3. A monopolist can use one of two alternative production technologies. One production function is y = min(K/10, L/11). The other production function is y = min(K/20, L/2). The prices of capital, r, and of labor, w are r = 2 = $1. This means that the cost function for the first technology is Ci(y) = 21y and the cost function for the second technology is C2(y) = 22y. The demand function is given by: P(y) = 100-y. The un- regulated monopolist would of course use the first technology because it implies lower costs for any level of output. (a) Calculate the unregulated monopolist's output choice, price, and profit if it uses the first technology. (b) Consider rate of return regulation that allows the monopoly to take $0.1 profit per each $1 of capital expenditures. What would be the output, price, and profit under each technology? (c) Calculate total surplus in the unregulated monoopoly situation under the above regulation, and in a situation in which the firm is subject to the rate of return regulation but only the first technology is available