Exercise – Markets for differentiated Products

Suppose there are only two firms selling coffee, called firm 1 and 2.

Let αi denote the advertising level of firm i, i=1,2. Assume that the

profits of the firms are affected by the advertising levels taken by

the firms. Formally, assume that

Calculate and draw the best-response function of

each firm. That is, for any given advertising level of

firm j, find the profit-maximizing advertising level of

firm i.

That is each firms selects its optimal advertising level, α1 and α2 respectively. Firm 1’s maximization problem:

Infer whether the strategies are strategically

complements or strategically substitutes

Since the BRF are upward sloping then

the strategies are strategically

complements. That is, if Firm 1

increases the advertising level, then

Firm 2 also increases its advertising.

Find the Nash equilibrium advertising levels.

Also, calculate the firm’s Nash equilibrium

profit levels.