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A monopolist faces a demand curve given by P = 10 - Q and has a constant marginal (and average)...

Question:

A monopolist faces a demand curve given by P = 10 - Q and has a constant marginal (and average) cost of $2. What is the economic profit made by this profit-maximizing monopolist?

a. $0

b. $12

c. $14

d. $16

e. none of the above

Profit:

The profit is the difference between the incomes earned and the costs incurred by the firm. The profits show that the firm should continue its operation in the market. The profits can be categorized as normal profit, economic profit, and accounting profit.

Answer and Explanation: 1

The correct answer is b. $12.

The total revenue and marginal revenue functions are:

{eq}\begin{align*} TR &= PQ\\ &= 10Q - {Q^2}\\ MR &= \dfrac{{\partial TR}}{{\partial Q}}\\ &= 10 - 2Q \end{align*} {/eq}

The profit maximizing price and quantity are determined below:

{eq}\begin{align*} MR &= MC\\ 10 - 2Q &= 2\\ Q &= 4\,{\rm{units}}\\ P &= \$ 6 \end{align*} {/eq}

The economic profit generated by the monopolist is:

{eq}\begin{align*} \pi &= TR - TC\\ &= \left( {6 \times 4} \right) - \left( {6 \times 2} \right)\\ &= \$ 12 \end{align*} {/eq}


Learn more about this topic:

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How to Calculate Economic Profit: Definition & Formula

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Chapter 3 / Lesson 11
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Learn what the definition of economic profit is, and understand how to calculate it using an equation.


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