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# Determining Profit Maximizing Price

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Suppose there are three firms with the same individual demand function. This function is Q=1,000-40P. Suppose each firm had a diffeerent cost function these functions are: Firm 1: 4,000+ 5Q
Firm 2: 3000 + 5Q
Firm 3: 3,000 + 7Q

What price should each firm charge if it want to maximize its profit or minimize its loss

Why the answer to the preceding question indicates that two of the of the firms should charge the same price and the third should charge a higher price?

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

Please show all work for a complete understanding of this problem .

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#### Solution Preview

Solution:

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

Firms sets their output such that MR=MC to maximize their profits.
We are given demand function as
Q=1000-40P

rewriting it we get
P=(1000-Q)/40
Total Revenue =TR=P*Q=(1000-Q)/40 * Q = 25Q -Q^2/40
Now we need to calculate Marginal Revenue i.e. MR
MR= dTR/dQ = 25 - 2Q/40

Now Calculate the MC. MC=dC/dQ
Firm 1: ...

#### Solution Summary

Solutions describes the steps to calculate profit maximizing price for the given firms. It also discusses the reasons for differences in prices.

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