Stuck - how to use formula to calculate Marginal costs/ learning curve

HASt

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[h=3]Here is the problem - I can't figure it out!?! Anyone patient enough to explain to me how to run through this?

Assume first that the progress ratio in this industry is 80%. We can then derive the coefficient b in the equation c(t) = c(0) x(t)^-b by comparing two points on the curve, for example at a cumulative production of 1 and 2 units. For any other progress ratio than 80%, please put in the relevant progress ratio for c(2).[/h][h=3]c(1) / c(2) = 1 / 0.8 = c(0) * 1^-b / c(0) * 2^-b, simplifies to[/h][h=3](1/2)^-b = 1 / 0.8, or[/h][h=3]-b = ln(1/0.8)/ln(1/2)[/h][h=3]giving b = 0.32.[/h][h=3]You can now insert b in the equation and compute any cost for any level of cumulative output, as long as you know the cost for the first unit. If you dont know the cost for the first unit you still know the relative cost reduction between any two doublings of output.[/h][h=3]In the following example, we will practice calculating marginal cost based on the learning curve. [/h][h=3]Let us presume that there are two competing plants which starts production on the same day. They are in an industry with a progress ratio of 80%. Let's call them plant A and B. Let's also assume that they both follow the same progress ratio and that the first unit produced costs 1 Euro to make. Plant A is built for a capacity of producing 100 units a month while plant B has a capacity of producing 200 units a month.[/h][h=3]The marginal cost schedules should be obtained for the two plants[/h]
Month 1Month 2Month 3Month 4Month 5
Cumulative production plant A100200300400500
Marginal cost A
Cumulative production plant B2004006008001000
Marginal cost B
 
Here is the problem - I can't figure it out!?! Anyone patient enough to explain to me how to run through this?

Assume first that the progress ratio in this industry is 80%. We can then derive the coefficient b in the equation c(t) = c(0) x(t)^-b by comparing two points on the curve, for example at a cumulative production of 1 and 2 units. For any other progress ratio than 80%, please put in the relevant progress ratio for c(2).


c(1) / c(2) = 1 / 0.8 = c(0) * 1^-b / c(0) * 2^-b, simplifies to

(1/2)^-b = 1 / 0.8, or

-b = ln(1/0.8)/ln(1/2)

giving b = 0.32.

You can now insert b in the equation and compute any cost for any level of cumulative output, as long as you know the cost for the first unit. If you dont know the cost for the first unit you still know the relative cost reduction between any two doublings of output.

In the following example, we will practice calculating marginal cost based on the learning curve.

Let us presume that there are two competing plants which starts production on the same day. They are in an industry with a progress ratio of 80%. Let's call them plant A and B. Let's also assume that they both follow the same progress ratio and that the first unit produced costs 1 Euro to make. Plant A is built for a capacity of producing 100 units a month while plant B has a capacity of producing 200 units a month.

The marginal cost schedules should be obtained for the two plants

Month 1Month 2Month 3Month 4Month 5
Cumulative production plant A100200300400500
Marginal cost A
Cumulative production plant B2004006008001000
Marginal cost B
Did you perform the first task as described in the problem:

Assume first that the progress ratio in this industry is 80%. We can then derive the coefficient b in the equation c(t) = c(0) x(t)^-b by comparing two points on the curve, for example at a cumulative production of 1 and 2 units.
 
I'm in need of assistance with the exact problem noted above. I has been some time since I last performed this type of problem, and would greatly appreciate anyone patient enough to walk me through the next steps to solve this problem.
 
I'm in need of assistance with the exact problem noted above. I has been some time since I last performed this type of problem, and would greatly appreciate anyone patient enough to walk me through the next steps to solve this problem.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment.
 
On this forum we do not offer step by step help to anyone. We prefer that the student solves their own problem with our help. Please tell us what is stopping you from making progress.
 
Did you perform the first task as described in the problem:

Assume first that the progress ratio in this industry is 80%. We can then derive the coefficient b in the equation c(t) = c(0) x(t)^-b by comparing two points on the curve, for example at a cumulative production of 1 and 2 units.
Hello Khan, will the value of b not be .32, as explained in the example.
Also I need help in understanding the formula to put the numbers. I'm clueless how! can you share a link where i can study this formula
 
Hello Khan, will the value of b not be .32, as explained in the example.
Also I need help in understanding the formula to put the numbers. I'm clueless how! can you share a link where i can study this formula
for the first month i applied the formula like this: C(1)=1*100(1)^-.32 which gives answer as 100 but that's not right. I also Tried C(1)=1*(100(1))^-.32= .229; which again is not true. 1 euro is the cost of producing 1st unit. t=1 month; x=100.
 
Hello I have the same problem I could not solve it :(
I just need an explanation on how to put the numbers in the formula so I can solve it
I only have one more try or else I will fail this quiz, please I need anyone to just explain it for me

Thanks
 
Here is my problem in trying to answer you: the problem itself is barely expressed in English. It talks about a coefficient when what it seems to mean is an exponent. You presumably have context that I do not have. I am guessing. c(t) stands for what? cost per unit produced at time t? Then what is x(t)?

[MATH]c(t) = c(0) \{x(t)\}^{-b}.[/MATH]
Is that the equation?

How does that relate to marginal cost? There does not seem to be an equation relating cost and quantity produced. Or is some special definition of marginal cost being used?

What is [\h][h=3]?

Now there may be explanations of what the functions and variables mean in wherever this problem came from, but they have not been supplied.
 
Here is my problem in trying to answer you: the problem itself is barely expressed in English. It talks about a coefficient when what it seems to mean is an exponent. You presumably have context that I do not have. I am guessing. c(t) stands for what? cost per unit produced at time t? Then what is x(t)?

[MATH]c(t) = c(0) \{x(t)\}^{-b}.[/MATH]
Is that the equation?

How does that relate to marginal cost? There does not seem to be an equation relating cost and quantity produced. Or is some special definition of marginal cost being used?

What is [\h][h=3]?

Now there may be explanations of what the functions and variables mean in wherever this problem came from, but they have not been supplied.

I attached the question.
c is the Cumulative production
t is the time (1 month, i think).
x is the number of products
b is the learning curve given (=-0.32)
 

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Sarah, I am sorry. I would like to help you you, but i find the problem as presented virtually incoherent.

Marginal cost is usually defined as dc/dq. No information on cost as a function of quantity appears to be provided. What is provided is information about c as a function of time.
 
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