ECO336Y

Solutions to Sample Questions 6

Here are the solutions to Sample Questions 6.

Please let me know if you have any questions.

Robert McMillan

1a) Please give two reasons why a Pigouvian tax is generally preferable to a Pigouvian subsidy. (4 points)

A Pigouvian tax is generally preferable to a Pigouvian subsidy because:

i. the tax generates revenues for the government whereas the subsidy requires the government to raise revenues elsewhere. This generally means that the government needs to introduce new distortions into the economy through taxation, raising inefficiency, unless it is able to carry out (non-distortionary) lump-sum taxation.

ii. The tax raises costs and lowers profitability in the industry, while the subsidy raises profitability. This may induce entry and have the perverse effect of raising overall levels of pollution.

1b) If markets fail, is government intervention always justified? Please set out your reasoning. [Two sentences.] (4 points)

If markets fail (because of externalities or market power), this provides a reason for considering government intervention as a means of correcting the failure. However, government intervention is often costly, and in some cases, the costs outweigh the benefits, so that government intervention is not always justified.

2) By drawing an appropriate diagram, please explain how the government would set a Pigouvian tax with reference to that diagram. (Your diagram should show the relevant marginal cost and benefit schedules associated with producing a given level of output Q.) Please label the diagram appropriately, and in giving your answer, make sure that you state the rule for setting the Pigouvian tax in an optimal way. (7 points)

The rule for setting a Pigouvian tax is as follows: calculate the socially efficient level of output, at which the marginal social cost (MSC) is equal to the marginal benefit (MB), and set the tax equal to the marginal damages at that level of output. By imposing a Pigouvian tax t* on each unit of output, the government shifts the firm’s MPC curve up vertically by an amount t* to MPC’. Thus in the face of the tax, the firm is now forced to internalize the externality fully and produce the socially efficient level of output.

Question 3 (worth 7 points)

Suppose there are two types of firm in an industry – type I and type II firms - and production by these firms gives rise to pollution emissions. Both types of firms have linear marginal benefit of emissions schedules that intersect the horizontal axis at the same point (e₀), but type I firms have steeper benefit schedules. In particular,

MB_I = 6 – e,

and

MB_II = 3 – 0.5 e.

3a) In the space below, draw a diagram representing the marginal benefits to each type of firm from higher emissions, with emissions (e) on the horizontal axis. (Assume that the marginal private cost of emissions is zero for both types of firm, in the absence of government intervention.) (1 point)

e

3

e₀ = 6

3b) In the absence of any regulation, what level of emissions will each type of firm choose to produce and why? Answer with reference to the diagram. (2 points)

In the absence of any regulation, both types of firm will choose to produce emissions of e₀. At e₀, the firm’s marginal benefit of emissions equals to the marginal private cost, equal to zero.

3c) Suppose the government knows the marginal damage of emissions, where MD = 2. What emissions standard (or quantity of emissions) would it set for each type of firm, and could the same standard for both types of firm be efficient? Solve for these explicitly. (4 points)

Solving for the emissions levels where MB(e) = MD(e) for each firm, we have

e_I* = 4 and e_II* = 2.

3d) Could the same standard for both types of firm be efficient? Please explain. (4 points)

The government would set an emissions standard of e_I for firms of type I and e_II for firms of type II. In each case, these standards would be efficient as they would equate the marginal benefit to society with the full social cost of an additional unit of emissions. Because the marginal benefit of emissions of the two firms differ, no single standard could ever be efficient. If MB=MSC for one type of firm, it could not at the same time be equal for the other type of firm.

Question 4 (worth 6 points)

In a particular community in Mississauga, officials are considering a scheme to improve local air quality by 10 percent. They have hired some economists to estimate the willingness of households to pay for air quality improvements, and these economists obtain reliable estimates indicating that, on average, households would pay 1.4 percent of their house value for a 10 percent improvement in air quality. Suppose that the average house price is $100,000, and that there are 100 families in the community. Suppose also that the improvement would cost $160,000 to implement, and ignore any possible benefits to the inhabitants of other communities. Should the improvement go ahead? Please set out your working clearly. (6 points)

The average willingness to pay for the improvement per household is $1400, or $140,000 across all households in the community. Thus comparing the total estimated benefits with the costs, the project should not go ahead. [Aside: econometric estimates have uncertainty associated with them, as captured in standard errors. If these standard errors are large, then it is still possible that the project might in fact be worthwhile.]

Question 5 (worth 14 points)

You have been asked to carry out an econometric exercise, measuring the dollar value of clean air using data on house prices in Ontario. Your data set consists of a random sample of houses in the province. Specifically, for each house, you have information on house’s price, house size, whether the house in a city or rural area, and an index measuring local air quality. (For this index, a higher value implies worse air quality.)

5a) Using the available data set, how would you go about measuring the value of clean air? Say what regression you would run, precisely. (3 points)

Using the available data, one could run the following regression:

P_i=a₀ + a₁S_i + a₂R_i + a₃A_i + e_i,

regressing the price of house i on a constant, the house’s size, the rural dummy variable (R_i=1 if house i is in a rural area), and the local air quality index. The coefficient estimate for a₃ using least squares would indicate the effect of a give change in air quality on house prices, thus giving us a dollar valuation of improvements in air quality in Ontario. [Note that we would expect our estimate of the coefficient to have a negative sign, as worse air quality (indicated by higher values of the index) would tend to be associated with lower house values.]

It is clear that the data set provides very little information about the true quality of a local neighborhood – to you, neighborhood quality is effectively unobserved. However, suppose that housing developers are able to observe the attributes of a neighborhood that make it a desirable place to live. And suppose that, as the neighborhood becomes more desirable, so developers would like to build larger houses.

5b) What will this type of behaviour tend to mean for any coefficient you estimate on house size? Will it be biased up or down? Please explain. [4 sentences] (7 points)

The coefficient on house size will tend to be biased upward. This is because, in the data, where neighbors are of high quality for unobserved reasons, so developers will build houses according to the mechanism described. In such locations, house prices will be high, given that the unobservable (e_i) will be high. Given that there are no adequate neighborhood quality measures in the data, “house size” will pick up the effect of a high e_i, so that this variable will tend to have a bigger positive estimated coefficient than in fact it should.

5c) What is this source of bias an instance of? (2 points)

This bias is an instance of omitted variables bias. We are omitting true neighborhood quality from a regression in which this is likely to be highly relevant.

5d) Can you suggest additional information that you might want to add to the data set that would help provide accurate house value estimates? Please be specific. [One sentence] (2 points)

One would like to add better information about neighborhood quality, as captured by measures such as crime rates, the percentage of people living in poverty, and the level of unemployment.