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Problem 1 of MIDTERM Page 268 #15

Problem 1 of MIDTERM Page 268 #15. Group 6 Ritchie Roi Chua Ramon Jose Miguel Naguiat Mary Jane L. Paglumotan Mark Anthony Salazar  Charlotte Tang Tong Ya(Nicole). Problem 1 (Page 268 #15).

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Problem 1 of MIDTERM Page 268 #15

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  1. Problem 1 of MIDTERMPage 268 #15 Group 6 Ritchie Roi Chua Ramon Jose Miguel Naguiat Mary Jane L. Paglumotan Mark Anthony Salazar  Charlotte Tang Tong Ya(Nicole)

  2. Problem 1 (Page 268 #15) • Given are the pairs of demand and cost functions for different commodities on which the specified amount of the unit tax is to be imposed. At the level of maximum profit to the monopolist, determine: • The volume of sales • The unit prices with tax and without tax • The amount of tax revenue • The amount of maximum profit obtainable p=(15-X)2 ,0 < X < 15, AC=X2 – 10X + 65, tu = 10

  3. Solution • The volume of sales that will maximize profit [Without Tax] po=(15-Xo)2 & ACo=Xo – 10Xo + 65 TRo=pXo =(15-Xo)2Xo =(225-30Xo+Xo ) Xo TRo=225Xo-30Xo+Xo 2 2 2 3

  4. 2 2 3 Solution ACo=TC/Xo TCo=ACo(Xo) =(Xo -10Xo + 65) (Xo) TCo= Xo -10Xo + 65Xo Where TRO is the total revenue function (w/o tax) & TCO is the total cost function (w/o tax). Therefore, the profit function, PO will be: PO=TRO-TCO =(225XO-30XO+XO)-(XO-10XO+65XO) =(225XO-30XO+10XO-65XO) PO =-20XO+160XO 2 3 3 2 2 2 2

  5. Solution To get the critical points: Po=-20Xo+ 160Xo Po=-40Xo+ 160 Po=0 0=-40Xo+ 160 Xo=4 To check whether Xo=4 is a max or min point: Po = - 40 Therefore Po is a maximumatXo=4, which means that the sales volume that will maximize profit is 4 units if no tax is imposed. 2 , “

  6. Solution WITH TAX IMPOSED: pu=(15-Xu)2 tu=10 TRu=225Xu - 30Xu + Xu TCu=Xu – 10Xu + 65Xu+ 10Xu TCu=Xu – 10Xu + 75Xu 2 3 3 2 3 2

  7. Solution 2 2 Pu =TRu-TCu =(225Xu-30Xu+10Xu-75Xu) Pu=-20Xu+150Xu To get the critical points PU =-20XU + 150XU PU =-40XU + 150 PU =0 0 = -40XU + 150 XU =3.75 To check whether XU =3.75 is a max or min point: PU = - 40 Therefore PU is a maximumatXU =3.75, which means that the sales volume that will maximize profit is 3.75 units if tax is Imposed. 2 2 , ,,

  8. Solution Conclusion (A): Without tax, the volume of sales should be 4 units to obtain a maximum profit. With tax, the volume of sales should be 3.75 units to obtain a maximum profit.

  9. Solution • UNIT PRICE Without TaxWith Tax po=(15-x)2 pU=(15-x)2 =(15-4)2 =(15-3.75)2 po =121 pU =126.56 Conclusion: The unit price with tax is Php 126.56 while the unit price without tax is Php 121.00

  10. Solution C. AMOUNT OF TAX REVENUE: Let TU be the amount of tax revenue. TU=tUXU=10(3.75)=37.50 Conclusion: Amount of tax revenue is Php37.50

  11. Solution D. MAX PROFIT OBTAINABLE With Tax: PU= -20XU+150XU = -20(3.75)2 + 150(3.75) = 281.25 WithoutTax: Po= -20Xo+150Xo = -20(4)2 + 150(4) = 320 Conclusion: The maximum profit obtainable is Php281.25, if tax was imposed. While max profit will be Php320.00 if no tax was imposed 2 2

  12. ACu= Xu2-10Xu+75Xu Graph P=(15-X)2 ACo= Xo2-10Xo+65Xo TCu= Xu3-10Xu2+75Xu TCo= Xo3-10Xo2+65Xo *All terms with subscript U are WITH TAX, while those with subscript O are WITHOU TAX TR= 225X-30X2+X3

  13. Web Links http://www.fred.ifas.ufl.edu/courses/AEB3510/2000/notes/ch10/ http://www.chass.utoronto.ca/~osborne/2x3/tutorial/MON.HTM http://www.fordham.edu/economics/alexander/ecga5710/Maple3.htm

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