Problem 1: Remember that even if firms have differentiated products in a duopoly model, they are engaged
in price competition. The regular offering of sale prices by these firms for many of their products
provides this evidence. Suppose that we have two dominant firms that simultaneously announce
one of two prices for a given product: a regular price or a sale price. Suppose that when one firm
announces the sale price and the other announces the regular price for a particular product, the
firm announcing the sale price attracts 1,000 extra customers to earn a profit of $5,000, compared
to the $3,000 earned by the firm announcing the regular price. When both firms announce the
sale price, the two firms split the market equally (each getting an extra 500 customers) to earn
profits of $2,000 each. When both firms announce the regular price, each company attracts only
its 1,500 loyal customers and the firms each earn $4,500 in profits. If you oversaw pricing at one
of these firms, would you have a clear-cut pricing strategy? If so, explain why. If not, explain why
not and propose a mechanism that might solve your dilemma.
Problem 2:
At a time when demand for ready-to-eat cereal was stagnant, a spokesperson for the cereal maker
Kellogg’s was quoted as saying, “ . . . for the past several years, our individual company growth
has come out of the other fellow’s hide.” Kellogg’s has been producing cereal since 1906 and
continues to implement strategies that make it a leader in the cereal industry. Suppose that when
Kellogg’s and its largest rival advertise, each company earns $0 in profits. When neither company
advertises, each company earns profits of $12 billion. If one company advertises and the other
does not, the company that advertises earns $52 billion and the company that does not advertise
loses $4 billion. Under what conditions could these firms use trigger strategies to support the
collusive level of advertising?