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Baa?21242 Posts
So I just took my microeconomics midterm, and all was fine and dandy with the exception of this one problem that seems like it raped everyone I talked to. Can someone explain to me WTF is going on here? My book is terribad so it's no help :[
Given F(K,L) = 2K + 10L^1/2, where K is capital and L is labor, find the following:
Marginal products of labor and capital.
This part seemed easy, I just had MPk = 2 + 10L^1/2, and MPl = 2k + 5L^-1/2. So far so good, right?
Then it asks for the MRTS, which was just MPl/MPk.
Then it said that in the short run, capital is held constant at 10, with wage = $2 and rent = $4 and it asked me to find the short-run cost. This is where things got confusing.
I had C = rK + wL = 4(10) + wL = 40 + 2L
I had Q = 2K [changes to 20] + 10L^1/2, simplifying eventually to L = [(Q-20)/(10)]^2, and plugged it back into the C equation to get some blob. Seemed fairly reasonable, but it seemed wrong for some reason. Someone confirm/tell me where I went wrong?
Then it asked for the Average Total Cost and Marginal Cost. This is where I began to be 99% certain I'm doing something wrong, since my ATC was my C divided by Q and it made no sense. My Marginal cost was w/MPl = 10/2k + 5L^-1/2 = .5 + 2L^-1/2.
With the result that my Elasticity of cost, ATC/MC, was a jumbled mess.
The examples my prof gave us totally didn't help since they were much simpler and hardly related to this bomb he dropped on the midterm x(
 
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Your MPk and MPl is wrong. It should be MPk = 2, MPl = 5L^(-1/2)
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Baa?21242 Posts
....Fuck I'm retarded ROFL. How did I not see that?
Well that just explained the source of my woes.
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Baa?21242 Posts
Now I'm really upset at how that horribly basic math mistake raped my entire problem. Sigh.
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On October 27 2009 05:10 gchan wrote:
Your MPk and MPl is wrong. It should be MPk = 2, MPl = 5L^(-1/2)
Yeah, those are the partials, which is what you want according to the ceteris paribus assumption.
On October 27 2009 04:41 Carnivorous Sheep wrote:
[...] L = [(Q-20)/(10)]^2, and plugged it back into the C equation to get some blob. Seemed fairly reasonable, but it seemed wrong for some reason.
No, I think that's right. I get C = 1/50 (Q - 20)² + 40. Though this is a little silly because total cost is decreasing until the minimum at Q = 20.
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since my ATC was my C divided by Q and it made no sense
That's the definition of average total cost, isn't it? Cost function over Q.
Also high five fellow economist (?)
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On October 27 2009 05:10 gchan wrote:
Your MPk and MPl is wrong. It should be MPk = 2, MPl = 5L^(-1/2)
*sigh* Beat me to it.
Whenever I can actually help someone, I always end up coming in too late. I mean how often do I actually get to DO or USE this stuff now? Oh well. I'd like to be first just once.
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On October 27 2009 06:56 Sadistx wrote:That's the definition of average total cost, isn't it? Cost function over Q. Also high five fellow economist (?)
Yes it is but to get ATC you should have the cost function as a function of Q rather than leaving it as a function of L and K. So you solve for L and K first in terms of Q then divide the whole equation (meaning the only variable is Q). Other wise you get a mess with 3 variables in it.
But before any of that you need to get the optimized cost function by doing a lagrangian. Hold on...doing it now...
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On October 27 2009 07:58 Savio wrote:
But before any of that you need to get the optimized cost function by doing a lagrangian. Hold on...doing it now...
Except it's short-run cost.
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On October 27 2009 10:51 butterbrain wrote:Show nested quote +On October 27 2009 07:58 Savio wrote:
But before any of that you need to get the optimized cost function by doing a lagrangian. Hold on...doing it now... Except it's short-run cost.
The lagrangian still works  But yes using it is unnecessary, as it's just the one variable you need to account for.
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EPT
