Determine the producers' surplus if the market price is set at the equilibrium price. (Round your answer to the nearest dollar.)

Question

Producers' Surplus, The demand function for a certain brand of CD is given by

p = −0.01x² − 0.2x + 15

where p is the unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. The supply function is given by

p = 0.01x² + 0.8x + 3



where p is the unit price in dollars and x stands for the quantity that will be made available in the market by the supplier, measured in units of a thousand. Determine the producers' surplus if the market price is set at the equilibrium price. (Round your answer to the nearest dollar.)

Answer 1

−0.01x² − 0.2x + 15 = 0.01x² + 0.8x + 3; 0.02x² + x - 12 = 0; x² + 50x - 600 = 0; x = - 25 ± 35; x = 10 or

x = - 60. Equilibrium price p = - 1 - 2 + 15 = 12;

PS = ∫₀¹⁰(12 - .0.01x² - 0.8x - 3)dx = (9x - 0.01x³/3 - 0.4x²)₀¹⁰ = 90 - 10/3 - 40 = $47