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

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 = 148 − 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=52+1/2x^2 dollars

Answer 1

148 - x² = 52 + x²/2; 3x²/2 = 96; x² = 64; x = 8. Equilibrium price p = 148 - 64 = $84 per hundred units.

CS = ∫₀⁸(148 - x² - 84)dx = (64x - x³/3)₀⁸ = $341.33

PS = ∫₀⁸(84 - 52 - x²/2)dx = (32x - x³/6)₀⁸ = $170.67