A monopoly’s demand function is given by: P = 800 4Q + 0.2A^0.5 where Q is quant

Question

A monopoly’s demand function is given by: P = 800 4Q + 0.2A^0.5 where Q is quantity and A is the level of advertising. Its marginal cost of production is constant at 2 and its cost for a unit of advertising is 1. What are the firm’s profit-maximizing price, quantity and level of advertising?ere Q is quantity and A is the level of advertising. Its marginal cost of production is constant at 2 and its cost for a unit of advertising is 1. What are the firm’s profit-maximizing price, quantity and level of advertising?

Explanation / Answer

P = 800 4Q + 0.2A^0.5

TR = 800Q - 4Q^2 + 0.2QA^0.5

MR = 800 - 8Q + 0.2A^0.5

MC = 2

Advertising cost per unit = 1

TC = 2Q + Q = 3Q

At profit maximising level,

MR = MC

800 - 8Q + 0.2A^0.5 = 3

or, 800 - 8Q + 0.2 = 3

or, Q = 99.65

P = 401.6

Level of advertising = 99.65

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