describe how (it at all) the solution when homogeneous good price competition takes place sequentially 3. There are two consumers who have quasilinear preferences represented by utility functions "(x. m) = avxi + m, and u2(x2, my) = 02 \\x2 + m2. We are given that az > aj. x is sup- plied by a monopolist that faces constant marginal cost, c. (a) First, assuming that the monopolist can engage in third degree price discrimination, solve for the profit-maximizing prices charged and relate the markups charged to the demand elasticity of each consumer. Determine whether each consumer achieves higher or lower utility under common pricing or under third-degree price discrimination. In general, are consumers always weakly better or worse off (or neither) under third-degree price discrimination as compared to standard monopoly pricing? Are consumers always weakly better or worse off (or neither) under third-degree price discrimination as compared to competitive market pricing? Be sure to justify your responses. (b) Next, consider the general case covered in class in which there are two consumer types with con- sumer 2 having higher utility and marginal utility of consumption at each quantity level. Suppose the monopolist engages in second degree price discrimination by offering two price-quantity packages for purchase. Write down and provide intuition for the two individual rationality con- straints and the two incentive compatibility constraints, and show rigorously which of these four constraints will bind (if any) when the firm chooses price/quantity bundles to maximize profits (again, this derivation needn't be specific to the utility functions given above). Finally, comment on whether the solution to (a) provides any information that can be used to simplify this general 1. degree price discrimination. Be sure to justify your resh