PROBLEM SET 2*
Tutor: Matthew Polissona
1. Fresher is a first-year PPEist. On Friday of Week 2, Fresher defines her budget
for the evening. She is given income m > 0 to spend at The Bar on two continu-
ous commodities: Beer and Juice. The quantities of Beer and Juice are denoted
by x1≥0 and x2≥0, respectively. The prices of Beer and Juice are denoted
by p1>0 and p2>0, respectively, where p1, p2< m. In order to encourage safe
drinking and to discourage drunkenness, The Bar imposes a tax t > 0 per unit
of consumption of Beer after ¯x1>0 units have been consumed. Draw Fresher’s
budget set with and without the tax.
2. What is the effect on a consumer’s budget set when all prices are doubled?
What if her income is doubled simultaneously?
3. Consider two commodities in a world of many: £5 notes and £10 notes. Imagine
that these commodities are continuous rather than discrete. Draw indifference
curves for a consumer with rational (complete, transitive), well-behaved (locally
non-satiated, convex), and continuous preferences over money, and indicate
with small arrows the direction of preferred consumption bundles.1What is the
consumer’s marginal rate of substitution (MRS )?
4. Explain why strictly convex preferences have indifference curves that are rotund
(or without flat spots).
5. A consumer has rational (complete, transitive), well-behaved (locally non-satiated,
convex), and continuous preferences represented by
u(x1, x2) = √x1x2,
where x1≥0 and x2≥0 denote quantities of Goods 1 and 2, respectively,
and where (x1, x2) denotes a consumption bundle.2Denote the marginal utility
from an infinitesimal increase in x1as MU1and the marginal utility from an
*This problem set corresponds to the 2009–2010 paper. All errors are my own.
aDepartment of Economics, University of Oxford
1Note that we only assume that a consumer prefers more money to less.
2Cobb-Douglas preferences are generally represented by u(x1, x2) = xα1
1xα2
2, where α1, α2>0 and
1
