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a. [This question is about a domestic monopolist.] Suppose that the market demand of a product faced by a monopolist is given by q = 50 - p, where is the market demand and p the market price. Determine the marginal revenue (MR). Show the demand curve and the marginal revenue curve in a diagram. Can you give an economics intuition of why for any positive output level MR is less than the price? [Invert the demand function so that you express the price in terms of quantity. Multiply the price by quantity to get revenue. Differentiate the revenue to get marginal revenue.) b. Suppose that the marginal cost MC of monopolist is given by MC = 2 + q. Assuming the market demand (and thus the marginal revenue) in the previous exercise, derive the optimal output level of the monopolist. For this output, what is the market price charged by the monopolist? What is the competitive price [denoted by pc in the class and lecture notes.]? c. Suppose now that the economy trades freely without any transport costs with the rest of the world under a given world price, pw = 34. Determine the domestic demand, output of the monopolist, and volume of export or import. d. Suppose that the local government does not allow any import while permitting free export of the product. Let the world price be pw = 34 and use the monopolist given in the previous exercise. Calculate the domestic demand, output of the monopolist, and volume of export or import