Question

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 $1 billion in profits. When neither company advertises, each company earns profits of $9 billion. If one company advertises and the other does not, the company that advertises earns $49 billion and the company that does not advertise loses $4 billion. For what range of interest rates could these firms use trigger strategies to support the collusive level of advertising?

Answer 1

Answer:

for interest rates equal to or lower than 200%, the firms will use trigger strategies to support the collusive level of advertising

Explanation:

Using the below expression to determine the range of interest rates could these firms use trigger strategies to support the collusive level of advertising; we have:

$\frac{current \ period's \ profit \ of \ the \ cheating \ firm \ - \ firm's \ profit \ in \ each \ period \ under \ collision }{ firm's \ profit \ in \ each \ period \ under \ collision \ - \ profit \ in \ each \ subsequent \ period \ of \ cheating \ firm } \leq \frac{1}{i}$

where;

$the \ current \ period's \ profit \ of \ the \ cheating \ firm \ = \ 49$

$firm's \ profit \ in \ each \ period \ under \ collision = \ 9$

$\ profit \ in \ each \ subsequent \ period \ of \ cheating \ firm } = \ 1$

Then :

= $\frac{49-9}{9-1} \leq \frac{1}{i}$

= $\frac{40}{8} \leq \frac{1}{i}$

$i \leq \frac{8}{40}$

$i \leq 200$%

Thus; for interest rates equal to or lower than 200%, the firms will use trigger strategies to support the collusive level of advertising