# How to Find Monopoly Profit Maximizing Price, Quantity, and Profit

for a monopolistically competitive firm, at the profit-maximizing quantity of output, This is a topic that many people are looking for. star-trek-voyager.net is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, star-trek-voyager.net would like to introduce to you How to Find Monopoly Profit Maximizing Price, Quantity, and Profit. Following along are instructions in the video below:

“In this video. We re gonna do a standard monopoly profit. Maximization. Problem a monopoly.

Monopoly. Faces an inverse market demand of. Price equals. 100 minus.

0375. Q. And its cost of production is given by. C.

Equals 1200 plus. 0125. Q..

. Squared. So we want to solve for the monopolist profit maximizing price quantity and level of profit. So we re going to set up a profit function. Pi represents profit profit is total revenue minus total cost where total revenue is the price times.

The quantity so moving on the next. Step what is price price is 100 minus 0375. Q. So that s prices in parentheses.

Right here and then we have this being all multiplied through by q and then total cost so we re going to subtract out the fixed cost of 1200 and then we need to subtract out the variable costs as well the 0125. Q. Squared all right simplifying. I m just gonna take this q and multiply through by what s in parentheses.

To leave us this step and the next thing. I m gonna do i m gonna add these q squared terms. I m gonna add these two terms over here and we have profit equals..

. 100. Q minus. 05. Q.

Squared minus 1200 rewriting that last step and we re gonna maximize this equation. So we re gonna take the derivative of the profit function with respect to. Quantity so the derivative of. 100.

Q is. 100 the derivative of minus. 05. Q.

Squared is just. Minus. Q i..

. Bring this 2 down in. Front so 2 times. 05. Is just 1.

We ve got the minus in front. Here. So. It s just minus 1.

And then the exponent here. 2. Minus. 1.

On the exponent. Just leaves. Q..

. Raised to the power of 1 or just write. It as cute since we re maximizing we set this equal to 0. So we re gonna solve this for q by q to both sides and q equals a hundred so that is a profit maximizing output to get the profit maximizing price. We re gonna take this q of a hundred and plug it into the inverse market demand inverse market demand given on the last slide.

What s this where we have the q. We will now plug in 100. So then profit maximizing price here is sixty two dollars and fifty cents and now to get the level of profit rewriting our profit equation and just plugging in for q. We re gonna plug in 100 and simplifying.

This this monopolist has a positive profit of three thousand eight hundred dollars. Okay. I hope you found this video helpful. ” .

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