ECO336Y

Solutions for Sample Questions 10

Here are my solutions. Please let me know if anything's unclear.

Robert McMillan

Question 1 (worth 4 points)

Please say whether the following statements are true or false. [One-word answers are fine.]

1a) “A tradeable permits scheme allows a given aggregate level of emissions to be attained in a way that minimizes total abatement costs.” (1 point) True

1b) “In the case of a pure public good, at the optimum everyone necessarily has the same marginal valuation of the public good.” (1 point) False

1c) “In the presence of uncertainty, it is always preferable for the government to choose a quantity instrument rather than a price instrument.” (1 point) False

1d) “Lindahl’s decentralized scheme for providing a public good involves charging each person a tax share (or personalized price) based on that person’s known valuation of the public good.” (1 point) True

Question 2 (worth 11points)

To a very close approximation, TV sets are hazardous waste once they are disposed of.

2a) Is this a reflection of some market failure? Please explain. (2 points)

A market failure is present in that the manufacturers of TV sets are not confronted with the environmental costs associated with the disposal of the ‘hazardous waste’ that they produce. Thus they have no incentive to build TV sets out of materials that would have fewer adverse environmental consequences.

2b) If so, can you suggest ways that the government might correct the market failure? [two sentences] (4 points)

The government could use either ‘price’ or ‘quantity’ instruments to force manufacturers to internalize the associated costs. In terms of quantity regulation, they could ban the use of certain materials like mercury in the manufacturing process; in terms of price regulation, they could impose taxes on components used in TV manufacture to reflect the damages arising once TVs were disposed of.

Aside: the government could also invest in TV disposal technology that would mitigate the problem of TVs being thrown into landfill sites, and from there contaminating ground water (for example). The costs of running the scheme could be levied on TV manufacturers, though the latter would doubtless object, especially if they had significant lobbying power.

2c) Would such government intervention have any effect on the prices of TV sets, and why? Please explain carefully. [3 sentences] (5 points)

Either restricting the components used or raising the cost of components would be likely to raise the production costs of TVs in the short run. Whether manufacturers would be able to pass costs on to consumers would depend on their market power: if firms had market power, then they would have some control over the prices they set, and would be better able to pass the higher costs on to consumers. In the longer term, it is possible that the regulation would spur greater innovation in the area of ‘green’ technology, leading to cost reductions and lower prices.

Note: increases in price would help reduce demand for TVs and provide a market check on the pollution problem. This is unsurprising: the price of TVs would now partly reflect the damages that arise when TVs are thrown away.

Question 3 (worth 7 points)

What desirable features does the equilibrium outcome under a permit trading scheme have? Does it achieve “overall efficiency”? Please explain carefully, and in doing so, say what is meant by “overall efficiency” here. [four sentences] (7 points)

Equilibrium under a permit trading scheme achieves a given emissions level (determined by the number of permits in circulation) at the minimum abatement cost to society. It does so in a way that is decentralized; the government does not need to know anything about firms’ marginal cost of abatement schedules, instead relying on profit maximizing behaviour by firms, and thereby economizing on information.

Overall efficiency characterizes an outcome in which each firm produces a level of emissions such that the marginal social cost of those emissions is exactly equal to the marginal benefit of the extra emissions to the firm. The equilibrium outcome under a permit trading scheme will typically differ from the overall efficient outcome, though the two would coincide if the marginal social cost of emissions was equal across all firms, and the total number of permits in circulation were set so that the equilibrium permit price were equal to that marginal social cost.

Question 4 (worth 18 points)

4a) Suppose the social planner knows the preferences of individuals over a pure public good completely. What decentralized scheme can the planner use to set the level of the pure public good? (1 point)

The planner can use Lindahl’s method to determine the optimal level of the pure public good in this case.

4b) Consider the preferences of two individuals for a public good as a function of the share each person has to contribute. For person 1,

Q = 1 – s₁

and for person 2

3Q = 2 – 6s₂,

where s₁ and s₂ are their respective contributions to the public good. Implementing the scheme referred to in part a) above, calculate the equilibrium shares for each person, explaining carefully the steps you take. (12 points)

We need to choose s₁* and s₂* such that both individuals choose the same level of the public good. Taking the second equation above, we have

Q = 0.666 – 2s₂.

Now, in Lindahl equilibrium,

s₂ = 1 – s₁.

Equating the level of Q demanded by persons 1 and 2 and using the fact that the shares must add up to 1 in Lindahl equilibrium, we have

1 – s₁ = 0.666 – 2s₂,

implying

s₂ = 0.666 – 2s₂

implying

s₂* = 2/9, which implies s₁* = 7/9.

4c) Also calculate the level of Q that will be provided in equilibrium. (4 points)

Using the fact that Q* = 1 – s₁*, we get that Q* = 2/9.

4d) Given this equilibrium level of Q, can a more efficient level of the public good be provided? Please explain. [One sentence.] (1 point)

No, this equilibrium is Pareto-efficient, satisfying the Samuelson Condition.

Question 5 (worth 6 points)

5a) Please state precisely the Samuelson Condition for the optimal provision of a pure public good in the case of a single private good X and a pure public good Q. [Hint: your answer should be in terms of the marginal rates of substitution and transformation.] (3 points)

The Samuelson Condition states that a pure public good should be provided up to the point Q* where the marginal rate of transformation of the private good for the pure public good equals the sum of the marginal rates of substitution of the private for the pure public good across all individuals.

5b) Please provide an intuitive interpretation of the Samuelson Condition. (3 points)

Intuitively, the Samuelson Condition says that a pure public good should be provided up to the point where the marginal cost of providing an additional unit of the good equals the total marginal benefit across all individuals in society (summing the marginal benefits across all these individuals).