Question 6
Now suppose that the preferences are strictly monotone and strictly
convex. What can we deduce from that?
Correct: For all points \((x_{1},x_{2})\) there exists some combinations
\((y,p_{1},p_{2})\) such that when faced with \((y,p_{1},p_{2})\) the
consumer will choose \((x_{1},x_{2})\)?
Correct: If we are allowed to run arbitrarily many experiments, exposing
the consumer to \((y,p_{1},p_{2})\) and observing his choice, then we
can learn arbitrarily precisely these preferences.
Correct: If \(y\) is fixed but we are allowed to run arbitrarily many
experiments exposing the consumer to \((y,p_{1},p_{2})\), where we can
pick \((p_{1},p_{2})\) and observe his choice, then we can learn
arbitrarily precisely these preferences.
Corrrect: If we know the consumer’s entire Marshallian demand function,
then we can recover his MRS at each point.
Corrrect: If we know the consumer’s entire Marshallian demand function,
then we can recover his preferences.
Explanation:
For any point \(A\) we will learn the MRS at that point if we expose the
consumer to the situation where the budget line goes through he point
and is tangent to the indifference curves through that point. From that
we can recover the indifference curves and by monotonicity the
preferences.