Answer to Question #273281 in Microeconomics for jane

Question #273281

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?


1
Expert's answer
2021-12-02T10:37:30-0500

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."

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