Question

3. The market supply and demand for a product are shown in the diagram below. O PRICE $6 Supply Demand 080 200 QUANTITY (a) Is the price elasticity of supply less than one, equal to one, or greater than one? Explain. (b) Calculate consumer surplus at the equilibrium price. Show your work. (C) Now suppose the government imposes a per-unit tax of $1 on producers. (i) What happens to total revenue received by producers after they pay the tax to the government? Explain. (ii) Will producer surplus increase, decrease, or stay the same? (iii) Will total surplus increase, decrease, or stay the same? Explain.

Answer 1

a) The given supply curve is a horizontal line and hence, the supply curve is perfectly elastic in nature. Any change in the price of the good, the quantity supplied would become zero.

The elasticity of the given supply curve is infinite (greater than 1).

b) Consumer surplus is the difference between the consumers' willingness to pay and the price actually paid.

Graphically, it is the area below the demand curve but above the price line. In the given graph, the supply curve denotes the price line. Therefore, the consumer surplus is denoted by the triangle as shown in the below graph.

O PRICE $6 Supply Demand 200 QUANTITY

Consumer Surplus = 0.5 * base * height = 0.5 * 80 * ($10 - $6) = 0.5 * 80 * $4 = $160

Producer Surplus = 0 (As the supply curve is same as the price line)

Total Surplus = Consumer Surplus + Producer Surplus = $160 + $0 = $160

c) Tax = $1

Supply curve shifts above by $1 i.e., P = $6 + $1 = $7

E PRICE Supply with tax - Supply Demand 200 QUANTITY 60 80

i) Before the imposition of tax:

Total Revenue = Price * Quantity = $6 * 80 = $480

After the imposition of tax and after paying tax revenue to the government:

Total Revenue after the tax payment = Price with tax * Quantity with tax - Tax * Quantity with tax = $7 * 60 - $1 * 60 = $420 - $60 = $360

Therefore, the total revenue of the firm has decreased with the imposition of tax.

ii) Producer surplus after the tax = 0 (The supply curve is still the same as the price line)

Therefore, the producer surplus stays the same

iii) Consumer surplus = Area of the triangle shown in the above graph = 0.5 * base * height = 0.5 * 60 * ($10 - $7) = 0.5 * 60 * $3 = $90

Total surplus = Consumer surplus + Producer surplus = $90 + $0 = $90

The total surplus has decreased.