Microeconomics II
Problem Set 1
[To be handed in in exactly one week, at the beginning of class]
Problem 1
Imagine an economy where the representative consumer’s preferences are given
by the utility function U(x1, x2) = x
1
2
1x
1
2
2. The goods’ prices are p1=p2= 2
euros, and the representative consumer’s income is 100 euros.
a) Calculate and graph the individual demand functions of the representative
consumer for both goods.
b) Calculate the optimal consumption bundle for this consumer given the prices
and income, and show them on the above graph. Also graph the consumer’s
budget constraint and indifference curves.
c) Calculate and interpret the price elasticity of demand at the optimal points,
for both demand curves.
d) Calculate and interpret the income elasticity of demand, for both demand
curves.
e) Calculate and interpret the cross price elasticity of demand for both demand
curves.
f) Suppose that the price of the first good increases to p1= 4 euros. How much
should we compensate the consumer in order for her to maintain her initial level
of welfare (before the price increase)? Calculate and clearly argue your answer
and represent it graphically.
g) How much would the consumer be willing to pay in order to avoid the above
price increase? Calculate and clearly argue your answer, and represent it graph-
ically.
h) Supposing that in this economy there are 100 consumers in total, all shar-
ing the same preferences and income as the representative consumer described
above, calculate the aggregate demand functions for both goods and graph them.
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