The inverse demand curve a monopoly faces is p= 130-Q The firms cost curve is C(q)=40+5Q What...

Question:

The inverse demand curve a monopoly faces is

p= 130-Q

The firms cost curve is

C(q)=40+5Q

What is the profit Maximizing solution ?

The profit-maximizing quantity is ?(Round your answer to two decimal places.)

The profit-maximizing price is $ (round your answer to two decimal places.)

What is the firms economic profit?

The firm earns a profit of ? ( round your answer to two decimal places)

Monopolist Profit Maximization:

Monopoly is the sole trader or producer of a good or service in the whole economy. Monopolist maximizes profit by restricting volume of output while selling at high price level. Monopolization through unfair competition is illegal in united states and would result to contravention of antitrust laws. Some monopolies still exist where provision of a good or service is impractical to be provided by multiple firms, for example, water and sewerage, electricity and railroads services.

Answer and Explanation:

The monopoly maximize profit by producing where marginal revenue (MR) is equal to marginal cost (MC). Use 'twice-as-steep' rule to get marginal revenue from inverse demand curve:

{eq}\begin{align*} P&=130-Q\\MR&=130-(2\times 1)Q\\MR&=130-2Q \end{align*} {/eq}

Take the first partial derivative of total cost function with respect to output Q to get the marginal cost:

{eq}\begin{align*} C&=40+5Q\\\displaystyle MC&=\frac{\partial C}{\partial Q}: 5\\\therefore MC=$5 \end{align*} {/eq}

Equate marginal revenue with marginal cost and solve for output Q that maximizes monopoly's profit:

{eq}\begin{align*} 130&-2Q=5\\125&=2Q\\Q&=62.50\,\text{units.} \end{align*} {/eq}


Plug in the quantity that maximizes profit into the inverse demand function and solve for price:

{eq}P=130-(62.50)\\P=$67.50 {/eq}


Profit is the difference between total revenues (TR) and total cost (TC). Multiply price by quantity to get total revenue:

{eq}\begin{align*} TR&=P\cdot Q\\&=$$67.50\times 62.50\\&=$4218.75 \end{align*} {/eq}

Plug in the output into the cost function and solve for total cost:

{eq}\begin{align*} TC&=40+5(62.50)\\&=$352.50 \end{align*} {/eq}

Now calculate the profit:

{eq}\begin{align*} \prod&=TR-TC\\&=$4218.75-$352.50\\&=$3866.25 \end{align*} {/eq}


Learn more about this topic:

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Natural Monopoly in Economics: Definition & Examples

from Intro to Business: Help and Review

Chapter 3 / Lesson 13
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