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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. 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.
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.