Question: Assume that the demand for diamond rings is Q = 24 - P, and each ring contains one diamond. The marginal cost for DeBeers of mining a diamond is $2, and an independent retailer's marginal cost of retailing is $4. If DeBeers did its own retailing, its costs would be $8 per ring (plus $2 for the diamond). Neglect any fixed costs.
a. [Required calculus] Show that If DeBeers deals with independent retailers it sells them nine diamonds at $11 each, for a profit of $81. Then show that if the company does its own retailing it sells five rings at $19 each, for a profit of $45.
b. How will your analysis of this problem change if DeBeers must deal with a monopoly retailer? Is it more or less likely that DeBeers will wish to go into retailing?
c. DeBeers actually operates 39 retail shops, all at very affluent locations like Fifth Avenue in New York and Boulevard Haussmann in Paris. Why might it market its own diamonds and jewelry in these neighborhoods but not others?