Suppose we have an economy which lasts only for one period. There are N individuals of each of two types. There is a single good produced (coconuts). There is no money. Because of these assumptions, there will be no trade in the goods market. (And there will be no credit market whatsoever.) This is essentially a big, N-person Robinson Crusoe setting in which everyone minds their own business, producing and consuming but not trading with others. Type 1 individuals have production functions given by Type 1 individual : fe(n1) = 0 + B1, Vnl : 01, B1 > 0 Type 2: individual : (n2) = 02 + B2 Vn2 : 0, B2 > 0 Individuals have preferences over consumption (c) and leisure ( = 1-n) that give rise to utility (V), represented by the following utility functions: with 8 V2 = c with y > 0 We begin by assuming that a, their technologies but not their preferences. az and B, > B, and 8 = y, so the two types of individuals differ by Now suppose we introduce a labor market, in which individuals can sell their labor services to "firms", where firms are just individuals who wish to buy the labor services of other individuals. The labor market is competitive despite differences in production functions, all jobs are equally (un)desirable and all individuals selling their labor services offer the same quality of labor services. so all economic agents view the real wage () as given. Furthermore, b) Let 7, be the profits for an individual firm with production function f. By solving the individual firm's profit-maximization problem, compute the labor demand for each type of firm as a function of the real wage, ).