Question

Consider the following utility function: U = M in(X; Y ). (I) Find the income and substitution e§ects. (II) Draw the compensated and Marshallian demand curves.

Answer 1

1)U= min{ X,Y}

The preference is perfect complement.

The utility Maximizing condition: x=y

Substitution effect shows the change in Optimal bundle due to change in relative price of goods .

So Utility Maximizing bundle is not effected by relative price of goods, so substitution effect is zero.

Imcome effect shows change in Optimal bundle due to change in real income.

So total price effect of price change is income effect.

B) x=y

Budget constraint:,

M=px*x+py*y

M=px*y+py*y

Y=M/(px+py) and X=M/(px+Py). [{ Marshallian demand}]

X= Y=Ū[{ Compensated demand function}]