l-u; + aui )' :( -!-iu5 -.=)triu, +Y2e)l l-ul + aui )' -0. This equation implies YiQ)+Yz(r) = 0, the first-order condition for maximizing their joint incomes.
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15.1 a. Themonopolistmaximizesprofit QQ50-Q) yieldingfirst-ordercondition 150-2Q:0 andmonopolyoutcome Pm =Q*:75 andflm =5,625. b. Cournot firm I maximizes profit q1(150 - {tt - q2) yielding first-order condition 150 - 2qt - qz :0 and best-response function Qt :75 - q2 l2 . Symmetrically, firm 2's best-response function
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  • Winter '08
  • Buddin
  • Trigraph, implicit function rule, best-response function, first-order condition, t- \xv, best-response function Qt

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PracticeProblems-2_Solutions - Practice Problems 2...

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