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.