Question

The estimated monthly sales of Mona Lisa paint-by-number sets is given by the formula q = 103e-3p+P, where is the demand in monthly sales and p is the retail price in yen. (a) Determine the price elasticity of demand E when the retail price is set at ¥2. E = Interpret your answer. The demand is going ? by % per 1% increase in price at that price level. Thus, a large price ? is advised. (b) At what price will revenue be a maximum? (c) Approximately how many paint-by-number sets will be sold per month at the price in part (b)? (Round your answer to the nearest integer.) paint-by-number sets per month

Answer 1

-3Р+P q = loze Taking natural log (In) both side In q = ln (103 & SP+P) - 3 pt P ine in q = in (103)+ ating = In (103) + (-3p²+ P) ding = - 3(2) Pt de dina = -6. Pt1 de ding - dina – ding & P elasticity (E)= ding de = de P E = {6P+1)* P E = -6p tp Eat P = 72 E= -6 (2) + P = -24 +02 E = -22

E= - 22. The demand is going to decrease by 822 % Per 1% increase in Price at that Price Level. Thues o Large Price elasticity is advised - Please check it in your options Available (6 for revencie maximum Price MR = Poq MR = Po (103 e 3P+P) AMR =P (103 e 3P+P (-6 Pt 1)) + 103e3171) = 0 de - 3p P = 103 e oth [-6 Prp to] =0 - - 6P² + P + 1 = 0 - 6P²P-1 = 0 - 6p² - 3p +2 P-1=0 -) P (2P-1) + 1(21-1) =0 (3P+ 1) (2 P-1) =0

I (3PH) (21-1)=0 - 21-1=0 or 3P+1 = 0 & P = 11 p = -1 (not possible] So at P = 0.57 Revenue will be maximized 3 (C) at P = 0.57 Rencueue is maxi at at 1-0.57 q= to 103 € 3për 9 (P=0.5) = 103 23 (0.53+0.5 -3 (0.25) + 0.5 loze - 10827 - 0.75 tog - - 0.25 = 103e q (P=0.5) = 103 = 103 = 80.21648 @ 0.25 1. 2840 25 Approximately 2=80
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