# Calculating Profit Maximization & Cost Function

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

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#### Solution Preview

See the attached file for complete solution. The text here may not be copied exactly as some of the symbols / tables may not print. Thanks

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

"

Firm 1 Firm 2 Firm 3

Price Demand TR TC Profit Price Demand TR TC Profit Price Demand TR TC Profit

$- 1,000 $- $9,000 $(9,000) $- 1,000 $- $8,000 $(8,000) $- 1,000 $- $10,000 $(10,000)

$1.00 960 $960 $8,800 $(7,840) $1.00 960 $960 $7,800 $(6,840) $1.00 960 $960 $9,720 $(8,760)

$2.00 920 $1,840 $8,600 $(6,760) $2.00 920 $1,840 $7,600 $(5,760) $2.00 920 $1,840 $9,440 $(7,600)

$3.00 880 $2,640 $8,400 $(5,760) $3.00 880 $2,640 $7,400 $(4,760) $3.00 880 $2,640 $9,160 $(6,520)

$4.00 840 $3,360 $8,200 $(4,840) $4.00 840 $3,360 $7,200 ...

#### Solution Summary

Shows how firms set the profit maximizing price and how different cost structures may affect their vulnerability to price war.