Question

In: Economics

1.         The market for ice cream is a perfectly competitive market and has the following inverse...

1.         The market for ice cream is a perfectly competitive market and has the following inverse demand curve and inverse supply curve, where p is $ per gallon and Q is billions of gallons of ice cream per year: Demand: p = 16 – 5Q; Supply: p = 4 + 2.5Q

a.         Provide a graph of the market for ice cream. Calculate and show the equilibrium price and quantity (in billions of gallons) in the market.

b.         Calculate the consumer surplus and producer surplus in the market (all of your answers should be in billions of dollars and rounded to the nearest hundredths for b, c and d).

c.         The government believes people are eating too much ice cream so they place a tax of $0.60 per gallon paid by sellers of ice cream to the government. Calculate the new equilibrium price and quantity sold in this market and show the effects on the graph in part a.

d.         As a result of the tax, calculate and explain the change in consumer surplus, the change in producer surplus, the tax revenue and the deadweight loss from the tax.

Solutions

Expert Solution

1. Demand: p = 16 – 5Q; Supply: p = 4 + 2.5Q

a. Graph is shown below

At equilibrium

16 - 5Q = 4 + 2.5Q

12 = 7.5Q

Q = 1.6 billion gallons

P = 16 - 5*1.6

= $8 per gallon

b) CS = 0.5*(max price - price paid)*qty = 0.5*(16 - 8)*1.6 = $6.4 billion

PS = 0.5*(price received - minimum price)*qty = 0.5*(8 - 4)*1.6 = $3.2 billion

c.         There is a tax of $0.60 per gallon paid by sellers of ice cream to the government.

After the tax the new supply is P = 4 + 2.5Q + 0.6 or P = 4.6 + 2.5Q

16 - 5Q = 4.6 + 2.5Q

11.4 = 7.5Q

Q = 1.52 billion gallons

P = $8.4 per gallon

Supply curve is shifted to the left in the diagram

d. change in CS = 0.5*(16 - 8.4)*1.52 - 6.4 = -$0.624 billion

change in PS = 0.5*(7.8 - 4)*1.52 - 3.2 = -$0.312 billion

Revenue for government = 0.6*1.52 = $0.912 billion

DWL = 0.5*0.6*(1.6-1.52) = $0.024 billion


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