Question

Consider the market for cheese curds in Madison. Assume the quantity (Q) is measured in pounds of cheese curds and the price (P) is measured in dollars per pound. Demand and supply in the market are given by following equations:

Demand: Qd = 300 - 50P Supply: Qs = 50P – 100

a) Draw a graph of the supply and demand curves in this market. Pay special attention to the y-intercept of the supply curve. Find the equilibrium price and quantity in the market and calculate consumer, producer and total surplus. Now suppose that the government decides to impose an excise tax of $1 per pound of cheese curds in order to control or limit the consumption of cheese curds.

b) Find the new equation for the supply of cheese curds with the imposition of this excise tax. What happens to the equilibrium quantity and price of cheese curds after the imposition of an excise tax? Calculate the value of consumer surplus, producer and total surplus in this market once this excise tax is implemented. How much tax revenue is generated when this excise tax is implemented? What is the amount of deadweight loss due to the excise tax?

Answer 1

We have Demand: Qd = 300 - 50P Supply: Qs = 50P – 100

a) Below is the graph of the supply and demand curves in this market. The equilibrium price and quantity in the market is 300 - 50P = 50P - 100

400 = 100P

P* = 4 and Q = 100 units.

Consumer surplus = 0.5*(max price - current price)*current quantity = 0.5*(6 - 4)*100 = 100, producer surplus = 0.5*(4 - 2)*100 = 100. Hence total surplus = 100 + 100 = 200

Now suppose that the government decides to impose an excise tax of $1 per pound of cheese curds i

b) The new equation for the supply of cheese curds is Q = 50(P + 1) - 100. The new equilibrium quantity and price of cheese curds after the imposition of an excise tax is

50P + 50 - 100 = 300 - 50P

100P = 350

P = 3.5 received by sellers

P + t = 3.5 +1 = 4.5 is the price paid by buyers.

Quantity = 300 - 50*4.5 = 75 units

New consumer surplus = 0.5*(6 - 4.5)*75 = 56.25, producer surplus = 0.5*(3.5 - 2)*75 = 56.25, total surplus in this market once this excise tax is implemented = 56.25 + 56.25 = 112.5. The tax revenue generated when this excise tax is implemented = tax size * quantity = 1*75 = $75 The deadweight loss due to the excise tax = 0.5*(1)*(100 - 75) = 12.5.