Question

Given the following price-demand function, find the elasticity of demand, E(p), and determine whether demand is elastic, inelastic, or has unit elasticity for the following values of p. (Round your answers to two decimal places.) x = 104,544 - 32p2 (a) p = 43 E(P) = Determine the demand. O elastic O inelastic O unit elasticity (b) p = 30 E(P) = Determine the demand. O elastic O inelastic O unit elasticity (c) p = 50 E() = Determine the demand. O elastic O inelastic O unit elasticity

Answer 1

Solution Given the demand function:- X = 104,544-32p2 - - we know that, elasticity of demand is - .0) In - 28 of hour inhere -hrs. ze Partial derivative of demand function with respect to Price P = given price a quantity associated with the given price (P). so ob = 0-2 (32)8 - – 64p [on partially differentiating + --6487 (a) p=43 X = 104,544 - 32(43)2 + x = 104, su4 - 59168 = 45376 So, (a = 45376] Now, E(P) = m = -64.P. 7 m = -64(43).(43) -- 118335 --2.608 45376 E(P) = -2.6081 Since, E(P)> , the demand is relatively elastic When 1243. The demand is elastic. I P=30 x = 104-544-32(30)2 = lousuu - 28800 = 75744 So, 1Q=75744 Now ELP)= =-64. P. P = - 64(30) (30) 75744 n=-57600 = -0.76 EP)--0.76 75744 121, the demand is relatively inelastic. ose, when P=30, the demand is inelastic. since, EPL1, the dena Therefore, w

② P=50 3 X = 104,544-32 (50)2 = 104544 – 80000 X = 24544 So, Q=24544 Now, HP) = m = -6400.f = -64150)(50) 24544 † ECP) =_160000 -6.519 16 (P) =-6-519 24544 since, E(P) > 1, the demand is relatively elastic. Therefore, when P=so, the demand is elastic.