PUBLIC ECONOMICS – Solutions to Old Exam Questions

November 24, 2015

Please fill in your full name and student number in the spaces below.

NAME:__Robert McMillan___

STUDENT NUMBER:__________________________

You have 1 hour and 40 minutes to complete this closed-book test. When the invigilator asks everyone to stop, you must stop writing. Students who continue writing will not have their exams graded. This should be entirely your own work – no conferring please.

The test is worth X points. Please attempt all the questions, and be sure to read each question carefully. The number of points each question is worth is indicated in brackets.

You should answer the test directly on this booklet, in the spaces provided. Please write legibly, and answer in proper sentences. If you need additional space, indicate clearly which question you are answering, and write on the reverse side of the page. [Approximate guidelines as to the length of the perfect answer are given in square brackets where necessary.]

Question 1 (worth 2 points)

a) In what sense is the concept of Pareto efficiency incomplete as a welfare notion? (2 points)

Pareto efficiency is incomplete as a welfare notion in that it has nothing to say about equity. Two allocations can be Pareto-efficient, but one involves giving everything to one person while the other involves dividing the available good up evenly among everyone.

Question 2 (worth 14 points)

a) The government sells an indexed bond with a face value of $100 to an investor at the start of year T, and the bond matures after three years (at the end of year T + 3). Inflation is 10 percent in the first year, 10 percent in the second year, and 10 percent in the third year. How much, in nominal terms, will the investor receive when the bond is redeemed at the end of the third year? Please show your calculations clearly. (3 points)

The nominal value of the bond after three years is given by

V = 100 (1.1)*(1.1)*(1.1).

We know that 1.1*1.1 = 1.21 [from the 11-times table]

Further, 1.21*1.1 = 1.21* (1 + 0.1) = 1.21 + 0.121 = 1.331.

So we get

V = $133.1 in nominal terms.

b) Explain how issuing indexed debt can help a government whose goal is to keep inflation low to establish credibility. [Hint: in answering this question, make clear what credibility is in this case.] [Two sentences.] (3 points)

Issuing indexed debt, in contrast to nominal debt, does not create any incentive to inflate the economy in an unexpected way, as this would simply increase the nominal value of principal and interest that needed to be paid back, leaving the real value of the government’s liability unchanged. The government establishes credibility if its actions are consistent with its stated objectives, as in this case: the government’s debt policy would help reinforce its anti-inflationary stance.

For parts c) and d) below, please refer to the following:

Governments may pursue objectives at odds with the interests of the general population. However, in a democracy, it is difficult for a government to ignore the interests of the general public entirely, given that doing so makes it more likely that the government will lose the next election. Suppose that the government objective can be represented by the following payoff function:

R = G + a S,

where R measures overall government utility, G is the private payoff to the government, S represents the welfare of the general public, and a is a parameter measuring how much weight the government attaches to the general public’s interests.

Consider two alternative options:

i. Option 1 involves the government issuing nominal debt, then subsequently inflating the economy. This yields a private payoff to the government of G₁ = 4 and a payoff to society,

S₁ = -9;

ii. Option 2 involves the government issuing indexed debt, then subsequently keeping inflation low. This yields a private payoff to the government of G₂ = 1 and a payoff to society,

S₂ = 3.

c) Suppose the parameter a = 0.3. Which option should the government choose and why? Please show your calculations. (5 points)

To solve for the intersection, we need to find the critical value of a* such that

or 4 + (-9)a = 1 + 3a.

This implies that 3 = 12a

or a* = 1/4.

For values of a above this critical value, Option 2 yields a higher payoff overall. Thus the government should choose this option.

d) Suppose the government’s political opposition falls into disarray, allowing the weight on the parameter a to fall. Generally speaking, would this make it more or less likely that the government would choose to issue indexed debt, given the structure of payoffs given above? Please explain clearly. (3 points)

If the parameter a were allowed to fall, this would make it less likely that the government would choose to issue indexed debt. This is because the government would not need to attach so much weight to the welfare of the general public, and would find it easier to pursue policies favouring its own self-interest, such as issuing nominal debt. (Note that the government payoff under Option 1 is increasing as parameter a falls.)

Question 3 (worth 8 points)

a) What shape would you expect indifference curves to have that had hours of work on the horizontal axis and income on the vertical axis? [Note: in this question, you must treat hours of work as increasing as we move from left to right, away from the origin.] Please explain both the likely slope and curvature, and draw a representative indifference curve in the space below. (4 points)

hours of work

We typically think of income being ‘good’ and additional hours or work as ‘bad.’ The utility of an individual is constant, by definition, at all points along a given indifference curve. If A is a point on a given indifference curve, with h_A the corresponding hours, and hours were then increased to h_B, we would expect an increase in income to be needed to keep utility constant. We would also expect the slope to become steeper as hours increased, as successively more I was needed to keep the individual indifferent.

b) Suppose you know that leisure is an inferior good for 40 percent of the population. A government economic advisor has commented that, in light of this fact, a cut in income taxes would not help the government achieve its objective of getting more individuals to increase their hours of work. [Note: here, the success of the policy is being gauged in terms of the number of people who work more.] Please evaluate the soundness of this comment. [Two sentences.] (4 points)

If leisure is an inferior good for 40 percent of the population, it must be a normal good for at most 60 percent of the population. Of that portion, it is conceivable that it could be strongly normal for all 60 percent of the population, in which case, a majority (60 percent) would work less if income taxes fell, in which case, the advisor’s prediction would not hold.