I. (Representative Consumer Utility Maximization with Quasilinear Quadratic Utility (and Linear Demand System) Consider a representative consumer with the following quasi-linear utility function over three goods: U010. 91: Q2) : (10 + @1611 + 06292 - [6197? + 2791972 + Emil/2: with 051' > 0, 5?; > 0, and 61/82 72 > 02 where go is the numeraire good. (Note: If the parameters make your calculations too tedious= you may assume some specic parameter values for simplicity. For instance, you may set Ozi : )8:- : 1 but keep 7.) 1. Derive the consumer's demands for goods 1 and 2 (both direct and inverse demand systems). . How should we parameterize the demand system in order to measure the degree of substitution / complementarity between the two goods (or the degree of prod- uct differentiation)? For instance, we can use 7 as an independent parameter, or set 61 : 62 = 1 7. Discuss your reasoning. . Derive the consumer's surplus (or indirect utility as a function of prices). . Suppose two rms produce these two goods at constant marginal cost c1 and c2, respectively. Compute the Bertrand-N ash equilibrium when the rms compete by setting prices simultaneously. Determine their own and cross costpass through (CPT) rates (i.e.= how the equilibrium prices change with respect to costs, respectively). Explain. . Suppose the two rms merge to become a monopolist over the two products (or they collude in setting prices). Compute the jointprotmaximizing prices as well as own and cross cost-passthrough (CPT) rates. Explain. . Compare the prices from (d) and (e) and explain the result