Chapter 22: Other Examples of Asymmetric Information
Question 1 a) The agent will report the sale price that minimizes the amount that he
must pay to the owner. One way of doing so is to report that the sale price is zero, since
under this report, his pay

Chapter 17: The Welfare Cost of Tax Interactions
a) The Marshallian demands can be found as the solution to a two equation system. Oneequation is the
budget constraint, and the other is the condition for a tangency between the budget constraint and an ind

Chapter 16: Taxation
Question 1
a) Robinson s budget constraint is:
c = 20h
Substituting this constraint into his utility function gives:
U = 20h h2
His utility is maximized when:
Robinson collects coconuts for 10 hours and consumes 200 coconuts. His util

Chapter 21: Regulation of a Natural Monopoly
a) Since raising revenue is costly, the government should set M as low as possible
is, M should be equal to e2. Under this rule, the net social value when is low is:
that
W = 12e 3e2
The best value of e satis e

Chapter 19: Asymmetric Information
Question 1 a) If is uniformly distributed on the interval [0, ], the average value of is /2. Here, is 1, so
the average value of is 1/2 and the average daily output of the workers is 3/2.
b) Since only the best workers l

Chapter 20: Preference Revelation
Question 1
Each person has the same marginal rate of substitution:
Substituting the marginal rates of substitution and the marginal rate of transformation into the Samuelson condition
gives:
For each person, consumption i

Chapter 18: The Theory of the Second Best
a)
The budget constraint is:
c = (1 t)h
Substituting the budget constraint into the utility function gives:
U
= 2(1 t)1/2h1/2 + z1/2 h
The utility-maximizing hours of work satisfy the condition:
implying:
h=1t
Sub

Chapter 5: Consumer and Producer Surplus
Question 1 The gure below shows the market before the government intervenes. Consumer surplus is the value
to consumers of q lifejackets less the amount paid for them. The value of the lifejackets to the consumers

Chapter 13: The Link Between Public Goods and
Externalities
Question 1
a) The marginal rates of substitution are:
and the marginal rate of transformation is:
so the Samuelson condition can be written as:
or equivalently:
(1) b) An allocation is Pareto opt

Chapter 10: Pure Public Goods
Question 1 The optimal quantity of the public good is provided when the sum of the fty people s marginal rates
of substitution is equal to the marginal rate of transformation. Since there are twenty people of the rst type and

Chapter 15: Pricing Rules under Imperfect Competition
Question 1
The highest price at which q units of goods can be sold is:
Firm 1 s pro ts are the difference between its revenues and its cost:
and its pro t-maximizing output satis es the condition:
Re-a

Chapter 9: Co-ordination Failures
Question 1
The gure above shows the graph of the relationship between n and m, as well as the graph of the equilibrium
condition. The intersection points of the two graphs are equilibrium group sizes. One of the equilibri

Chapter 8: Renewable Common Property
Resources
Question 1
a) The replacement of the manager has no immediate impact on the stock, but the newmanager increases the
number of boats to reach the mcp curve. Consequently, the state of the shery changes from F

Chapter 14: Monopoly
Question 1 a) The monopolist is maximizing its pro ts when it sets output so that marginal cost is equal to
marginal revenue. Marginal cost is the increase in total cost associated with an increase in output:
while marginal revenue is

Chapter 6: Externalities and Negotiation
a) If the rm has the property rights and there is no agreement, the rm will choose the level of output that
maximizes its pro ts , which are equal to the difference between its revenue from the sale of goods and it

Chapter 11: Two Examples of Public Goods
Question 1 a) Firm is pro ts are: The pro t-maximizing value of
xi e
Evaluating the derivative gives:
+ (n 1)xe
Re-arranging this equation gives rm is best response function: xi = 4 (n 1)xe
In a symmetric equilibri

Chapter 7: Permit Trading
Question 1
Abatement
Abatement costs under direct emissions controls are:
costs under
permit
trading differ in the two cases described
in the
text. Let
s
consider these cases in turn.
Case 1. In this case, abatement costs are:
Pe

Chapter 4: The Production Economy
Question 1 a) Both production functions are Cobb-Douglas. Applying the rule for quick Cobb-Douglas
derivatives and simplifying gives:
Chapter 4: The Production Economy
b) The marginal products are:
i)
ii)
iii)
Moving one

Chapter 3: An Algebraic Exchange Economy
Question 1
a) Harold s endowment of bread is 8 loaves.
b) If Harold wishes to consume a pints of ale, he is able to sell 6 a pints of ale. The
bread value of this ale is p(6 a) loaves.
c)
If Harold wishes to consum

Solutions to Textbook Questions
Chapter 2: The Exchange Economy
Question 1 In parts a) and b), E is the endowment point, X is George s best attainable commodity bundle, and Y
is Harriet s best attainable commodity bundle. In part c), E is the endowment po