# Answer on Microeconomics Question for Manisha

Question #41650

Bringing Up Baby has a monopoly in the production of step-by-step manuals for child rearing. Its total cost of producing manuals is given by TC = 12.5Q, and the demand for manuals is given by the non-linear demand, Q = 25,000P –2.

Calculate the profit maximizing price and quantity of manuals

Calculate the profit maximizing price and quantity of manuals

Expert's answer

TC = 12.5Q, Q = 25,000/P^2, P = (25,000/Q)^0.5

Profit maximizing quantity of manuals can be found in the point, where marginal revenue equals marginal cost (MR = MC) and the price can be found from the demand curve at this quantity.

MC = TC' = 12.5

MR = TR' = (P*Q)' = ((25,000/Q)^0.5*Q)' = (158.11Q^0.5)' = 79.06/Q^0.5

MR = MC, so:

79.06/Q^0.5 = 12.5

Q = (79.06/12.5)^2 = 40 units - profit-maximizing quantity

P = (25,000/40)^0.5 = $25 - profit-maximizing price.

Profit maximizing quantity of manuals can be found in the point, where marginal revenue equals marginal cost (MR = MC) and the price can be found from the demand curve at this quantity.

MC = TC' = 12.5

MR = TR' = (P*Q)' = ((25,000/Q)^0.5*Q)' = (158.11Q^0.5)' = 79.06/Q^0.5

MR = MC, so:

79.06/Q^0.5 = 12.5

Q = (79.06/12.5)^2 = 40 units - profit-maximizing quantity

P = (25,000/40)^0.5 = $25 - profit-maximizing price.

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