Question

Consider the following utility function: U = Min(X,Y).

a. Find the income and substitution effects.

b. Draw the compensated and Marshallian demand curves.

Answer 1

We have:

U = Min(X,Y)

This implies that in equilibrium, X=Y.

Budget: PxX+ PyY = M

where, Px = Price of X, Py = price of Y, M = Income.

Using X=Y and budget we get:

X = Y = M / (Px+Py)

In Y-X plane, the allocation is shown as 45 degree line which implies no substitution effect but only income effect.