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Compilation - Reyes PSET - Number 1 Setting up the profit...

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Number1 Settinguptheprofitfunctionforthefirm. ProfitisequaltoTotalRevenue - TotalCost Usingthegivenourprofitfunction is: = H 4350 - 13 * q L q - H q^2 - 5.5 * q + 150 L q H 4350 - 13q L q - q I 150 - 5.5q + q 2 M SolvingforFirstOrderCondition, Solve @ D @ , q D 0, q D Derivativeof withrespecttoqgivesus: 88 q fi - 40. < , 8 q fi 35. << Thevaluethatweconsiderwillbethepositivevalue, sincethereisnonegativequantity.Therefore, q = 35. Checkingforsecondordercondition: Solve @ D @ , q, q D 0, q D Secindderivativeof withrespecttoqgivesus: 88 q fi - 2.5 << Whichisanegativevalue, thereforewesatisfytheconditionformaximization. Solvingformaximumprofit, wepluginthevalueofqtotheprofitfunction. = H 4350 - 13 * 35 L 35 - H 35^2 - 5.5 * 35 + 150 L 35 94937.5 Wegetthemaximiumprofit, giventhemaximumvaluesofq. Number2 9.4 6 Settingupourproduction, revenue, costandprofitfucntions: In[122]:= Clear @ r, c D In[129]:= Q = L Out[129]= L In[130]:= R = P 0 * Q Out[130]= LP 0 In[131]:= Cost = W 0 * L + f Out[131]= f + LW 0 In[132]:= Profit = R - Cost Out[132]= - f + LP 0 - LW 0 SolvingforFOC, wegetthederivativeofprofitwrttoL:
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In[133]:= D @ Profit, L D Out[133]= P 0 - W 0 Themaximumprofitcanbederivedfrom subtarcting thepricewiththecostoflabor, whichiswage. H C L IfthesecondpartialoftheprofitfunctionwithrespecttoLisnegative, exhibitngdiminishing MPLthenwecanensurethatourprofitismaximized byourLabor. Number3 Givenourinversedemandfunctionandtotalcostfunction, wecanderivethemaximizingconditionforaMonopoly. TogetTRwemultiplythe inversedemandfuncionpbyq, givingus: TR = H Α - Β * Q L Q TC = Γ * Q + Δ + t * Q Q H Α - Q Β L Qt + Q Γ + Δ TosolveforthemaximiinglevelofQforthemonopolist, weequateMRto MC.EquatingtheMRofthemonopolytoitsMC, weget:
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