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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