college algebra help
- Thread starter Irene Joy
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mmm4444bot
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Hello Irene. We set up any given word problem based upon the information that we are given. It usually begins by assigning symbols to represent unknown numbers, followed by using what we know to express relationships between the various quantities in the problem. From that, we build an equation to solve (in general).
Please post an actual exercise with which you need help. (Kindly start a new thread for each individual exercise.) Give us all of the information that you received. Tell us about any parts that you do not understand. For the quickest and best response, please show any work or calculations that you've been able to complete thus far, so that we can get an idea of what you're trying to do.
Explaining your reasoning or asking specific questions is the best way to request help here because then the volunteers on these boards can easily determine where in the exercise to begin assisting you.
Also, check out the post titled, "Read Before Posting", for additional guidelines.
Cheers ~ Mark
CCampbell57
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I was hoping you could look at my homework assignment I got a "C" because my instructor says I need to redo calculations of tvc,avc, atc, wprod. A copy of my homework is attached with homework problem. What am I doing wrong?
PROBLEM:
The firm currently uses 50,000 workers to produce 200,000 units of output per day. The daily wage per worker is $80, and the price of the firm’s output is $25. The cost of other variable inputs is $400,000 per day.
Assume that total fixed cost equals $1,000,000. Calculate the values for the following four formulas:
•Total Variable Cost = (Number of Workers * Worker’s Daily Wage) + Other Variable Costs
•Average Variable Cost = Total Variable Cost / Units of Output per Day
•Average Total Cost = (Total Variable Cost +Total Fixed Cost) / Units of Output per Day
•Worker Productivity = Units of Output per Day / Number of Workers
Then, assume that total fixed cost equals $3,000,000, and recalculate the values of the four variables listed above.
For both cases, calculate the firm’s profit or loss.
For both sets of calculations, compare the firm’s output price and the calculated average variable cost and average total cost. Should the firm shutdown immediately when the total fixed cost equals $1,000,000? Should the firm shut down immediately when the total fixed cost equals $3,000,000?
For one of the cases, if the firm can operate at a loss in the short-run, how many employees need to be laid off in order for the company to break even? To calculate the number of workers to be laid off, divide the loss for the two situations by the daily wage per worker. Given a lower number of employees now working at the company, what is the change in worker productivity? Is the change in worker too large, and the firm should shut down immediately? Or in your opinion, can the workers increase their productivity, assuming that the units of output per day remain fixed at 200,000 units, so that the firm operates at a breakeven state?
Provide a two to four page report to management of the firm that discusses what should be done.
Be sure to show your work to support the decision you outline in your report.
MY ANSWER:
UNIT. 3. PRODUCTION AND PERFECT COMPETITION
Assume that total fixed cost equals $1,000,000. Calculate the values for the following four formulas:
1. Total variable cost = (50,000*80) +400,000 = $4,400,000 in variable costs.
The fixed cost = (1,000,000 + 4,400,000) = $5,400,000 is the fixed costs.
Total Revenue = (200,000 * 25) = $5,000,000. The firm lost $400,000.
2. Average Variable Cost = (4,400,000 / 25) = $160,000 is the average variable cost
3. Average Total Cost = (4,400,000 + 5,400,000) = $9,400,000 / 25 = $376,000 Average total cost.
4. Worker Productivity = (25 / 50,000) = 2,000 is the worker’s productivity.
Assume that total fixed cost equals $3,000,000. Calculate the values for the following four formulas:
1. Total Variable Cost = (50,000*80) + 400,000 = $4,400,000 in variable cost.
The Fixed Cost = 3,000,000 + 4,400,000 = $7,400,000 is the fixed cost.
Total Revenue = 200,000 * 25 = 5,000,000 and (7,400,000 – 5,000,000) = $2,400,000 is the total revenue. The firm made a profit of $2,400,000.
2. Average Variable Cost = 4,400,000 / 25 = $160,000 is the average variable cost
3. Average Total Cost = (4,400,000 + 7,400,000) = $11,400,000 / 25 = $456,000 is the average total cost
4. Worker’s Productivity = (25 / 50,000) = 2,000 is the worker’s productivity.
Should the firm shut down immediately when the total fixed cost immediately when the total fixed cost equals 1,000,000?
This firm is losing $400,000 a day and should shut down immediately. But the firm should decide to operate under the short run. Even though the total cost is included in the fixed cost and fixed cost must be still paid and since it cannot be changed in the short run the fixed cost is irrelevant and they need to decide to operate in the short run and not the long run. Even though fixed cost plays no role in the short run there are other factors and cost to consider and that is other costs and the variable cost.
Should the firm shut down immediately when the total fixed cost immediately when the total fixed cost equals 3,000,000?
Definitely not there profits are $2,400,000 a day and doing very well. This firm can operate in the long run with profits very beneficial.
For one of the cases, if the firm can operate at a loss in the short-run, how many employees need to be laid off in order for the company to break even?
The first firm operating under the short-run would have to be laid off: 10,000 employees
Assume the total fixed cost equals $1,000,000. Calculated the values for the four formulas above:
1. Total variable cost = (40,000*80) = $3,200,000 + 400,000 = $3,600,000 is the total variable costs.
The Fixed Cost = (1,000,000 + 3,600,000) = $4,600,000 is the fixed costs
Total Revenue = (200,000 * 25) = $5,000,000 and (5,000,000 – 4,600,000) = $400,000 the firms new profits.
2. Average Variable Cost = (3,600,000 / 25) = $144,000 is the average variable costs.
3. Average Total Cost = (3,600,000 + 4,600,000) = $8,200,000 (8,200,000 /25) = $328,000 is the average total cost
4. Worker Productivity = (25 / 40,000) = 1,600 is the workers new productivity.
So laying off 10,000 workers would help the company to break even. This lay off would turn that negative number into a positive profit.
The Workers Productivity is now going to be 1600.
Is the change in worker too large, and the firm should shut down immediately?
Yes. I calculated the change in employees to be laid off of 10,000 workers and if the company choose to operate under a short-run and the average market price is below the minimum average variable cost the firm’s total revenue is not going to cover the average variable cost. So given the lower number of employees is still too large and should probably shut down immediately.
If 25,000 employees were laid off the total variable costs would be $2,400,000 the fixed cost would be $3,400,000 then their total profits would be $1,600,000 and the worker’s productivity would be a 1000.
In my opinion the workers at the lower number could increase their productivity assuming the units of output per day remain at the 200,000 units, and then operating on a short run instead of a long run they just may be able to break even. This s based on the layoff of 10,000 employees.
PROBLEM:
The firm currently uses 50,000 workers to produce 200,000 units of output per day. The daily wage per worker is $80, and the price of the firm’s output is $25. The cost of other variable inputs is $400,000 per day.
Assume that total fixed cost equals $1,000,000. Calculate the values for the following four formulas:
•Total Variable Cost = (Number of Workers * Worker’s Daily Wage) + Other Variable Costs
•Average Variable Cost = Total Variable Cost / Units of Output per Day
•Average Total Cost = (Total Variable Cost +Total Fixed Cost) / Units of Output per Day
•Worker Productivity = Units of Output per Day / Number of Workers
Then, assume that total fixed cost equals $3,000,000, and recalculate the values of the four variables listed above.
For both cases, calculate the firm’s profit or loss.
For both sets of calculations, compare the firm’s output price and the calculated average variable cost and average total cost. Should the firm shutdown immediately when the total fixed cost equals $1,000,000? Should the firm shut down immediately when the total fixed cost equals $3,000,000?
For one of the cases, if the firm can operate at a loss in the short-run, how many employees need to be laid off in order for the company to break even? To calculate the number of workers to be laid off, divide the loss for the two situations by the daily wage per worker. Given a lower number of employees now working at the company, what is the change in worker productivity? Is the change in worker too large, and the firm should shut down immediately? Or in your opinion, can the workers increase their productivity, assuming that the units of output per day remain fixed at 200,000 units, so that the firm operates at a breakeven state?
Provide a two to four page report to management of the firm that discusses what should be done.
Be sure to show your work to support the decision you outline in your report.
MY ANSWER:
UNIT. 3. PRODUCTION AND PERFECT COMPETITION
Assume that total fixed cost equals $1,000,000. Calculate the values for the following four formulas:
1. Total variable cost = (50,000*80) +400,000 = $4,400,000 in variable costs.
The fixed cost = (1,000,000 + 4,400,000) = $5,400,000 is the fixed costs.
Total Revenue = (200,000 * 25) = $5,000,000. The firm lost $400,000.
2. Average Variable Cost = (4,400,000 / 25) = $160,000 is the average variable cost
3. Average Total Cost = (4,400,000 + 5,400,000) = $9,400,000 / 25 = $376,000 Average total cost.
4. Worker Productivity = (25 / 50,000) = 2,000 is the worker’s productivity.
Assume that total fixed cost equals $3,000,000. Calculate the values for the following four formulas:
1. Total Variable Cost = (50,000*80) + 400,000 = $4,400,000 in variable cost.
The Fixed Cost = 3,000,000 + 4,400,000 = $7,400,000 is the fixed cost.
Total Revenue = 200,000 * 25 = 5,000,000 and (7,400,000 – 5,000,000) = $2,400,000 is the total revenue. The firm made a profit of $2,400,000.
2. Average Variable Cost = 4,400,000 / 25 = $160,000 is the average variable cost
3. Average Total Cost = (4,400,000 + 7,400,000) = $11,400,000 / 25 = $456,000 is the average total cost
4. Worker’s Productivity = (25 / 50,000) = 2,000 is the worker’s productivity.
Should the firm shut down immediately when the total fixed cost immediately when the total fixed cost equals 1,000,000?
This firm is losing $400,000 a day and should shut down immediately. But the firm should decide to operate under the short run. Even though the total cost is included in the fixed cost and fixed cost must be still paid and since it cannot be changed in the short run the fixed cost is irrelevant and they need to decide to operate in the short run and not the long run. Even though fixed cost plays no role in the short run there are other factors and cost to consider and that is other costs and the variable cost.
Should the firm shut down immediately when the total fixed cost immediately when the total fixed cost equals 3,000,000?
Definitely not there profits are $2,400,000 a day and doing very well. This firm can operate in the long run with profits very beneficial.
For one of the cases, if the firm can operate at a loss in the short-run, how many employees need to be laid off in order for the company to break even?
The first firm operating under the short-run would have to be laid off: 10,000 employees
Assume the total fixed cost equals $1,000,000. Calculated the values for the four formulas above:
1. Total variable cost = (40,000*80) = $3,200,000 + 400,000 = $3,600,000 is the total variable costs.
The Fixed Cost = (1,000,000 + 3,600,000) = $4,600,000 is the fixed costs
Total Revenue = (200,000 * 25) = $5,000,000 and (5,000,000 – 4,600,000) = $400,000 the firms new profits.
2. Average Variable Cost = (3,600,000 / 25) = $144,000 is the average variable costs.
3. Average Total Cost = (3,600,000 + 4,600,000) = $8,200,000 (8,200,000 /25) = $328,000 is the average total cost
4. Worker Productivity = (25 / 40,000) = 1,600 is the workers new productivity.
So laying off 10,000 workers would help the company to break even. This lay off would turn that negative number into a positive profit.
The Workers Productivity is now going to be 1600.
Is the change in worker too large, and the firm should shut down immediately?
Yes. I calculated the change in employees to be laid off of 10,000 workers and if the company choose to operate under a short-run and the average market price is below the minimum average variable cost the firm’s total revenue is not going to cover the average variable cost. So given the lower number of employees is still too large and should probably shut down immediately.
If 25,000 employees were laid off the total variable costs would be $2,400,000 the fixed cost would be $3,400,000 then their total profits would be $1,600,000 and the worker’s productivity would be a 1000.
In my opinion the workers at the lower number could increase their productivity assuming the units of output per day remain at the 200,000 units, and then operating on a short run instead of a long run they just may be able to break even. This s based on the layoff of 10,000 employees.
Are you the same person as Irene Joy, who started this thread?
Anyhow, you're told :
" Average Variable Cost = Total Variable Cost / Units of Output per Day"
And you do this :
" Average Variable Cost = (4,400,000 / 25) = $160,000 is the average variable cost"
Do you see why that's WAY wrong? :shock:
Anyhow, you're told :
" Average Variable Cost = Total Variable Cost / Units of Output per Day"
And you do this :
" Average Variable Cost = (4,400,000 / 25) = $160,000 is the average variable cost"
Do you see why that's WAY wrong? :shock:
CCampbell57
New member
- Joined
- Jun 30, 2011
- Messages
- 2
No. I do not know why it is wrong? I know nothing of Collee algebra....
No I am not Irene and I don't know why I am not supose to complete my assignment this way. This is why I am asking for help.
No I am not Irene and I don't know why I am not supose to complete my assignment this way. This is why I am asking for help.
J
JeffM
Guest
First, it helps to let us know what you know. It looks as though you are taking a microeconomics course without having studied college algebra or differential calculus. This course is going to be a bear for you. However, FOR THIS PROBLEM, you just need high school algebra.
Second, read mmm's answer to Irene. You will get better help here if you follow his advice.
Third, you have to define things for us.
"tvc" is what? I am guessing that it stands for "total variable cost." But why should I guess when you can tell me? By the way, mathematicians hate the economist's habit of using multiple letters to stand for a single variable. A mathematician is going to read tvc as t times v times c and wonder what each means.
Let's proceed like this.
Step 1: Start by assigning a single letter to each variable.
a = total variable cost per day.
b = number of workers
c = one worker's daily wage
d = other variable costs per day
e = units produced per day
f = average variable cost per unit of output.
Keep on doing that until you have a letter assigned to each variable.
Step 2: Then write down the given relationships USING your symbols:
b = 50,000
c = 80
d = 400,000
e = 200,000
a = (b * c) + d = (50,000 * 80) + 400,000 = 4,000,000 + 400,000 = 4,400,000
f = (a / e) = 4,400,000 / 200,000 = 22.
Keep on doing that until you have each relationship given to you written down.
Step 3: If you need some relationships not given to you, use algebra on the other relationships to get them.
Step 4: Think about what the numbers mean.
Second, read mmm's answer to Irene. You will get better help here if you follow his advice.
Third, you have to define things for us.
"tvc" is what? I am guessing that it stands for "total variable cost." But why should I guess when you can tell me? By the way, mathematicians hate the economist's habit of using multiple letters to stand for a single variable. A mathematician is going to read tvc as t times v times c and wonder what each means.
Let's proceed like this.
Step 1: Start by assigning a single letter to each variable.
a = total variable cost per day.
b = number of workers
c = one worker's daily wage
d = other variable costs per day
e = units produced per day
f = average variable cost per unit of output.
Keep on doing that until you have a letter assigned to each variable.
Step 2: Then write down the given relationships USING your symbols:
b = 50,000
c = 80
d = 400,000
e = 200,000
a = (b * c) + d = (50,000 * 80) + 400,000 = 4,000,000 + 400,000 = 4,400,000
f = (a / e) = 4,400,000 / 200,000 = 22.
Keep on doing that until you have each relationship given to you written down.
Step 3: If you need some relationships not given to you, use algebra on the other relationships to get them.
Step 4: Think about what the numbers mean.