# calculate demand and price for two different demand functions that have the same cost function

I need to know how to calculate demand and price for two different demand functions that have the same cost function.

P1 = 20 - .0125Q1

P2 = 40 - .025Q2

ATC = MC = 3.00.

How do I calculate the price and quantity for each? How does ATC/MC factor into the price/quantity estimate?

What is the economic profit for each?

Thanks

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#### Solution Preview

For the first demand, the firm's total revenue is

TR = Q1*P1 = (20 - .0125Q1)*Q1 = 20 Q1 - .0125Q1^2

Then the Marginal revenue is

MR1 = dTR / dQ1 = 20 - .025Q1

we know that ...

#### Solution Summary

The economic profit for each is given. The different demand functions that have the same cost function is analyzed.

Profit Maximization

Suppose there are three firms with the same individual demand function. This function is Q = 1,000 - 40P. Suppose each firm has a different cost function. These functions are:

Firm 1: 4,000 + 5Q

Firm 2: 3,000 + 5Q

Firm 3: 3,000 + 7Q

a) What price should each firm charge if it wants to maximize its profit (or minimize its loss)?

b) Explain why the answer to the preceding question indicates that two of the firms should charge the same price and the third should charge a higher price?

c) Which firms will be most vulnerable to a price war? Explain

Calculating Profit Maximization & Cost Function

Suppose there are three firms with the same individual demand function. This function is Q = 1,000 - 40P. Suppose each firm has a different cost function. These functions are:

Firm 1: 4,000 + 5Q

Firm 2: 3,000 + 5Q

Firm 3: 3,000 + 7Q

NOTE*

On this problem you are given the demand function (Q=1000-40P). Use pricing in whole dollar increments from $0 - $20, solve for Q. MAKE THIS INTO A TABLE AND ALSO INCLUDE TR IN THAT TABLE.Using the quantities that you just determined, determine TC for the first firm. Then do the same for firms 2 and 3. Since you now know TR and TC, you can determine the profit/loss at each level of output, and can now identify the maximum profit points for each firm (part a).

a) What price should each firm charge if it wants to maximize its profit (or minimize its loss)?

b) Explain why the answer to the preceding question indicates that two of the firms should charge the same price and the third should charge a higher price?

c) Which firms will be most vulnerable to a price war? Explain