# Maximizing Profit with Calculus: Understanding the Profit Formula

• xmf77
In summary, the conversation discusses finding the profit-maximizing price for a monopolist's product, given a demand equation and average-cost function. The formula for profit is mentioned, but the speaker is having trouble substituting numbers and asks for help. The question of whether 'q' represents quantity and 'p' represents price is raised, and the speaker is reminded to include the quantity multiplier in their substitution.
xmf77
Homework Statement
For a monopolist's product,

the demand equation is

p=30−2q

and the average-cost function is

c=2+40q.

Find the profit-maximizing price.
Relevant Equations
Calculus, maximizing, profit, price
I know the formula profit = (price-cost)quantity.
but when ı applied the numbers ı can not substitute them
profit = ((30-2q-2-(40/q))

but don't know what ı need to do ?
would appreciate any help given please.

xmf77 said:
Homework Statement:: For a monopolist's product,

the demand equation is

p=30−2q

and the average-cost function is

c=2+40q.

Find the profit-maximizing price.
Relevant Equations:: Calculus, maximizing, profit, price

I know the formula profit = (price-cost)quantity.
but when ı applied the numbers ı can not substitute them
profit = ((30-2q-2-(40/q))

but don't know what ı need to do ?
would appreciate any help given please.
You need to express your profit equation in terms of price, not in terms of demand.

İs there anyone?

Is 'q' quantity? Is 'p' price? Did you include the quantity multiplier in your substitution into the profit equation?

## 1. What is "Calculus Maximizing Profit"?

Calculus Maximizing Profit is a mathematical concept used in economics to determine the optimal level of production for a business in order to maximize profits.

## 2. How is "Calculus Maximizing Profit" calculated?

The calculation involves taking the derivative of the profit function with respect to the variable being optimized (usually the quantity of production) and setting it equal to zero. The resulting value is then plugged into the original profit function to find the maximum profit.

## 3. What are the assumptions made in "Calculus Maximizing Profit"?

The main assumptions are that the cost and revenue functions are continuous and differentiable, and that the market is perfectly competitive with no external factors affecting the price.

## 4. Can "Calculus Maximizing Profit" be applied to any business?

Yes, the concept can be applied to any business that operates in a competitive market and has a profit function that is continuous and differentiable.

## 5. Are there any limitations to using "Calculus Maximizing Profit" in business decision making?

While it is a useful tool, it does have limitations. It assumes that all costs and revenues are known and can be accurately predicted, which may not always be the case. It also does not take into account other factors such as market demand and competition, which can also impact profits.

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