Question

The inverse demand curve a monopoly faces is p equals 15 Upper Q Superscript negative 0.5. What is the​ firm's marginal revenue​ curve? Marginal revenue​ (MR) is MRequals 7.5 Upper Q Superscript negative 0.5. ​(Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts.​ E.g., a superscript can be created with the​ ^ character.) The​ firm's cost curve is Upper C left parenthesis Upper Q right parenthesis equals 5 Upper Q. What is the​ profit-maximizing solution? ​ (Round all numeric to two decimal​ places.) The​ profit-maximizing quantity . The​ profit-maximizing price is ​$

Answer 1

Demand is given by : p = 15Q^-0.5

TR = Total revenue = pQ = 15Q^+0.5

MR = Marginal Revenue = d(TR)/dQ = 0.5*15Q^-0.5 = 7.5Q^-0.5

=> MR = 7.5Q^-0.5

In order to maximize profit a monopolist produces that quantity at which MR = MC

where MC = Marginal Cost = dC/dQ. Here, C(Q) = 5Q

=> MC = dC/dQ = 5

Thus, MR = MC => 7.5Q^-0.5 = 5

=> Q = 2.25

=> P = 15Q^-0.5 = 15*2.25^-0.5 = 10

Hence, The​ profit-maximizing quantity = 2.25 . The​ profit-maximizing price is ​$10