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pg77 - Managerial Economics(MG608 Assignment#2 Victor Smith...

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(MG608) nment #2 tor Smith 2/10/2003 Problems (see Appendix for Graphs) p77 #2) Solve the following demand equations for TR(max). Provide TR equation with P(max) and Q(max) (max) = max. revenues Demand 1 Demand 2 Demand 3 Demand Equation Q = 450 - 16P Q = 360 - 80P Q = 1500 - 500P Q - 450 = -16P Q - 360 = -80P Q - 1500 = -500P Step1: Solve for P -1/16(Q) + 28.125 = P -1/80(Q) + 4.5 = P -1/500(Q) + 3 = P Step2: Solve for TR TR = Q * P TR = Q * P TR = Q * P TR = Q * (-1/16(Q) + 28.125) TR = Q * (-1/80(Q) + 4.5) TR = Q * (-1/500(Q) + 3) Step 3: Take 1st Deriv. Of TR dTR/dQ = 28.125 - 1/8(Q) dTR/dQ = 4.5 - 1/40(Q) dTR/dQ = 3 - 1/250(Q) Step4: Find Max Rev. Set dTR = 0, solve for Q(max) dTR/dQ = 0 = 28.125 -1/8(Q) dTR/dQ = 0 = 4.5 -1/40(Q) dTR/dQ = 0 = 3 -1/250(Q) 1/8(Q) = 28.125 1/40(Q) = 4.5 1/250(Q) = 3 Graph the Demand and TR Curves Demand Q P Q P Q P 450 0 360 0 1500 0 225 14.06 180 2.25 750 1.5 0 28.13 0 4.5 0 3 TR Curve Q TR Q TR Q TR 0 0 0 0 0 0 113 2380.06 90 303.75 113 287.92 225 3164.06 180 405 225 472.5 337 2380.06 270 303.75 337 556.72 450 0 360 0 450 540 (see Appendix for Graphs) p77 #2) Find AC, AVC and MC equations and curves for the folloing TC equations TC 1 TC 2 TC 3 TC Equation Q = 1500 + 300Q AC Equation AC = TC / Q AC = TC / Q AC = TC / Q Step1: Solve for AC AC = 1/Q(1500) + 300 + 25Q AC = 1/Q(1500) + 300 Step2: Solve for AVC AVC = 300 + 25Q AVC = 300 Step3: Solve for MC MC = dTC / dQ
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