An agent consumes quantity (x 1 , x 2 ) of goods 1 and 2. She has utility u(x 1 , x 2 ) = x 1 a x 2 1a . The prices of the goods are p 1 and p 2 . The consumer has income m.

1. Derive the agents demand functions as a function of income, M, and prices p 1 and p 2 using the MRS and the budget line.

2. Suppose a = 4 1 , M = 100, p 1 = 2, p 2 = 1 but then p 1 falls to 1. For good 1 compute the substitution and income eects of this price change, and show ths eects on a clear complete graph.

3. Determine whether x 1 is normal, inferior, ordinary or Gien. Explain.