Question

The demand for milk and supply of milk in the U.S: QD = 152 – 20 P , Qs = - 4 + 188 P

Q: measured in billions of gallons per year P is measured in dollars per gallons.

1) Calculate the competitive market equilibrium price and quantity and total surplus at that price. Illustrate your answer.

2) If price floor Pf = $1.25, how much do the government pay to buy the excess supply?

Answer 1

1) Let's calculate the competitive market equilibrium price and quantity:

$$Q_D=Q_S,$$ $$152-20P_E=-4+188P_E,$$ $$156=208P_E,$$ $$P_E=\$0.75,$$ $$Q_E=152-20\times0.75=137\ billion\ gallons.$$

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:

$$Q_D=152-20P=0,$$ $$P=\$7.6.$$

Then, we get:

$$CS=\dfrac{1}{2}\times137\times(\$7.6-\$0.75)=\$469.23.$$

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:

$$Q_S=-4+188P=0,$$ $$P=\$0.021.$$

Then, we get:

$$PS=\dfrac{1}{2}\times137\times(\$0.75-\$0.021)=\$49.94.$$

Finally, we can find the total surplus:

$$TS=CS+PS=\$469.23+\$49.94=\$519.17.$$

2) Let's first find the quantity of milk demanded at the price of $1.25:

$$Q_D=152-20\times\$1.25=127.$$

Then, we can find the quantity of milk supplied at the price of $1.25:

$$Q_S=-4+188\times\$1.25=231.$$

Finally, we can find the excess quantity that the government must buy:

$$Q_{Excess}=Q_S-Q_D=231-127=104.$$

The government must pay:

$$P=P_f\times Q_{Excess}=\$1.25\times104=\$130.$$