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Define Q to be the level of output produced and sold, and assume that the firm's cost function is given by the relationship:

TC = 20 + 5Q + Q^2 (Q is squared)

Furthermore, assume that the demand for the output of the firm is a function of price P given by the relationship:

Q = 25 - P

1. Define total profit as the difference between total revenue and total cost, and express terms of Q the total profit function for the firm. (Note: Total revenue equals price per unit times the number of units sold.)

2. Determine the output level where total profits are maximized.

3. Calculate total profits and selling price at the profit-maximizing output level.

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Solution Summary

Calculate total profits and selling price at the profit-maximizing output level.

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Update: If the fixed cost increases from $20 to $25 in the above equation, it will not change the profit maximizing output quantity, but will reduce the total profit by $5 (so total profit will now be $25]

You can put in 25 in the cost equation and follow the steps I took. Your answers should be:

Q = 5
P = 20
Total Profit = $25

Define Q to be the level ...

Solution provided by:
Gaurav Agarwal, MS
Education
  • BE, Bangalore University, India
  • MS, University of Wisconsin-Madison
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