Answer to Question #256172 in Microeconomics for ad7

Question

4. The supply and demand for broccoli are described by the following equations: Supply: QS = 4P – 80 Demand: QD = 100 – 2P Q is in tonnes, and P is in dollars per bushel. /6 a. What is the equilibrium price and quantity? b. Calculate consumer surplus, producer surplus, and total surplus at the equilibrium. c. If a dictator who hated broccoli were to ban the vegetable, who would bear the larger burden—the buyers or sellers of broccoli?

Answer 1

(a) We can find the equilibrium price and quantity as follows:

$Q_D=Q_S,$ $100-2P_E=4P_E-80,$ $6P_E=180,$ $P_E=\$30,$ $Q_E=100-2\times\$30=40.$

(b) Let's first find the consumer surplus. By the definition of the consumer surplus, we have:

$CS=\dfrac{1}{2}\times Q_E\times(Max\ Price\ Willing\ to\ Pay-P_E).$

Let's find the maximum price the consumer is willing to pay:

$Q_D=100-2P=0,$ $P=\$50.$

Then, we get:

$CS=\dfrac{1}{2}\times40\times(\$50-\$30)=\$400.$

Let's find the producer surplus. By the definition of the producer surplus, we have:

$PS=\dfrac{1}{2}\times Q_E\times(P_E-Minimum\ Price\ to\ Sell).$

Let's find the the minimum price at which the seller is willing or able to sell:

$Q_S=4P-80=0,$ $P=\$20.$

Then, we get:

$PS=\dfrac{1}{2}\times40\times(\$30-\$20)=\$200.$

Finally, we can find the total surplus:

$TS=CS+PS=\$400+\$200=\$600.$

(c) If dictator will ban the broccoli, the buyers of broccoli will bear the larger burden.