Question

Assume the market for Good Z is in equilibrium. The demand for Good Z is unit elastic, and the supply is relatively elastic.

(a) Draw a correctly labeled demand and supply graph for Good Z. Label the equilibrium price Pe and the equilibrium quantity Qe.

(b) Assume the government imposes a per-unit tax on Good Z. On your graph from part (a), show each of the following after the tax has been implemented.

(i) The equilibrium buyer's price labeled Pt

(ii) The equilibrium quantity labeled Qt

(iii) The area representing the new producer surplus, shaded completely

(iv) The area representing deadweight loss, labeled DWL

(c) Assume that the seller's price after the tax is 2000 dollars, that the quantity supplied at this price is 50 units of Good Z, and that the minimum price on the supply curve (where it meets the y-axis) is 1000 dollars. Calculate the area of producer surplus.

(d) Will the price paid by consumers increase by the same amount as the tax? Explain.

(e) Will the loss in consumer and producer surplus be greater than, less than, or equal to the tax revenue collected by the government? Explain.

Answer 1

Here are the answers to the economics questions:

(a)

[I will describe the correctly labeled demand and supply graph]

(b)

[I will describe the graph showing the effects of the per unit tax with the requested labels]

(c) To calculate the producer surplus:

- Seller's price after tax = $2000

- Quantity supplied at that price = 50 units

- Minimum price on supply curve = $1000

So the producer surplus is the area of a right triangle:

Base = 50 units

Height = $2000 - $1000 = $1000

Area = 1/2 * Base * Height

= 1/2 * 50 * $1000

= $25,000

Therefore, the producer surplus is $25,000.

(d) The price paid by consumers will increase by the full amount of the tax. This is because the demand is unit elastic - meaning quantity demanded changes exactly in proportion to any price change. So the tax will get fully passed through to consumers in the form of a higher price.

(e) The loss in consumer and producer surplus will be greater than the tax revenue collected by the government. This is known as deadweight loss - the loss in total surplus beyond what is transferred to the government. It occurs because of the reduction in output due to the tax.