Question

Monopoly ABC is asking you to perform some calculations to determine its profit at the profit maximizing quantity. The equation of demand for the monopoly is P = 109 - 3Q. The TC function = 30 + 3Q. The MR function = 109 - 6Q. Let us assume constant MC at $3. (Note that P = price, Q = quantity, MR = marginal revenue and MC = marginal cost.). For Monopoly ABC calculate the profit (or loss) at the profit maximizing quantity. Please ensure that you show detailed calculations.

Answer 1

A profit maximizing monoply always produces at the point where MR = MC and sets it's profit maximizing price at the point where profit maximizing quantity lies on the demand curve.

Therefore, setting MR = MC we get,

109 - 6Q = 3

Or, 6Q = 106

Or, Q = (106/6)

From the demand equation we get, when Q = (106/6),

P = 109 - 3(106/6) = 109 - 53 = $56

Total revenue = price * quantitity = $(56) * (106/6) = $989.33

At Q = (106/6), TC = 30 + 3(106/6) = 30 + 53 = $83

Profit = TR - TC = $(989.33 - 83) = $906.33