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You have opened your own word-processing service. You bought a personal computer, and paid $5,000 for it. However, due to the cost changes in the computer industry, the current price of an equivalent machine is $2,500. You could sell any used machine for $1,000. If you were not word processing, you could earn $20,000 per year at an alternative job. Assume that the interest rate is 10%. You can also hire an assistant who can do everything that you can do for $20,000 per year (you would still continue to do word processing).

One person using one computer can produce 11,000 typed pages per year, and the price per page for your service is $2.

You are considering three options: (1) expand your business by hiring an assistant; (2) leave your business the way it is; (3) shut down. Based on the costs and revenues above, which should you do? Explain and show any relevant calculations.

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Answer:

Option 1:
Revenue = $22,000
Opportunity cost of your time = 20,000
Opportunity cost of interest on salvage value of existing computer = 100
Economic profit = $1,900
Option 2:
You still earn $1,900 as above.
Revenue from additional worker = 22,000
Wages = 20,000
Opportunity cost of interest on purchase of new computer = 250
Depreciation = 1,500
Economic profit from additional worker = $250
Total economic profit = $2,150
Option 3:
Revenue = 0
No costs, since opportunity costs no longer apply, and fixed costs are sunk.
Economic profit = 0
(Could possibly view the $1,000 you get from selling the used computer as revenue, but makes
no difference to final solution of problem.)
Option 2, expand your business, is the best option.

To determine the best option, let's evaluate the costs and revenues associated with each option:

1) Expand your business by hiring an assistant:
- Cost of hiring an assistant: $20,000 per year

The revenue generated by one person using one computer is given as $2 per page, and they can produce 11,000 pages per year. So, the revenue generated by the assistant per year would be:

Revenue per assistant per year = $2 × 11,000 = $22,000

Considering the cost of hiring an assistant ($20,000 per year) and the revenue generated by the assistant per year ($22,000), the net profit from expanding the business would be:

Net Profit = Revenue - Cost of hiring an assistant
Net Profit = $22,000 - $20,000
Net Profit = $2,000

2) Leave your business the way it is:
In this case, you would continue to operate the business without hiring an assistant.

The revenue generated by one person using one computer per year is given as $2 × 11,000 = $22,000.

The net profit from operating the business without an assistant would be:

Net Profit = Revenue - Alternative job income
Net Profit = $22,000 - $20,000
Net Profit = $2,000

3) Shut down the business:
In this case, you would not generate any revenue and incur an opportunity cost of $20,000 per year.

Now, let's compare the net profits from each option:

- Expand the business: Net Profit = $2,000
- Leave the business as is: Net Profit = $2,000
- Shut down the business: Net Profit = -$20,000

Based on the calculations, both expanding the business and leaving it as is will result in a net profit of $2,000 per year. However, shutting down the business would result in a net loss of $20,000 per year.

Therefore, the best option would be to either expand the business or leave it as is, as both options result in the same net profit. The final decision would depend on other factors like growth potential, workload, and personal preferences.

To determine which option to choose - hiring an assistant, leaving your business as it is, or shutting down - we need to analyze the costs and revenues associated with each option.

1) Expand your business by hiring an assistant:
- By hiring an assistant, you would incur an additional cost of $20,000 per year.
- However, with the assistant's help, you would be able to double your production capacity to 22,000 typed pages per year.
- The price per page for your service is $2, so doubling your production would result in additional revenue of 22,000 pages * $2 = $44,000.
- Additionally, you would still be able to earn $20,000 per year from word processing.
- Therefore, the total revenue from expanding your business would be $44,000 + $20,000 = $64,000.
- However, you need to subtract the additional cost of hiring the assistant, which is $20,000.
- So the net revenue from expanding your business would be $64,000 - $20,000 = $44,000.

2) Leave your business the way it is:
- In this case, your total revenue would be based on the annual production of 11,000 typed pages, multiplied by the price per page of $2.
- Therefore, your total revenue would be 11,000 pages * $2 = $22,000.
- You would still be able to earn $20,000 per year from word processing.
- So the net revenue from leaving your business as it is would be $22,000 + $20,000 = $42,000.

3) Shut down:
- If you shut down your business, you would not have any revenue from word processing.
- However, you could sell your used computer for $1,000.
- The current price of an equivalent machine is $2,500, so you would need to deduct the difference, which is $2,500 - $1,000 = $1,500.
- So the net revenue from shutting down would be $1,000 - $1,500 = -$500 (a loss of $500).

Considering these calculations, you should expand your business by hiring an assistant. This option would result in the highest net revenue of $44,000. Leaving your business as it is would give you a net revenue of $42,000, while shutting down would result in a net loss of $500.