Click here for solutions

Question 1: A utility function is given by u(x₁,x₂)=x₁+log(x₂). Prices are given by p₁, p₂, and income by m.

• Determine the demand functions for goods 1 and 2.
• How does an increase of p₁ affect demand for good 2?
• How does an increase of p₂ affect demand for good 1?

Question 2: Assume that p₁=2, p₂=3 and m=12. Determine the optimal consumption choice for the following utility functions:

• u(x₁,x₂) = x₁+3x₂.
• u(x₁,x₂) = 3x₁+x₂.
• u(x₁,x₂) = 2x₁+3x₂.

Question 3: A utility function is given by u(x₁,x₂)=2log(x₁)+log(x₂). Prices are given by p₁, p₂, and income by m. Determine the demand functions for goods 1 and 2.

Question 4: A utility function is given by u(x₁,x₂)=x₁+2x₂^1/2. Prices are given by p₁, p₂, and income by m. Determine the demand functions for goods 1 and 2.

Question 5: In the following graph, indifference curves are indicated by the blue lines and a budget line by the straight (red) line.

• Determine graphically some optimal consumption choices.
• Is one of the goods an inferior good?
• Show graphically that there exist prices and incomes for which good 2 is a Giffen good, i.e., find a budget line such that an increase in the price of good 2 results in an increase of demand of good 2.

To the title page