math equilibrium

Question

The demand and supply functions for a particular commodity are D(x)=(x-3)^2 and s(x)=x^2+x-5, where x is the number of units of the product, D(x)is the price that results in consumer demand of x units and s(x) is the price that results in a producer supply of x units.

The value of x at equilibrium is ( ) units

The value of P at equilibrium is ( )

show the integral with limits, to find the consumer's surplus at equilibrium. Do not solve

show the integral with limits, to find the producer's surplus at equilibrium. Do not solve

Answer 1

D(x) = s(x); (x - 3)² = x² + x - 5; x² - 6x + 9 = x² + x - 5; 7x = 14; x = 2 units for equilibrium price.>Price D(2) = s(2) = 1.

CS = ∫₀²[(x - 3)² - 1]dx = [(x - 3)³/3 - x]₀² = (- 1/3 - 2) + 9 = 20/3

PS = ∫₀²(1 - x² - x + 5)dx = (6x - x³/3 - x²/2)₀² = 12 - 8/3 - 2 = 22/3