Question

The demand function P=40-2q² and the supply function P=24+4q. Find the consumer surplus.

A. 11
B. 10
C. 12
D. 9

Answer 1

The consumer surplus can be found by calculating the area between the demand and supply curves up to the equilibrium quantity. In this case, the consumer surplus is 8.

Step-by-step explanation:

The consumer surplus can be found by calculating the area between the demand and supply curves up to the equilibrium quantity.

1. Set the demand and supply functions equal to each other: 40-2q² = 24+4q
2. Rearrange the equation to one side: 0 = 2q² + 4q -16
3. Factor the quadratic equation: 2(q-2)(q+4) = 0
4. Solve for q: q = 2 or q = -4 (ignore the negative value)
5. Substitute the value of q into either demand or supply function to find the equilibrium price: P = 40 - 2(2)² = 40-8 = 32
6. Calculate the consumer surplus by finding the area between the demand curve and the equilibrium price up to the quantity demanded: Consumer Surplus = 0.5(32-24)(2) = 8

Therefore, the consumer surplus is 8.