Question

Which statement about interior solutions to a consumer’s choice problem is true?

Group of answer choices

if the utility function is U(X,Y)=XY, then tangency condition does not necessarily hold at an interior solution

if the utility function is U(X,Y)=XY, then the optimal solution might or might not be interior, depending on the shape of the budget

suppose the preference features perfect substitutes and there exists one interior solution, then there are more than one interior solutions

if the preference features perfect substitutes, then the optimal solution is always corner

Answer 1

Correct Answer : if the preference features perfect substitutes, then the optimal solution is always corner.

If the utility function is U(X,Y)=XY, then the tangency condition for the optimum solution is an interiror solution because at the point of optimum the slope of the indifference curve is equal to the slope of the budget constraint and in case of convex indifference curve as mentioned above, the solution is always an interior solution because budget constraint is downward sloping. Thus, option A and B are incorrect.

In the case of perfect substitutes, the optimal solution is always the corner solution because the indifference curve is linear in shape. Thus, option C is incorrect and Option D is correct.