19.4 Suppose a firm's costs for dollars spent on product differentiation (or advertising) activities (z) and quantity

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19.4 Suppose a firm's costs for dollars spent on product differentiation (or advertising) activities

(z) and quantity {q) can be written as TC = g(q) + z g'(q)>0, and that its demand function can be written as q=q{P,z).

Show that the firm's profit-maximizing choices for Pand z will result in spending a share of total revenues on z given by

(This condition was derived by R. Dorfman and P. Steiner in "Optimal Advertising and Optimal Quality," American Economic Review [December 1954]: 826-836.)

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