In some economies there is an arrangement for capital ownership and use so that the companies rent the means of production from the rental companies that own them. There is perfect competition in the rental market.

The rental price per unit of funds is L. The leasing companies buy each unit of capital at the price P. The real interest rate is r and the depreciation rate is d. The production function is Y = square root (KN) where K is the capital stock and N is the number of workers. Salary is W. There is perfect competition in the product market and the profit of the manufacturing companies is H = P * Y - W * N - L * K

a. Find the desired capital stock from the perspective of the producing firms as a function of L, P, and N. (Hint: Plug the formula for Y into the profit function and differentiate to find the first-order condition for the maximum. Solve for Kd.) b. Find the rental price of capital, L, in competitive equilibrium as a function of r, d, and P. c. Use the results of I and II to find the long-term value of the capital stock K as a function of r, d and N.