1. (89 points) Elasticity, Slutsky, compensating and equivalent variations Ike has utility function u (X1, I2) = 142 where r1 and 2 are his consumptions of goods 1 and 2, respectively. He has a budget m to spend entirely on goods 1 and 2 who's prices are p, and p2. a) (4 points) Compute Ike's ordinary demand for good 1 and 2: T1 (P1, P2, m), T2(P1, P2, m). Show the main steps. (note, make sure this is correct as it will be used extensively in the following exercises). Ike's optimal consumption solves MU1 TMS = MU2 P2 T2 T1 P2 We inject in Ike's budget constraint PIX1 + P242 = m m P2 Pidi + TIPI m m X1 (P1, P2, m) = 2P1 Similarly m X2 (P1, P2, m) = 2p2 b) (6 points) Compute Ike's i) own-price point elasticity of demand of good 1 (61,1), ii) cross-price point elasticity of demand for good 2 with respect to the price of good 1 (E1,2), iii) income point elasticity of demand of good 1 (label it n,). Use derivative for your calculations. Simplify as much as possible. Note: use derivatives. d.1 Pi m P1 1 61,1 = dp1 X1 2pi m 2 ) 2p1 dx2 P1 82,1 0Pl = 0 dp1 X2 T2 dx 1 m m = 1 midm X1 m 2P1 2p1