Question

Consider a market characterized by the following inverse demand and supply functions: P X = 10 - 2Q X and P X = 2 + 2Q X. Compute the surplus received by consumers and producers.

Answer 1

Answer:

Consumers surplus = $4

Producers surplus = $4

Explanation:

Quantity demanded = Quantity supplied (when there is equilibrium).

Given:

Demand function: PX = 10 -2Q

Supply function: PX = 2 + 2Q

We first solve the equation:

10 - 2Q = 2 + 2Q

Bringing like terms, we have:

2Q + 2Q = 10 -2

4Q = 8

Q = 2

Substituting 2 for Q in the demand function, we have:

P = 10 - (2 x 2) =

= 10 - 4 = 6

(When Q=2, P will be 6)

Therefore, from the demand function, when Q = 0, P = 10

Therefore, consumer's surplus will be:

CS = (1/2) x ($10 - $6) x 2 =

=(1/2) x 4 x 2 = $4

From supply function, When Q = 0, P = 2 (Minimum acceptable price)

Therefore, producer's surplus will be:

PS = (1/2) x ($6 - $2) x 2

= (1/2) x 4 x 2 = $4