Question 7
Suppose we have three goods and we know that the consumer has strictly
convex and strictly monotonic preferences. If we can run an unlimited
number of experiments where we expose the consumer to prices
\((p_{1},p_{2},p_{3})\) and give him income \(y\), can we fully learn
the consumer’s preferences?
Correct: We can always entirely learn the consumer’s preferences.
False: We might not be able to learn the consumer’s preferences.
Explanation:
In three dimensions, the budget set is given by
\(\{\left(x_{1},x_{2},x_{3}\right):p_{1}x_{1}+p_{2}x_{2}+p_{3}x_{3}\leq y\}\),
where \(y\) is the consumer’s disposable money. Geometrically, this set
is bounded by a plane (with equation
\(p_{1}x_{1}+p_{2}x_{2}+p_{3}x_{3}=y\)). The diagram below
displays one such plane (in green).
Since the consumer has strictly convex and strictly monotonic
preferences, the indifference sets are given by surfaces like the blue
surface in the diagram below: