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.