Help me with my homework please

[Magrat]

I'm tutoring a student in economics and I've honestly no idea how to do this problem:

Picture frames are produced in a perfectly competitive market. Each identical firm has a short
run total cost curve of TC = 10 + 14Q − 2Q^2 + 0.15Q^3 where Q is the quantity of picture
frames produced (in thousands per month).
a. What is the price below which a firm in the market will not produce an output in the short
run?
b. Derive the supply curve for a firm

I know I need to take the dervative from the TC but I don't know how to do that. Please does anyone know how to solve this? I have a Masters in accounting but I never went beyond algebra II lol Thank you!

 

[jimbob]

Well if you just differentiated with respect to Q
Remember that if
y(x)= Ax^N
dy/dx = NAx^N-1
So for dTC/dQ (not sure if that's the correct derivative) would be

for each of the terms.

d (10)/dQ = 0 (no change with respect to Q)
plus
d (14Q) /dQ = 14
plus...
d(-2Q²)/dQ = -4Q¹ =-4Q

plus

d(0.15Q³)/dQ = 0.45Q²

so I make it 14 -4Q + 0.45Q²

 

[Magrat]

Can you explain to me how to find the derivative? I don't understand what that means?

 

[jimbob]

Ah, that is the gradient, or rate of change relative to the variable (in this case the quantity of frames)

so thinking about the equation.

there is a fixed cost of 10 (maybe rent etc) this doesn't change with respect to Q so has no effect. If it was a map it's like saying what is the slope of something 10ft above sea level or 100ft above sea level - it's somewhat meaningless unless you have a change in height with distance.

then as you increase production there is the 14Q, which is say the linear cost of the raw materials so you double the number of frames, you spend twice as much on that. This has a slope of 14

Then the -2Q² which I don't know, some decrease in cost due to producing larger batches, so you can produce more in the same time. (just riffing on this). This has a slope of -2 x 2 Q^2-1
and then similarly for the cubic term that differentiates to a quadratic.

 

[jimbob]

I drive my car 40 miles in 2 hours (because I'm on the M25)

My speed is the derivative of the distance with respect to time (miles PER hour or miles divided by time)

My average speed is 40miles/2hours or 20 mph

 

[theprestige]

Derivatives are a part of calculus. If the subject calls for calculus and you don't know how to do calculus, then the correct answer to this problem is that you are not a fit tutor of the subject. You should refer your client to a more qualified tutor, and take a course in calculus before offering to tutor this subject.

 

[Gord_in_Toronto]

Or you could just ask ChatGPT.

I did.

In a perfectly competitive market, the firm's profit-maximizing output level is where marginal cost (MC) equals price (P).

The marginal cost of producing Q units is the derivative of the total cost function with respect to Q:

MC = dTC/dQ = 14 - 4Q + 0.45Q^2

To find the output level where the firm will not produce any output, we need to find the shutdown point, which is where the firm's total revenue is less than its variable cost (i.e., where P < AVC).

The average variable cost (AVC) of producing Q units is the variable cost (VC) divided by Q:

VC = 14Q - 2Q^2 + 0.15Q^3
AVC = VC/Q = 14 - 2Q + 0.15Q^2

Setting P = AVC, we get:

P = 14 - 2Q + 0.15Q^2

To find the price below which the firm will not produce any output, we need to find the shutdown point, where P is equal to the minimum AVC. The minimum AVC is the derivative of AVC with respect to Q, which is:

dAVC/dQ = -2 + 0.3Q

Setting dAVC/dQ = 0, we get Q = 6.67.

Therefore, the shutdown point occurs at Q = 6.67, and the minimum AVC at this point is:

AVC = 14 - 2(6.67) + 0.15(6.67)^2 = 5.99

Thus, the price below which a firm in the market will not produce any output in the short run is $5.99 (per thousand picture frames).

It's all over folks. The Universe doe not need us anymore.

 

[Magrat]

But how do I know chat gpt is right? I'd hate to tell a student something wrong.

Sent from my SM-G970U using Tapatalk

 

[Magrat]

I drive my car 40 miles in 2 hours (because I'm on the M25)

My speed is the derivative of the distance with respect to time (miles PER hour or miles divided by time)

My average speed is 40miles/2hours or 20 mph

So for example the slope of a line is a derivative?

Thank you for taking the time to explain. I have a bachelor's in accounting and a masters in health care administration. I signed up to tutor high school economics. This is econ302. It may have been best to get another tutor, AFAIK I'm the only finance/econ person they have right now. So I'm doing my best.

Also if you'd like to make a little extra $$ tutoring send me a dm and I'll hook you up. I make $30/hr and it's all online.

Sent from my SM-G970U using Tapatalk

 

[psionl0]

I'm tutoring a student in economics and I've honestly no idea how to do this problem:

Picture frames are produced in a perfectly competitive market. Each identical firm has a short
run total cost curve of TC = 10 + 14Q − 2Q^2 + 0.15Q^3 where Q is the quantity of picture
frames produced (in thousands per month).
a. What is the price below which a firm in the market will not produce an output in the short
run?
b. Derive the supply curve for a firm

I know I need to take the dervative from the TC but I don't know how to do that. Please does anyone know how to solve this? I have a Masters in accounting but I never went beyond algebra II lol Thank you!

The total cost of producing nothing is $10 and the cost of producing a single frame is 10 + 14(1) - 2(1)^2 + 0.15(1)^3 = $22.15. So, if the firm can't get at least $22.15 for a frame, they won't produce any.

You are probably expected to use a derivative for this question but picture frames are a discrete quantity so a difference equation would be more appropriate:

The marginal cost of producing the Qth picture frame is given as
MC = TC(Q) - TC(Q-1)
= 10 + 14Q - 2Q^2 + 0.15Q^3 - (10 + 14(Q-1) -2(Q-1)^2 + 0.15(Q-1)^3)
= 10 + 14Q -2Q^2 + 0.15Q^3 - 10 - 14Q + 14 +2Q^2 -4Q +2 -0.15Q^3 + 0.45Q^2 - 0.45Q + 0.15
= 16.15 - 4.45Q + 0.45Q^2

Assuming that picture frames sell at a constant price per frame (P), the marginal revenue for the Qth picture frame is simply P.

Maximum profit is where marginal cost = marginal revenue or
0.45Q^2 - 4.45Q + 16.15 = P
ie 0.45Q^2 - 4.45Q + (16.15-P) = 0

This is a quadratic equation which must be solved for Q.

I get Q = (4.45 + sqrt(1.8P - 9.2675)) / 0.9 (E & OE).

ETA

If we use the derivative, then DC/DQ = 0.45Q^2 - 4Q + 14 and the maximum profit is given by

0.45Q^2 - 4Q + (14-P) = 0 or Q = (4 + sqrt(1.8P - 9.2)) / 0.9

Either way, it seems like you will need to upgrade your maths skills if you wish to keep tutoring in Economics.

 

[lionking]

Derivatives are a part of calculus. If the subject calls for calculus and you don't know how to do calculus, then the correct answer to this problem is that you are not a fit tutor of the subject. You should refer your client to a more qualified tutor, and take a course in calculus before offering to tutor this subject.

The subject is economics and you have judged Magrat as an unfit economics tutor. Utter ******* ********.

 

[Gord_in_Toronto]

But how do I know chat gpt is right? I'd hate to tell a student something wrong.

Sent from my SM-G970U using Tapatalk

Same way you'd know if a human was right. You don't.

 

[Pulvinar]

Same way you'd know if a human was right. You don't.

Or you can ask GPT4 "What is a good way to check this answer?"

A good way to check this answer is by using graphical methods to visually verify the relationships between the total cost, average variable cost, marginal cost, and the price. Here are the steps to check the answer:

Plot the total cost (TC) function:
TC = 10 + 14Q - 2Q^2 + 0.15Q^3
Plot the average variable cost (AVC) function:
AVC = 14 - 2Q + 0.15Q^2
Plot the marginal cost (MC) function:
MC = 14 - 4Q + 0.45Q^2
Verify the minimum AVC and the shutdown price:
a. Find the minimum point of the AVC curve by checking if it corresponds to the calculated value of Q (6.67) and AVC_min (7.778).
b. Ensure that the MC curve intersects the AVC curve at its minimum point. This is because, in the short run, the firm will produce where MC = AVC when the price is at the shutdown price.
Check the supply curve:
a. For different price levels above the shutdown price, find the corresponding quantities of output (Q) by solving the equation 0.45Q^2 - 4Q + 14 - P = 0 for Q.
b. Plot the supply curve by connecting these points (P, Q) on the graph.
c. Verify that the supply curve is upward-sloping and intersects the MC curve above the shutdown price.

 

[theprestige]

The subject is economics and you have judged Magrat as an unfit economics tutor. Utter ******* ********.

The problem being set for this economics student requires knowledge of calculus. I don't know why these economics students aren't being taught the necessary calculus to solve typical problems in economics. And I don't know why otherwise-qualified economists don't know the necessary calculus for economics already. But that's the scenario Magrat describes.

 

[Magrat]

Yes. I do. Thank you for the explanation.

Ffo ****.

 

[Gord_in_Toronto]

Or you can ask GPT4 "What is a good way to check this answer?"

A good way to check this answer is by using graphical methods to visually verify the relationships between the total cost, average variable cost, marginal cost, and the price. Here are the steps to check the answer:

Plot the total cost (TC) function:
TC = 10 + 14Q - 2Q^2 + 0.15Q^3
Plot the average variable cost (AVC) function:
AVC = 14 - 2Q + 0.15Q^2
Plot the marginal cost (MC) function:
MC = 14 - 4Q + 0.45Q^2
Verify the minimum AVC and the shutdown price:
a. Find the minimum point of the AVC curve by checking if it corresponds to the calculated value of Q (6.67) and AVC_min (7.778).
b. Ensure that the MC curve intersects the AVC curve at its minimum point. This is because, in the short run, the firm will produce where MC = AVC when the price is at the shutdown price.
Check the supply curve:
a. For different price levels above the shutdown price, find the corresponding quantities of output (Q) by solving the equation 0.45Q^2 - 4Q + 14 - P = 0 for Q.
b. Plot the supply curve by connecting these points (P, Q) on the graph.
c. Verify that the supply curve is upward-sloping and intersects the MC curve above the shutdown price.

Followed by a request to ChatGBT to explain how I know the checking is correct?

 

[Magrat]

I've decided to ask the company to find her someone who knows calculus. I think that would be more beneficial in her specific course than me with econ but no calculus.

Second time this has happened. A course is called one thing but is really something else. I have a high school student who is in a course called personal finance but the material is 10th grade general math.

Ffo ****.

 

[Pulvinar]

Followed by a request to ChatGBT to explain how I know the checking is correct?

Well actually yes, ask it to explain whatever doesn't make sense. This is checking the answer by an alternate method, by graphing.

I hope we wouldn't just trust any human's answer either.

 

[lionking]

The problem being set for this economics student requires knowledge of calculus. I don't know why these economics students aren't being taught the necessary calculus to solve typical problems in economics. And I don't know why otherwise-qualified economists don't know the necessary calculus for economics already. But that's the scenario Magrat describes.

QFT

 

[Magrat]

To be clear, I'm not an economist. I am an accountant. And I have a masters in health care administration. The company I freelance with didn't have anyone with economics degrees available for this student. I have taught high school economics so they asked me to see if I could help this student.

I do not know if she has taken calculus. If she has, she didn't recognize it could be used on this problem. I don't get a whole story on a student. I get the course description, a name, and contact info. That's it.

As I mentioned above, sometimes the course title/description we are given isnt accurate. I dont know if that's an issue with the description from the school, or what the student gave the sales department when they signed up for tutoring.

I was hoping I was just missing something with this question (other than an entire school of mathematics lol)

Accountancy doesn't require complex math. Mostly just Excel. I've never needed to learn anything beyond algebra because I make the computer do it for me lollll

Ffo ****.

 

[thines]

Personal finance.

Personal finance probably requires 10th grade math.

 

[jeremyp]

The total cost of producing nothing is $10 and ]the cost of producing a single frame is 10 + 14(1) - 2(1)^2 + 0.15(1)^3 = $22.15. So, if the firm can't get at least $22.15 for a frame, they won't produce any.

Nope. That is the cost to produce 1000 picture frames per month. Always read the question carefully before answering.

 

[jt512]

Derivatives are a part of calculus. If the subject calls for calculus and you don't know how to do calculus, then the correct answer to this problem is that you are not a fit tutor of the subject. You should refer your client to a more qualified tutor, and take a course in calculus before offering to tutor this subject.

+1

 

[jeremyp]

The subject is economics and you have judged Magrat as an unfit economics tutor. Utter ******* ********.

I have just done a bit of Googling, knowing nothing about economics, and it looks like, if you want to solve this question analytically, you need to be able to differentiate an equation, not exactly the one mentioned in the OP.

Basically, you need to figure out the optimal quantity i.e. the Q where TR - TC is maximum (TR is total revenue). So in this case you need to find the maximum of

profit = 1000PQ - (10 + 14Q − 2Q^2 + 0.15Q^3)

where P is the price per frame (remember Q is the number of 1000s of frames). You can do this by finding where the derivative of the above equation wrt Q and solving it for the zero value. The derivative is

1000P - 14 + 4Q - 0.45Q^2

Apparently, the supply curve can then be found by solving that equation when setting it to zero. I'm assuming that one of the two solutions yields a negative P and can thus be discarded.

The question cannot be answered analytically without knowledge of simple calculus. It is possible to solve it numerically e.g. by drawing graphs or feeding numbers into spreadsheets, but if the syllabus requires the student to be able to solve it analytically, both they and the tutor must know basic calculus.

NB as I said, I know nothing about economics and I got a lot of the above from this page:

https://socialsci.libretexts.org/Bo...Maximization/12.02:_Deriving_the_Supply_Curve

 

[psionl0]

Nope. That is the cost to produce 1000 picture frames per month. Always read the question carefully before answering.

Well spotted.

 

[Brainster]

Or you could just ask ChatGPT.

I did.



It's all over folks. The Universe doe not need us anymore.

If you want to feel a little better about humans and a whole lot less confident in ChatGPT, try calcing this out:

AVC = 14 - 2(6.67) + 0.15(6.67)^2 = 5.99

I get 7.33, not 5.99. In fact, I can't imagine how ChatGPT got that answer.

ETA: Here's another mistake, from the "check answer" question asked by Pulvinar:

a. Find the minimum point of the AVC curve by checking if it corresponds to the calculated value of Q (6.67) and AVC_min (7.778).

The Q of 6.67 is correct, but the AVC minimum is 7.33 as noted above.

ETA2: You can find the AVC for any quantity without calculus--it's (14Q-2Q^2+.15Q^3)/Q or 14-2Q+.15Q^2. If you calc that you will find that the minimum AVC is about 7.33, which is for a quantity of 6.67 or so (thousands). That is the price below which a company would shut down.

 

[Gord_in_Toronto]

If you want to feel a little better about humans and a whole lot less confident in ChatGPT, try calcing this out:



I get 7.33, not 5.99. In fact, I can't imagine how ChatGPT got that answer.

ETA: Here's another mistake, from the "check answer" question asked by Pulvinar:



The Q of 6.67 is correct, but the AVC minimum is 7.33 as noted above.

Curiously enough I get 7.33 too. Not Ready for Prime Time? (but just wait a year).