Budget Constraint

Mia consumes two goods 𝑥1 and 𝑥2. Her preferences are represented by 𝑢(𝑥1, 𝑥2) =𝑥1𝑥2. The price of good 𝑥1 is denoted by 𝑝1, the price of good 𝑥2 is denoted by 𝑝2, and her income is denoted by 𝑚. Suppose Mia gets a weekly allowance of £100. Suppose both goods are £1 per unit.


Graph her budget constraint, and write down the equation of her budget line. In the same graph show Mia’s indifference curves corresponding to the utility levels 𝑢 = 1000, 𝑢 = 2500 and 𝑢 = 4000. Solve for Mia’s optimal consumption bundle and indicate it in your graph.

Derive her demand functions for good 1 and good 2 as functions of her income, 𝑚, price of good 1, 𝑝1, and price of good 2, 𝑝2. Is good 1 normal or inferior? Ordinary or Giffen? Are goods 1 and 2 substitutes or complements?

Suppose the price of good 1 rises to £2. Calculate the equivalent variation in
income.