Question

Consider the utility function U(x1,x2) = ln(x1) +x2. Demand for good 1 is: •x∗1=p2p1 if m≥p2 •x∗1=mp1 if m < p2 Demand for good 2 is: •x∗2=mp2−1 if m≥p2 •x∗2= 0 if m < p2 (a) Is good 1 Ordinary or Giffen? Draw the demand curve and solve for the inverse demand curve. (b) Is good 2 Ordinary or Giffen? Draw the demand curve and solve for the inverse demand curve. (c) Is good 1 Normal or Inferior? Derive and draw the Engel curve. (d) Is good 2 Normal or Inferior? Derive and draw the Engel curve. (e) Draw the income offer curve. (f) Is good 1 a gross substitute/complement for good 2? (g) Is good 2 a gross substitute/complement for good 1?

Answer 1

f)

Two goods are gross substitutes if an increase in the price of one good increases demand for other. That is for two goods x and y

Two goods are gross complements if an increase in the price of one good decreases the demand for other. That is for two goods x and y

The demand for good 1

Therefore,

Then good 1 and 2 are gross substitutes.

g)

The demand for good 2 does not depend on the price of good 1. Then good 2 is neither substitutes nor compliment of good 1.