ECON2131/6034 Public Sector Economics
Tutorial 2
The economic rationale of government
Discussion
For each program listed below, discuss what market failures, including merit good considerations, might be (or are) used as a partial rationale:
(a) National defence
(b) Unemployment compensation
(c) Federally insured mortgages
(d) Law requiring lenders to disclose the true rate of interest they are charging on loans
(e) Government prohibition of the use of narcotics
Questions
1. Individual 1 and individual 2 have quite different tastes for shirts and beer such that Individual 1 wants many shirts and individual 2 wants large quantities of beer, but at the margin they must be prepared to exchange the same amount of beer for a shirt. Identify the critical assumption about individual preferences that makes this possible. Provide a graphical representation.
2. A consumer views two goods as perfect substitutes one for one (i.e. the consumer considers each unit of good 1 to be worth 1 unit of good 2).
(a) Sketch the indifference curves of the consumer.
(b) If an economy is composed of two consumers with these preferences, demonstrate that any allocation is Pareto efficient.
(c) If an economy has one consumer who views its two goods as perfect substitutes one for one and a second that considers each unit of good 1 to be worth 2 units of good 2, find the Pareto efficient allocations.
3. Consider an economy with two goods x and y, and 2 individuals A and B with preferences represented by the utility functions:
UA (xA, yA ) = xAyA
UB (xB, yB ) = xByB
where xi and yi represent the consumption of goods x andy by each individual i = A,B. The initial endowment of the goods is that A has 12 units of x and 2 units of y while B has 8 units of x and 18 units of goody.
(a) Show how the two goods must be allocated among the two individuals at any Pareto efficient allocation in this economy. Draw the corresponding contract curve in the Edgeworth box.
(b) Assume A gets to choose a new allocation to maximize utility subject to the constraint that B’s utility is no lower than at the endowment point. Solve formally for the Pareto efficient allocation.