HW #1 Solution Question 1. (1) Ann's utility maximization problem is maxa1,b1 (a1) 1 4 (b1) 3 4 subject to budget constraint pa1 + b1 = 40p + 20 First order conditions imply u1 a1 u1 b1 = 1 4 a 3 4 1 b 3 4 1 3 4 a 1 4 1 b 1 4 1 = b1 3a1 = p, which gives us b1 = 3pa1. Plug this into the budget constraint gives us pa1 + 3pa1 = 40p + 20, therefore Ann's demand for ale is a1 = 40p+20 4p = 10p+5 p . Ann's demand for bread is therefore b1 = 30p + 15. (2) Bob's utility maximization problem is maxa2,b2 (a2) 1 2 (b2) 1 2 subject to budget constraint pa2 + b2 = 20p + 40 First order conditions imply u2 a2 u2 b2 = 1 2 a 1 2 2 b 1 2 2 1 2 a 1 2 2 b 1 2 2 = b2 a2 = p, which gives us b2 = pa2. Plug this into the budget constraint gives us pa2 + pa2 = 20p + 40, therefore Bob's demand for ale is a2 =