Consider the following game. e At t=0 Uh-Oh Insurance Company makes a one-time take-it-or-leave-it employment offer to a prospective hire. The offer promises to pay a first year salary of s > 0 regardless of effort. The prospective hire can either accept the salary and begin working or reject it and seek employment elsewhere. Currently the prospective hire has no other offers, so assume their reservation salary (the minimum offer needed to incentivize work) is zero. e At t=1 the employee, if they have accepted the salary offer, will begin work. They will provide a quality of work w > 0 that will lead to firm profits for Uh-Oh Insurance Company. Those profits accrue for the firm according to the function 7y = Aw s and income accrues to the employee according to the function Ty = 8 ax2w2 .Assume that A > 0 and @ > 0. This is a one-shot game where firms and employees match for a single negotiation, then must move on in the next period (regardless of whether the offer is accepted or rejected). A. Solve for the selfish sub-game perfect equilibrium (wage offer and effort level) of this game where the worker only cares about their income and the firm only cares about their profits. (1/2 point) B. Solve for the socially efficient wage offer and effort level. By socially efficient we mean the wage and effort levels that maximize the joint profits of the firm and their prospective hire. Describe and explain how this answer compares to what you found in part (A). (1/2 point)