Long free-response question

A fertilizer plant's pollution

Units 2 and 6
10 points
About 25 minutes

You can use a calculator on this question, just like on exam day.

A long question with several lettered parts built around one scenario, often a firm in a particular market structure, and it can pull in other units such as a labor market or a payoff matrix. You identify outcomes, explain them, do a calculation, and describe a correctly labeled graph that shows the situation and how a change affects it. On the exam: Question 1 of 3 in Section II (60 minutes including a 10-minute reading period; 33.35% of the exam score); 10 points, half of the section score. About 25 minutes suggested. Four-function calculator allowed.

The question and its sources

The market for fertilizer is perfectly competitive. Producing fertilizer releases pollution that harms people who live downstream, an external cost of $20 per ton that producers do not pay. There are no external benefits. The table shows marginal private benefit (the market demand curve), marginal private cost (the market supply curve), and marginal social cost at selected quantities. All three curves are straight lines.

Table 1. The fertilizer market

Quantity (thousands of tons)	Marginal private benefit (per ton)	Marginal private cost (per ton)	Marginal social cost (per ton)
20	$80	$40	$60
30	$70	$50	$70
40	$60	$60	$80
50	$50	$70	$90

Source: Hypothetical data

Suggested time: 25 minutes

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Part (a)

1 point

Identify the market equilibrium price and quantity of fertilizer.

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Part (b)

1 point

Identify the socially optimal quantity of fertilizer.

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Part (c)

1 point

Explain why the market produces more fertilizer than the socially optimal quantity.

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Part (d)

2 points

Describe a correctly labeled graph of the fertilizer market. Show (i) the market equilibrium quantity, labeled Qm; (ii) the socially optimal quantity, labeled Qs; and (iii) the area of deadweight loss.

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Part (e)

1 point

Calculate the deadweight loss caused by the externality. Show your work.

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Part (f)

1 point

Identify the per-unit tax that would lead the market to produce the socially optimal quantity.

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Part (g)

2 points

With the tax you identified in part (f), (i) identify the price buyers pay and the price sellers keep after paying the tax, and (ii) calculate the government's tax revenue. Show your work.

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Part (h)

1 point

Suppose that the demand for fertilizer were more price elastic than shown, with supply unchanged. Would buyers bear a larger or a smaller share of the $20 tax? Explain.

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