10.17. ADVERTISING COSTS. Consider the following model of entry into an advertising- intensive industry. To simplify the analysis, and to concentrate on the effects of adver- tising, suppose that there is no price competition. Specifically, the value of the market, in total sales, is given by S. (One can think of a demand curve D(p) and an exogenously given price, whereby S = p D(p).) S is therefore a measure of market size. Each firm must decide whether or not to enter the industry. Entry cost is given by F. If a firm decides to enter, then it must also choose how much to invest in advertising; let a; be the amount chosen by firm i. Finally, firm i's market share, s, is assumed to be equal to its share of the industry total advertising effort: a aj Si - A where n is the number of firms in the industry and A= 2-1 is total industry advertising. (a) Show that each firm i's optimal level of advertising solves S(A - 2)/A - 1 = 0. (b) Show that, in a symmetric equilibrium, a = S(n-1), where a is each firm's level of advertising. (c) Show that equilibrium profit is given by = S? - F. (d) Show that the equilibrium number of entrants is given by the highest integer lower than S/F. (e) Interpret this result in light of the previous discussion on the effects of endogenous entry costs. 10.17. ADVERTISING COSTS. Consider the following model of entry into an advertising- intensive industry. To simplify the analysis, and to concentrate on the effects of adver- tising, suppose that there is no price competition. Specifically, the value of the market, in total sales, is given by S. (One can think of a demand curve D(p) and an exogenously given price, whereby S = p D(p).) S is therefore a measure of market size. Each firm must decide whether or not to enter the industry. Entry cost is given by F. If a firm decides to enter, then it must also choose how much to invest in advertising; let a; be the amount chosen by firm i. Finally, firm i's market share, s, is assumed to be equal to its share of the industry total advertising effort: a aj Si - A where n is the number of firms in the industry and A= 2-1 is total industry advertising. (a) Show that each firm i's optimal level of advertising solves S(A - 2)/A - 1 = 0. (b) Show that, in a symmetric equilibrium, a = S(n-1), where a is each firm's level of advertising. (c) Show that equilibrium profit is given by = S? - F. (d) Show that the equilibrium number of entrants is given by the highest integer lower than S/F. (e) Interpret this result in light of the previous discussion on the effects of endogenous entry costs