Consider a perfectly competitive economy with a single consumption good, X, and two factors of production: labor, L, and capital, K. The production function of a representative firm is X = K1/2 /1/2. As in the model explained in class, there are two types of agents: workers and capitalists. Assume that labor supply is infinitely inelastic at the quantity L=1. There is one capitalist in the economy (that behaves in a "perfectly competitive" way). Her endowment of k is k = 100, and her utility function is given by u(c, kc) = c+ Log[kc], where c is consumption of X (price of X is 1) and k. her "consumption" of k, i.e. the amount of capital that she keeps. Assume that an ad- valorem tax on capital incomes (paid by the capitalist) of 7=0.25 (25%) is established. Thus, the budget constraint of the capitalist is c = (100-k.) r(1-7), where r is the return to capital. The government transfers the whole tax revenue to the worker . 1) Find the wage rate, the price of capital r and the amount of capital used by firms when 7=0