In their study of cigarette advertising, Roberts and Samuelson (1988) found that the advertising of a particular brand affects overall market demand for cigarettes but does not affect the brand’s share of market sales. Suppose the demand for brand i is q_i = a + b(A_i + A_j)^0.5, where A_i is brand i’s advertising expenditure. Brand i’s profit function is π_i = p_i (a + b(A_i + A_j)^0.5) - A_i.
a. Does brand B’s advertising expenditure affect A’s market share, q_A/(q_A + q_B)?
b. In terms of a and b, what are the Nash equilibrium advertising expenditures? How does an increase in b affect the equilibrium expenditures?