Find the consumer's and producer's surplus for an item with the following.

Question

Supply: p=5q^2 Demand= 4800-q^2/3. Professor said this had multiple steps. I know you set Supply=Demand to get equilibrium but how do you solve for X and then after how do you find the consumers and producers surplus? Thank you!

Answer 1

5q^2 = 4800 -(1/3)q^2 0 15q^2 = 14,400-q^2 or 16q^2= 14,400

take square root of both sides and get 4q=120 or q = 30 when q = 30 p=4500.

Total expenditure = 30* 4500 =135,000. (1)

The area under the demand curve is given by the integral evaluated fro 0 to 30

or 4800q - (q^3)/9 = 4800*30 - 27,000/9 = 144,000-3,000 =139,000 (2)

Consumer Surplus = (2)-(1) = 4000

The are under the supply curve is (5/3)q^3 evaluated from zero to 30.

or (5/3)*(30^3) =45,000 (3)

Producer Surplus = (1)-(3) = 90,000

Answer 2

Samantha,

Is that q^2/3 or q²/3?

Carol

Answer 3

supply = demand when q = 30 but beyond that it seems information is missing to answer your question