Question A

Rob lives in a three-good world. For each period t = 1, 2, 3, you observe the price vector pt = (135,233,193) that prevails in that period and the consumption bundle 33* = ($5,313,333) chosen by Rob in that period: 391 = (1,1,2), m1=(5,19,9), :92 = (1,1,1), m2=(12,12,12), :93 = (1,2,1), m3=(27,11,1). (a) Does Rob's behaviour satisfy the Strong Axiom of Revealed Preference (SARP)? (b) Does Rob's behaviour satisfy the Weak Axiom of Revealed Preference (WARP)? A price-taldng rm producing a single product according to the production function y = f(:r:1, 32) faces price p for its output and prices 131,102 for its inputs. Assume that HI], 0} = 0 and that f is strictly,r increasing, strictly concave, twice dierentieble, and such that for all $1,:G'2 3v 0. Let 31(p,w1,w2}end $2@,W1,w2} be the rm's unconditional demand functions for inputs 1 and 2. Prove that the demand for input 1 is increasing in the price of input 2, that is, 3:1: 1(p! ml. I 1'92) } D 3102 for all 31,32 3 0. You may use without proof the fact that the demand for input 2 is decreasing in its own price, that is, an 811,2(33, 101,113.12) 4 0