1    Review questions

Indicate whether each statement is true, false, or uncertain, and give a brief explanation.

1. The empirical evidence is that automatic contributions and government subsidies are equally good at increasing wealth at retirement.

2. If the government introduces a carbon trading scheme, it does not matter at all how permits are initially allocated.

3. The free rider problem yields zero private provision of public goods.

4. It is rational for someone to want the government to tax everyone in order to fund a public good and then for that person to try to avoid paying the tax herself.

2    Problems

2.1    Public Goods

Two neighboring suburbs–Camperdown A and Camperdown B–are in discussions to de- velop a joint fire department to provide fire protection services for both suburbs. The two suburbs (i = A,B) have identical preferences, given by:

ui (xi ,F) = ln(xi ) + 3ln(F)

where xi  is private consumption of suburb i (i.e., consumption of goods other than the public good) and F  is the sum of all contributions to the new fire department  (i.e., F = A + B).  Assume that px  = pF   = 1.  Finally, assume that Camperdown A has a budget of $100 and Camperdown B has a budget of $50.

(a) What are the characteristics of a pure public good?  Do fire departments and fire

protection services fit these characteristics? Explain why or why not.

For the rest of the problem, assume that the fire department is a pure public good.

(b) Write down the budget constraint and determine the private equilibrium level of contributions for each city, FA  and FB .

(c) Show that total fire services Fprivate  are equal to 60% of the total budget.

(d) Derive the socially optimal contribution to the fire department Fso(*)cial  and express it as a percentage of the total budget. Why is this percentage higher than in part (c)?

The leaders of the two suburbs, Joe and Zach, are aware of the difference in private equilibrium contributions versus the social optimum level of fire protection for the two suburbs.  They propose a block grant of $30 that is to be distributed proportionally to the suburbs’existing budgets (i.e., $20 to Camperdown A and $10 to Camperdown B).

(e) Derive the new levels of private contributions FA  and FB  in equilibrium after the block grant has been distributed.

(f) Does the block grant help achieve socially-optimal level of fire services spending

under the free market allocation? Why or why not?

Joe and Zach decide to forego the block grant and try a different scheme. They approach a prominent economist at the University of Sydney and ask them to design a matching grant that would achieve the socially-optimal level of fire services.

(g) Derive the private equilibrium level of contributions for each city, FA  and FB  when the matching grant at rate g is in place. Your answer will be a function of g . [Hint: The matching grant changes the budget constraint so that if FA  = $1, the cost to Camperdown A is $(1/1+g) .]

(h) Derive the matching grant rate g that can deliver the social optimal level of fire services.

2.2    Income Taxation

This problem is intended to be a short refresher on income taxation.

Bob starts a new job as a cashier at Judy’s Juice Jamboree, which is located in the small fictional country of Waupaca.  The job is unusually flexible:  Bob can pick to work any number of hours between 0 and 4,000 in a given year at a wage rate of $50 per hour. His utility is given by:

200l2

2

Bob faces the following progressive income tax schedule:

Bracket 1: 0 W income < $100, 000 ⇒ MTR = 0

Bracket 2: $100, 000 W income ⇒ MTR = 15%

(a) Solve for Bob’s optimal choice of consumption and labor supply without the pro- gressive income tax.

(b) Solve for Bob’s optimal choice of consumption and labor supply with the progressive income tax. [Hint:  optimize on each portion of the budget constraint separately, as if that budget constraint applied everywhere.]

(c) What is the impact of the progressive income tax on Bob’s optimal choice of labor supply?