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

Question

p = 148 - x^2

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

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.)

consumers surplus $

producers surplus $

Answer 1

set the 2 equations equal and solve for x. x=8

plug that into either equation to solve for p. p=84

1st equation is the demand function. subtract 84 from it and find the integral. evaluate the integral at x=8. That's consumer surplus about 341

2nd equation is the supply curve. 84 minus that equation. Take the integral. evaluate at x=8. That's producer surplus, the area below p=84 and above the supply curve. about 119.