microeconomics, homework, models, utility-functionI’m attempting to answer the question, but am having a great difficulty setting up the equations. I tried to set it up as an utility maximization problem with the budget constraint equal to initial endowment plus a portion of profit $(P_yX^a - P_xX)$, but that didn’t seam to work. Any help would be appreciated.
Consider a two-commodity, productive economy of n individuals, each with preferences over the two commodities represented by $u(x,y)=xy$. The individuals are co-owners of a single firm whose production function is given by $y=x^a$, $a \in (0,1)$. In addition to an intiial endowment of one unit of x, individual i recieves a fraction $B_i \in (0,1)$ of the firm’s profit. All profit is distributed. With the price of x set equal to one, show that $P_y = [n^{(1-a)}][(1+a)^{(a-1)}]a^{-a}$
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