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6. Suppose that De Beers is a single-price monopolist in the market for diamonds. De Beers has five potential customers: Raquel, Jackie, Joan, Mia, and Sophia. Each of these customers will buy at most one diamond—and only if the price is just equal to, or lower than, her willingness to pay. Raquel’s willingness to pay is $400; Jackie’s, $300; Joan’s, $200; Mia’s, $100; and Sophia’s, $0. De Beers’s marginal cost per diamond is $100. This leads to the demand schedule for diamonds shown in the accompanying table. Price of Quantity of Diamonds diamond &nb sp; demanded $500 &n bsp; 0 400 &nb sp; 1 300 &nbs p; 2 200&n bsp; 3 100 & nbsp; 4 0 &nb sp; 5 a. Calculate De Beers’s total revenue and its marginal revenue. From your calculation, draw the demand curve and the marginal revenue curve. b. Explain why De Beers faces a downward-sloping demand curve. De Beers faces a downward sloping demand curve because the willingness to pay for diamonds decreases as the price of the diamond increases. This is typical of monopoly markets where a monopolist must set a lower price in order to sell more output c. Explain why the marginal revenue from an additional diamond sale is less than the price of the diamond The monopolist’s downward-sloping demand curve means that it can increase sales only by charging a lower price. Consequently, marginal revenue is less than price (average revenue) for every level of output except the first. This is because the lower price applies not only to the extra output sold but also to all prior units of output. The monopolist could have sold these prior units at a higher price if it had not produced and sold the extra output. Each additional unit of output sold increases total revenue by an amount equal to its own price less the sum of the price cuts that apply to all prior units of output. d. Suppose De Beers currently charges $200 for its diamonds. If it lowered the price to $100, how large is the price effect? How large is the quantity effect? Moving from $200 to $100, one incremental diamond will be sold (though total revenue will decrease from 600 to 400) e. Draw the marginal cost curve into your diagram and determine which quantity maximizes De Beers’s profit and which price De Beers will charge. 2 diamonds is the profit maximizing quantity at a price of $300