Question

Suppose that, in the market for soft drinks (in litres),

     demand is given by P = 20 – 0.3Q; and

     supply is given by P = 0.1Q.

In order to raise revenue, the government decides to impose a $0.5 per litre tax on soft drinks. Use these facts to answer the following questions.

    A) On a graph, demonstrate the effect of the tax on the equilibrium price and quantity. (Clearly label the value of each both before and after the tax.)

    B) Show on the graph and calculate the tax revenue and deadweight loss that result from the tax. Briefly explain why a per-unit tax results in a deadweight loss.

    C) Graphically show the incidence of the tax i.e. the consumers and producers burden of the tax.

        i)Who bears the greater burden of the tax, producers or consumers? Explain why this is the case.

        ii)If the elasticity of supply increased, what do you expect to happen to the incidence of the tax? Explain.

    D) Apart from a per-unit tax, what is another measure that the government could impose to reduce the quantity of soft drink consumed? Evaluate whether this is better than a per-unit tax. Is there a measure which will not result in a deadweight loss?

    E) Given that a per unit tax creates deadweight loss and is not Pareto efficient, identify a Pareto improving transaction to eliminate this deadweight loss.

Answer 1

A)

Tax is the financial charge that the government levies on the taxpayers to finance various public expenditures. It is one major source of income to the government. A tax drives a wedge between the market price and the price sellers receive and creates a deadweight loss to the society. The deadweight loss is called the excess burden of tax. A tax is efficient if it raises enough revenue to outweigh the excess burden it imposes on the society.

The consumer surplus is the difference between market price and the price the consumer wants to pay. The price the consumer wants to pay for any particular unit is determined through the demand curve. The difference between the price the consumer wants to pay and the equilibrium price is given by the area enclosed by the demand curve and equilibrium price line up to equilibrium quantity.

The producers’ surplus is the difference between market price and the price the producer wants to receive. The price the producer wants to receive for any particular unit is determined through the supply curve. The difference between the price the producer wants to receive and the equilibrium price is given by the area enclosed by the supply curve and equilibrium price line up to equilibrium quantity.

The figure below gives the market for any good with after and before tax:

The demand curve D gives the marginal benefit received by the consumer and the supply curve S gives the marginal cost of the producer. At equilibrium the consumer surplus is given by the area A+B+C+D. The producers’ surplus is given by the area E+F+G+H+I. The government imposes a tax that increases the market price of each unit by the amount of tax. The supply curve shifts upward to S₂ by the amount of tax. At new equilibrium, the price rises to P₂ and quantity decreases to Q₂.

At new equilibrium, the consumer surplus reduces to area A. The producers’ receives the price P_s. Then the producers’ surplus is given by the area H+I. The tax is (P₂-P_s) for the quantity sold Q₂. The total tax revenue is given by the area B+C+E+F. After the tax the producers’ and consumer surplus decreased. The area D+G represents loss to the society and called the excess burden of the tax.

At new equilibrium, the consumer surplus reduces to area A. The producers’ receives the price P_s. Then the producers’ surplus is given by the area H+I. The tax is (P₂-P_s) for the quantity sold Q₂. The total tax revenue is given by the area B+C+E+F.

A tax is efficient if the deadweight loss created by the tax is less than the revenue it collects. Here the total revenue from the tax is B+C+E+F. The deadweight loss from the tax is D+G.

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B)

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C)