14.7: Exercises for Chapter 14

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EXERCISE 14.1

An economy is composed of two individuals, whose demands for a public good – street lighting – are given by P=12–(1/2)Q and P=8–(1/3)Q.

Graph these demands on a diagram, for values of .
Graph the total demand for this public good by summing the demands vertically, specifying the numerical value of each intercept.
Let the marginal cost of providing the good be $5 per unit. Illustrate graphically the efficient supply of the public good () in this economy.
Illustrate graphically the area that represents the total value to the consumers of the amount .

EXERCISE 14.2

In Exercise 14.1, suppose a new citizen joins the economy, and her demand for the public good is given by P=10–(5/12)Q.

Add this individual's demand curve to the graphic for the above question and graph the new total demand curve, specifying the intercept values.
Illustrate the area on your graph that represents the new total value to the three citizens of the optimal amount supplied.
Illustrate graphically the net value to society of the new – the total value minus the total cost.

EXERCISE 14.3

An industry that is characterized by a decreasing cost structure has a demand curve given by P=100–Q and the marginal revenue curve by MR=100–2Q. The marginal cost is MC=4, and average cost is AC=4+188/Q.

Graph this cost and demand structure. [Hint: This graph is similar to Figure 14.2.]
Illustrate the efficient output and the monopoly output for the industry.
Illustrate on the graph the price the monopolist would charge if he were unregulated.

EXERCISE 14.4

Optional: In Question 14.3, suppose the government decides to regulate the behaviour of the supplier, in the interests of the consumer.

Illustrate graphically the price and output that would emerge if the supplier were regulated so that his allowable price equalled average cost.
Is this greater or less than the efficient output?
Compute the AC and P that would be charged with this regulation.
Illustrate graphically the deadweight loss associated with the regulated price and compare it with the deadweight loss under monopoly.

EXERCISE 14.5

Optional: As an alternative to regulating the supplier such that price covers average total cost, suppose that a two part tariff were used to generate revenue. This scheme involves charging the MC for each unit that is purchased and in addition charging each buyer in the market a fixed cost that is independent of the amount he purchases. If an efficient output is supplied in the market, illustrate graphically the total revenue to be obtained from the component covering a price per unit of the good supplied, and the component covering fixed cost.