Question

The demand function for a Christmas music CD is given by

q=D(p)=0.25(225−p2)

where qq (measured in units of a hundred) is the quantity demanded per week and pp is the unit price in dollars.

(a) Find the elasticity function E(p)=  

(b) Evaluate the elasticity at 10. E(10)=  

(c) Should the unit price be lowered slightly from 10 in order to increase revenue?   ?    yes    no   

(d) Use the elasticity of demand to find the price which maximizes revenue for this product. p= dollars

Round your answer to two decimal places as needed.

Answer 1

Griuen a= 0.25(225-p bierenhiati eauation C uor.t get 0-0.25x2 P day -0.SP Formulas for elasficity is ELPI- da dp Supshitute the Valu dp Neelgagan

Date Jomala for elatkeity gel, ELP) -O.5 x P =0Spx P (56-25-0.25p2) ECP) -(-0.5) x p2 (56-25-0-25p2) (10) (56-25-0-25x10o) ( ELIO) 0.Sx 81.25 1.6

ECIO)-16 maams tuat a 1 decreaue in price belous 10 iu imureaue the'auanhty domanded 6% Thare will be tuo elacts Fixatly Sezandly on 9reuanue reuenu uu dareaue dueo decraae in pniu ancl 9leuenue Luiu inureae due to inuuae in Quanhty demandeal In this case 9reuenue due to fall in pnce uill be les tham the incruau m 9auenue due to inoreaue in Quanhty olemandeol as implied bg the elasticity Elb):-1-6 Hence the oueaall ellact wuy be tnoreau in euine So, thu anir is Yes deraeare in ie (d) we Rnous, TR P.au ox du condihon for Figust greuenue manimtsahom e oim gespeit to pnu is

No. Date d(TR) dp う 4 + P.das dp ニ0 Pda 1 + ECP)0 tu valua o E (P) from Subshitute part we I (-0.5)x P 56-25-0-25p) 2 1 = (56.25-0-25p2) 05 p2 0-75pと-56.25 56-25-0.25p Necles

Date 56.25 75 +53 うP: 1 Sinu bria cannot be migabu, tas means Pz 53 s the greuenu triu maximising 8.66