Questions:
- (24 marks) Consider the matter of economic modelling:
a. Briefly explain how a map is a model.
b. Briefly explain how a road map is an example of how a particular model can be
appropriate in one context and inappropriate in another.
c. Identify the two attributes of a “good” economic model, and briefly explain the
fundamental tradeoff between them.
d. Briefly explain why a model must accept as exogenous at least some features of the
setting being modelled. - (24 marks) Consider the basic competitive model for an exchange economy:
a. What does it mean for an allocation along with a set of prices to be a competitive
equilibrium? What does it mean for an allocation to be Pareto efficient?
b. State the First Welfare Theorem (no mathematical notation required).
c. State the Second Welfare Theorem (no mathematical notation required).
d. An exchange economy has two goods and two consumers with utility functions
?
1 = ?1
1 + ?2
1
and ?
2 = min{?1
2
, ?2
2
}, where the superscript denotes the consumer.
The endowments are ?
1 = (1,2) and ?
2 = (3,1), and good two is designated the
numeraire so that the price of good two is 1 and that of good one is ?. {Hint:
answering this question requires no calculus; just logical reasoning.}
i. Derive the contract curve.
ii. Derive the set of competitive equilibria and identify those that are Pareto
efficient.
iii. In an appropriate Edgeworth box, illustrate the correct answers to (i) and
(ii). - (20 marks) Consider the self-control (i.e. dynamic inconsistency) problem:
a. Explain what is meant by dynamic consistency and dynamic inconsistency, and
relate these concepts to the problem of preference reversal. Unlike a naïve agent,
how does a sophisticated agent achieve dynamic consistency? Very briefly describe
a decision-making situation in which dynamic inconsistency applies (i.e. present self
vs. future self).
b. Consider an agent who chooses the number of calories ??
to consume in each period
?, where a delayed utility cost (e.g. decreased health, weight gain etc.) arises from
consumption in the previous period. In respect of time ?, the immediate utility ?(??)
is strictly concave and the delayed utility cost ?(??−1) is strictly convex, where both
functions are differentiable. At time ?, the discounted net utility of last period’s
consumption combined with an infinite consumption plan ??
, ??+1, … for the present
and future is given by:
?? = ?(??
) − ?(??−1
) + ? ∑?
?[?(??+?
) − ?(??−1+?
)]
∞
?=1
where 0 < ? ≤ 1 is the commitment (i.e. self-control) parameter and 0 < ? ≤ 1 is the discount rate. With time ? representing the present period, let ?? ∗ and ??+1 ∗ be the optimal levels of consumption in the present period and next period, respectively. {Hint: There is insufficient information to derive specific values for optimal consumption, so you should use the properties of differentiability, convexity and concavity to answer this question.} i. Show that ?? ∗ = ??+1 ∗ if the agent is sophisticated (? = 1). ii. Show that ?? ∗ > ??+1
∗
(i.e. indulgence occurs in the present period) if the
agent is naïve (? < 1).
iii. When the agent is naïve, why is there a tendency for him to indulge in the
present period? What is the directional effect on ??
∗
and ??+1
∗ of an increase in
self-control? - (32 marks) Consider the matter of public goods:
a. Briefly describe why markets are expected to provide inefficiently low levels of
public goods, and identify the property of public goods that causes this inefficiency
to arise and the mechanism by which it arises. What condition of the basic
competitive model is violated by a public good?
b. Consider an economy of ? people who consume a composite private good ? and
share consumption of a public good ?. Utility for person ? ∈ {1,2, … ?} is given by
??(??
, ?) and the total social cost of the public good is ?(?) in units of ?, where both
functions are differentiable. Each person has income ? in units of ?.
i. Characterize the Samuelson Rule for efficient provision of ? in this economy.
ii. Suppose people have identical preferences represented by ?(?, ?) = ln ? +
? ln ?, where ? > 0, and that ?(?) = ??, where ? > 0. Let ?
∗
and ?
∗ be the
efficient levels of ? and ? as functions of the model’s parameters ?, ?, ? and
?. Derive the expressions for ?
∗
and ?
∗
.
c. What does it mean for a good to be a local public good? State the Tiebout Hypothesis
and briefly explain how, under this hypothesis, preference revelation, and thus
efficient provision, is achieved for a local public good.
d. What does it mean for a good to be a club or common good, and why are markets
generally able to provide private and club goods, but not public and common goods,
efficiently? Briefly explain how, in the Greater Toronto Area of Ontario, Highway
401 is primarily a common good while Highway 407 ETR is a club good. Identify the
rationale for Highway 407 ETR’s application of time-of-use pricing.