f) (3 points) Compute the own-price arc elasticity of demand 61,1 between (17, 12) and (IP , I! ).? g) (3 points) What income would Ike need in order for him to be able to consume his old bundle (11, 12 ) at the new prices (P1, P2) = (4, 2)? Note this compensated income m'. h) (2 points) If Ike had income m' (instead of m = 8) and the prices were the new prices (p1, p2) = (4, 2), what would be his optimal consumption choice? Note this compensated bundle (If, I, ) i) (6 points) The whole Slutsky decomposition can be expressed as An = A'n +"m where . Ar] is the change in consumption of good 1 following the change in price from P1 = 2 to pi = 4. . A'r] is the substitution effect. . A"r] is the income effect. Find Ari, A'r, and A" r1. j) (20 points) Represent on a graph: The three bundles, (of, 23). (af. of), and (rf, 25) . The initial budget constraint, the final budget constraint (with m and p, ), and the compensated budget constraint (with m' and p; ) . The approximate indifference curves passing through each bundles. They do not have to be mathematically exact, but be sure they make sense given Ike's consump- tion choices. . The total effect Ary, the substitution effect Ary, and the income effect ANTI. Be sure to show the important number on the axes.\f1. (89 points) Elasticity, Slutsky, compensating and equivalent variations Ike has utility function u (71,12) = 4142 where x, and 12 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 pi and p2. a) (4 points) Compute Ike's ordinary demand for good 1 and 2: r1 (p1, p2, m), x2(P1, P2, m). Show the main steps. (note, make sure this is correct as it will be used extensively in the following exercises) . b) (6 points) Compute Ike's i) own-price point elasticity of demand of good 1 (e1,1 ), ii) cross-price point elasticity of demand for good 2 with respect to the price of good 1 (61,2), iii) income point elasticity of demand of good 1 (label it 7, ). Use derivative for your calculations. Simplify as much as possible. Note: use derivatives. c) (5 points) Only based on your previous calculations at b), what do you conclude about the nature of goods 1 and 2 (ordinary / normal / inferior / Giffen / luxury / complement / substitute). Say as much as possible. d) (2 points) Ike's budget is m - 8 and the initial prices of goods 1 and 2 are p1 = 2, p2 - 2. How much is Ike consuming of good I and good 2? Label this initial consumption bundle (rf, 52). e) (2 points) If the price of good 1 doubles to p, = 4, what is Ike's new consumption bundle? Note it (xP. 52 )