Consider a Monopolist that is facing the market demand function Q = 400 (1/2)p, where Q is total quantity demanded and p is the price that the monopolist charges per unit of output (in dollars). The monopolist has the cost function c(y) = y, which is the minimum level of ccsts for producing y units of output. a) In a diagram with dollars on the vertical and output on the horizontal, plot the market demand function, the monopolist's marginal function and the monopolist's marginal revenue function. b) Find the monopolist's profit maximizing level of output ym and the monopoly price pm. c) Calculate the monopolist's profits (i.e. producer's surplus). Choose any other arbitrary y ym and show that profits are larger under ym compared to y. d) Calculate Consumers' surplus, and the dead-weight of the monopoly. e) Suppose that the monopolist was forced to operate as a competitive firm. How much output would she produce? Calculate Producer's and Consumers' surplws under this assumption. f) Redo the question under the assumption c(y) =