Determine the consumers' surplus and the producers' surplus when the market unit price is set at the equilibrium price. (Round your answers to the nearest dollar.)

Question

Consumers' and Producers' Surplus

 The management of the Titan Tire Company has determined that the quantity demanded x of their Super Titan tires/week is related to the unit price p by the relation

p = 140 − x²

where p is measured in dollars and x is measured in units of a thousand. Titan will make x units of the tires available in the market if the unit price is

p=44+1/2x^2

Answer 1

140-x^2 = 44 + x^2/2

(3/2)x^2 =96

x^2 = (2/3)96 =2(32) = 64

x = sqr64 = 8

p = 140=64 = $76

CS = integral of 140-76 - x^2 = 64 -x^2: 64x -(1/3)x^3 evaluated at 8 = 64(8) =512-64(8)/3 = (2/3)512 = 1024/3 = $341

PS= integral of 76-44 -x^2/2 = -(1/6)x^3 +32x evaluated at 8: 256 - 512/6 = 256 -85= $171

total surplus (CS+PS) = integral of 140-x^2 -(44+x^2/2)

= integral of 96 - 3x^/2 = 96x -x^3/2 evaluated at 8: 96(8)-(512)/2 = 768-256 =512

=341+172