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Increasing or decreasing return to scale?

gerrandesquire
Posts: 1,258
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11/5/2011 12:27:59 PM
Posted: 5 years ago
Sorry for posting a textbook question again but this question has caused quite a bit of confusion in the class. And our teacher isn't helping.

If a simultaneous and equal percentage decrease in the use of all physical inputs leads to a larger percentage decrease in physical output, a firms production function is said to exhibit:
decreasing return to scale
constant return to scale
increasing return to scale
diseconomies of scale
gerrandesquire
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11/7/2011 5:49:48 AM
Posted: 5 years ago
Yeah and that would be because if you increase the input by the same amount, the output would increase by a greater percentage, right? Because the others are arguing that the average cost in this case rises, which occurs in decreasing return to scale, and our teacher is kinda siding with them.
I-am-a-panda
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11/8/2011 3:41:36 PM
Posted: 5 years ago
At 11/7/2011 5:49:48 AM, gerrandesquire wrote:
Yeah and that would be because if you increase the input by the same amount, the output would increase by a greater percentage, right? Because the others are arguing that the average cost in this case rises, which occurs in decreasing return to scale, and our teacher is kinda siding with them.

AC rises when production decreases or increases?
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LeafRod
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11/8/2011 4:13:48 PM
Posted: 5 years ago
Call the initial amount of input X and the initial amount of output Y.

Input X is decreased by a factor of n, to X'. Subsequently, output Y is decreased by a factor of m, to Y'. m > n.

Now, at initial input and output X' and Y', the company increases input by a factor of n, and the input rises to X. Since input X results in output Y, our output is Y. Hence, Y' increased to Y, which we know is a factor of m. We know that m > n.

Therefore, increasing returns to scale.

I dunno how rigorous that was and it was kind of cumbersome, but something like that might help others realize.
gerrandesquire
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11/9/2011 10:27:39 AM
Posted: 5 years ago
At 11/8/2011 4:13:48 PM, LeafRod wrote:
Call the initial amount of input X and the initial amount of output Y.

Input X is decreased by a factor of n, to X'. Subsequently, output Y is decreased by a factor of m, to Y'. m > n.

Now, at initial input and output X' and Y', the company increases input by a factor of n, and the input rises to X. Since input X results in output Y, our output is Y. Hence, Y' increased to Y, which we know is a factor of m. We know that m > n.

Therefore, increasing returns to scale.

I dunno how rigorous that was and it was kind of cumbersome, but something like that might help others realize.

Thank you. I understand this, I even presented almost the same argument to the class, and they understood but they are bringing cost into the equation. Basically, they are saying that if the input falls by x and output falls by amount more than x, that would imply that the average cost would rise, which would imply diseconomies of scale. I just can't find the kink in their argument. Diseconomies of scale and increasing return to scale cannot occur simultaneously, can it?
LeafRod
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11/24/2011 1:00:03 PM
Posted: 5 years ago
http://en.wikipedia.org...

Well, according one of the sections there, they might actually have a point. But with the information you've given I don't see how you could use that kind of cost information. You can only do a more simple analysis with what we have.
sadolite
Posts: 8,842
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11/24/2011 4:23:08 PM
Posted: 5 years ago
At 11/5/2011 12:27:59 PM, gerrandesquire wrote:
Sorry for posting a textbook question again but this question has caused quite a bit of confusion in the class. And our teacher isn't helping.

If a simultaneous and equal percentage decrease in the use of all physical inputs leads to a larger percentage decrease in physical output, a firms production function is said to exhibit:
decreasing return to scale
constant return to scale
increasing return to scale
diseconomies of scale

Um, sounds like you trying to say "Cash in minus cash out = profit/loss" in they most obscure and confusing manner possible.
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darkkermit
Posts: 11,204
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11/24/2011 6:12:12 PM
Posted: 5 years ago
At 11/9/2011 10:27:39 AM, gerrandesquire wrote:
At 11/8/2011 4:13:48 PM, LeafRod wrote:
Call the initial amount of input X and the initial amount of output Y.

Input X is decreased by a factor of n, to X'. Subsequently, output Y is decreased by a factor of m, to Y'. m > n.

Now, at initial input and output X' and Y', the company increases input by a factor of n, and the input rises to X. Since input X results in output Y, our output is Y. Hence, Y' increased to Y, which we know is a factor of m. We know that m > n.

Therefore, increasing returns to scale.

I dunno how rigorous that was and it was kind of cumbersome, but something like that might help others realize.

Thank you. I understand this, I even presented almost the same argument to the class, and they understood but they are bringing cost into the equation. Basically, they are saying that if the input falls by x and output falls by amount more than x, that would imply that the average cost would rise, which would imply diseconomies of scale. I just can't find the kink in their argument. Diseconomies of scale and increasing return to scale cannot occur simultaneously, can it?

No it wouldn't. If
AC' = TC/Q. AC = (TC+deltaC)/(Q + deltaQ). The quantity increase is more then the cost increase, so the average cost will decrease.

Also sadolite, we already realize your too stupid to understand this material anyways. Why did you bother posting?
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gerrandesquire
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11/26/2011 7:43:29 AM
Posted: 5 years ago

No it wouldn't. If
AC' = TC/Q. AC = (TC+deltaC)/(Q + deltaQ). The quantity increase is more then the cost increase, so the average cost will decrease.

But aren't we decreasing the input and output? I.e, isn't the total cost decreasing by deltaC, output decreasing by deltaQ and delta Q is more than deltaC? So that would mean the average cost rises, wouldn't it?
darkkermit
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11/26/2011 11:37:40 AM
Posted: 5 years ago
At 11/26/2011 7:43:29 AM, gerrandesquire wrote:

No it wouldn't. If
AC' = TC/Q. AC = (TC+deltaC)/(Q + deltaQ). The quantity increase is more then the cost increase, so the average cost will decrease.

But aren't we decreasing the input and output? I.e, isn't the total cost decreasing by deltaC, output decreasing by deltaQ and delta Q is more than deltaC? So that would mean the average cost rises, wouldn't it?

But your essentially reading the graph backwards. You read the slope from left to right, from low quantity to high quantity.

If the average costs are increasing if you lower the quantity, that means its increasing if you increase the quantity, which is economics of scale.
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darkkermit
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11/26/2011 12:07:21 PM
Posted: 5 years ago
At 11/26/2011 11:37:40 AM, darkkermit wrote:
At 11/26/2011 7:43:29 AM, gerrandesquire wrote:

No it wouldn't. If
AC' = TC/Q. AC = (TC+deltaC)/(Q + deltaQ). The quantity increase is more then the cost increase, so the average cost will decrease.

But aren't we decreasing the input and output? I.e, isn't the total cost decreasing by deltaC, output decreasing by deltaQ and delta Q is more than deltaC? So that would mean the average cost rises, wouldn't it?

But your essentially reading the graph backwards. You read the slope from left to right, from low quantity to high quantity.

If the average costs are increasing if you lower the quantity, that means its lowering if you increase the quantity, which is economics of scale.

fixed
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gerrandesquire
Posts: 1,258
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11/27/2011 2:56:22 AM
Posted: 5 years ago
At 11/26/2011 12:07:21 PM, darkkermit wrote:
At 11/26/2011 11:37:40 AM, darkkermit wrote:
At 11/26/2011 7:43:29 AM, gerrandesquire wrote:

No it wouldn't. If
AC' = TC/Q. AC = (TC+deltaC)/(Q + deltaQ). The quantity increase is more then the cost increase, so the average cost will decrease.

But aren't we decreasing the input and output? I.e, isn't the total cost decreasing by deltaC, output decreasing by deltaQ and delta Q is more than deltaC? So that would mean the average cost rises, wouldn't it?

But your essentially reading the graph backwards. You read the slope from left to right, from low quantity to high quantity.

If the average costs are increasing if you lower the quantity, that means its lowering if you increase the quantity, which is economics of scale.

fixed

OH yeah. Seems dumb now, thanks. This has been troubling me for weeks. I thought it had to do with the price of input not being fixed.
sadolite
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11/27/2011 10:40:31 AM
Posted: 5 years ago
Forgive my ingnorence, but I do have a question that is relevant to the queation at hand. How does one apply this in a real world situation with ragard to economics or business> In other words how does it solve a problem. I own a business and I am truely interested in expanding my knowledge in any way possible with regard to controling costs. Or does this have nothing to do with costs and output.
It's not your views that divide us, it's what you think my views should be that divides us.

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darkkermit
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11/27/2011 11:59:52 AM
Posted: 5 years ago
At 11/27/2011 10:40:31 AM, sadolite wrote:
Forgive my ingnorence, but I do have a question that is relevant to the queation at hand. How does one apply this in a real world situation with ragard to economics or business> In other words how does it solve a problem. I own a business and I am truely interested in expanding my knowledge in any way possible with regard to controling costs. Or does this have nothing to do with costs and output.

I apologize for my remarks earlier.

Sort of. A lot of its theoretical. I'm assuming that a main problem isn't necessarily how much of a good or service you can produce but finding buyers for the product or service.

It affects the decision of whether you want to expand your business or increase the amount of labor or capital used. Basically, does increasing marginal costs (either increasing the amount of labor or capital used. ) increase marginal revenue. Should be noted that marginal cost is increasing by one unit. One unit of labor, or one unit of capital. It should also be noted that these models don't necessarily figure out what the best combination of labor and capital is.

Economics of scales occurs If it is (usually) good to expand business since the average costs are decreasing with more output.
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