SOLUTION: Karen runs a print shop that makes posters for large companies. It is a very competitive business. The market price is currently $1.00 per poster. She has fixed costs of $500.00. H
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Question 998970: Karen runs a print shop that makes posters for large companies. It is a very competitive business. The market price is currently $1.00 per poster. She has fixed costs of $500.00. Her variable costs are $1,500 for the first thousand posters, $1,200 for the second thousand, and then $800 for each additional thousand posters.What is her ATC per poster if she prints 1,000?
What is her ATC per poster if she prints 2,000?
What is her ATC per poster if she prints 10,000?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
her revenue is 1 dollar * the number of posters she sells.
her cost will vary depending on the number of posters she prints.
her costs are:
500 fixed.
1500 for the first 1000 posters / 1000 = 1.5 for each poster.
1200 for the second 1000 posters = 1.2 for each poster.
800 for each additional 1000 posters above 2000 / 1000 = .8 for each poster.
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if she prints 1000 posters, her total cost will be:
500 + 1000 * 1.5 which becomes:
500 + 1500 which becomes:
2000.
her total cost is 2000 if she prints 1000 posters.
500 is her fixed cost.
1500 is the cost for the first 1000 posters.
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if she prints 2000, her total cost will be:
500 + 1.5 * 1000 + 1.2 * (2000 - 1000) which becomes:
500 + 1500 + 1.2 * 1000 which becomes:
500 + 1500 + 1200 which becomes:
3200.
her total cost is 3200 is she prints 2000 posters.
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if she prints 10,000, her total cost will be:
500 + 1.5 * 1000 + 1.2 * 1000 + .8 * (10,000 - 2000) which becomes:
500 + 1500 + 1200 + .8 * (8000) which becomes:
500 + 1500 + 1200 + 6400 which becomes:
3200 + 6400 which becomes:
9600
her total cost is 9600 if she prints 10,000 posters.
500 is her fixed cost.
1500 is the cost for the first 1000 posters.
1200 is the cost for the next 1000 posters.
6400 is the cost for the last 8000 posters.
her average cost is calculated as follows:
if she prints 1000 posters, her average cost is 2000 / 1000 = 2 dollars per poster.
if she prints 2000 posters, her average cost is 3200 / 2000 = 1.6 dollars per poster.
if she prints 10,000 posters, her average cost is 9600 / 10,000 = .96 dollars per poster.
if she can only make 1 dollar per poster, she's losing money unless she sells something very close to 10,000 posters.
THE FOLLOWING IS EXTRA THAT I DON'T THINK YOU NEED TO KNOW TO SOLVE YOUR PROBLEM, BUT IT IS INTERESTING TO SEE HOW THE BREAK EVEN POINT WOULD BE CALCULATED IN THIS PROBLEM.
READ ON IF INTERESTED.
STOP HERE IF NOT.
you can solve for her break-even point as follows:
the break even point is when the revenue is equal to the cost.
since we know she has to sell more than 2000, the equation becomes:
revenue = cost.
revenue = 1 * x, where x is the number of posters sold.
cost = 3200 + (x - 2000) * .8
the 3200 is the total cost for the first 2000 posters.
revenue = cost becomes:
1 * x = 3200 + (x - 2000) * .8
remove parentheses to get:
1 * x = 3200 + .8 * x - 2000 * .8
simplify to get:
1 * x = 3200 + .8 * x - 1600
combine like terms to get:
1 * x = .8 * x + 1600.
subtract .8 * x from both sides of the equation to get:
x - .8 * x = 1600
simplify to get:
.2 * x = 1600
divide both sides of this equation by .2 to get:
x = 1600 / .2 = 8000.
she would break even if she printed and sold 8000 posters.
her revenue would be 8000.
her cost would be 500 + 1500 + 1200 + .8 * (8000 - 2000) which becomes:
500 + 1500 + 1200 .8 * 6000 which becomes:
3200 + 4800 which becomes:
8000.
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