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Homework answers / question archive / Suppose the demand curve is: P = 300 - 2QDD and the supply curve is: P = 100 + 3QSS

Suppose the demand curve is: P = 300 - 2QDD and the supply curve is: P = 100 + 3QSS

Economics

Suppose the demand curve is: P = 300 - 2QDD and the supply curve is: P = 100 + 3QSS. What is the sum of the consumer and producer surplus in the market at the equilibrium price and quantity?

A. $3200

B. $1600

C. $2400

D. $4000

E. Cannot be determined from the information given.

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  • The correct option is D. $4000.

The maximum willing price is determined when Qd = 0. That is P = 300. Also, the minimum willing price is determined when Qs = 0. That is P = 100. Also, the equilibrium is determined at a level where Qd = Qs.

300-2Q = 100+3Q

By solving this we get Q = 40 units. Now substitute the value of Q in the demand equation. That is

P = 300 - 2(40)

P = $220

We know that

Consumer Surplus = 1/2 * (Maximum willingness to pay - Market price) * Quantity

Consumer Surplus = 1/2 * (300-220) * 40

Consumer Surplus = $1600

Producer Surplus = 1/2 * (Market Price - Minimum Willingness to pay) * Quantity

Producer Surplus = 1/2 * (220-100) * 40

Producer Surplus = $2400

Thus, the sum of consumer and producer surplus is $4000.

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