Public Economic

Homework 5 ECON4821 Public Economics

Spring 2015 Due: May 7, before the lecture

Problem 1 In class we mentioned three fundamental principles of tax incidence:

• The statutory burden of a tax does not describe who really bears the tax.

• The side of the market on which the tax is imposed is irrelevant to the distribution of tax burdens.

• Parties with inelastic supply or demand bear taxes; parties with elastic supply or demand avoid them.

We illustrated these in the case of perfectly competitive markets. This question investigates what happens in a monopolistic market. Suppose that a monopolist operates with a technology with cost function

C(q) = 5 + q2 (1)

and faces the downward sloping demand curve

p(q) = 20 − f(q) (2)

for some differentiable function f. Suppose the government is considering placing a per-unit tax of τ in this market. Does it matter whether this tax is imposed on consumers or the monopolist? That is, are the consumer and producer tax burdens different depending upon who is legally required to pay the tax?

Problem 2 Suppose that demand DW and supply SW in the market for widgets are given by

DW (p) := 12 − 2p SW (p) := 2p

and that demand DS and supply SS in the market for shmidgets are given by

DS(p) := 8 − p SS(p) := p.

Suppose that the government needs to raise $6 of revenue from taxes on either widgets or shmidgets or both. Answer the following questions.

1. What is the lowest tax τW one would have to impose on widgets to raise $6 of revenue in that market? What is the associated deadweight loss?

2. What is the lowest tax τS one would have to impose on shmidgets to raise $6 of revenue in that market? What is the associated deadweight loss?

3. Suppose a friend suggests that because demand for shmidgets is relatively inelastic compared with widgets, the government can minimise the deadweight loss by imposing no taxes on widgets and a tax of τS on shmidgets. Is this good advice?

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