Please be detailed. Answer question 2 only. Contains all information needed

Question 2: Spanofcontrol with Capital Suppose we add capital to the model: Y; = Alf-\"(K'le'aT' for each firm i E [0.1]. Assume firms hire workers at wage w and rent capital at price R. Assume A, ~ U[O,1] Derive the profit of rm i as a function of managerial ability, wages, and rental prices In. Suppose total capital and total labor are fixed (no free entry into entrepreneurship): I; X, (if = K and I; Lidi = L. Derive an expression for Y = I011} di as a function of K and L. That is, derive the aggregate production function. c. Suppose total capital and labor are NOT fixed, but instead that there is free entry into entrepreneurship. lfthev are a worker, they supply 1 infinitesimal unit of capital to the entrepreneurs in return for rental price R, and 1 infinitesimal unit of labor in return for the wage w. Write down the three equations you would have to solve to find the number of workers, the equilibrium wage, and the equilibrium rental price. (You do NOT have to solve the equations} .._-a.:__ '1.II__I_..-a.___I:.__.|.l__I_-___.I. -1' H:-.|._..a.:__