Economics Question - Please Help!

Jeice

A profit maximizing firm has a production firm Y = K^(1/2) * L^(1/2)

and the firm's MP subscript{k} = L^(1/2) / 2K^(1/2) and MP subscript{L} = K^(1/2) / 2L^(1/2)

This firm uses 13 units of capital and 21 units of labour in equilibrium with a total cost of $2,211.

a) Find the Marginal Rate of Substituion.

b) Using the given information, the MRTS, and the isocost line, find the input prices (r and w)

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I know MRTS = MPL / MPK = K/L, so that answers part a, but for part b, I don't know what to do.

I know that: TC = rK + wL, so given the information from the question, $2,211 = 13r + 21w.

After this step, I get stuck.

The answer is suppose to be r = $85.04 and w = $52.64. But, I don't know how to do it. Please help.

Cauld

It's been a while since I've done something like this. And I can't figure out how to explain it, maybe posting this will help though. Since the MRTS is K/L you can just substitute 21w for 13r into the total cost equation to find the answer. Or 13r for 21w.

So $2211 = 21w + 21w
w = $52.64

or $2211 = 13r + 13r
r = $85.04

Sorry I can't remember all the details

Dunadan019

Cauld wrote: »

It's been a while since I've done something like this. And I can't figure out how to explain it, maybe posting this will help though. Since the MRTS is K/L you can just substitute 21w for 13r into the total cost equation to find the answer. Or 13r for 21w.

So $2211 = 21w + 21w
w = $52.64

or $2211 = 13r + 13r
r = $85.04

Sorry I can't remember all the details

basically the marginal rate of substitution means "how much of x can I add for 1 unit of Y while keeping the price the same".

an MRS of K/L means that for every unit of K you add, you need to take away a unit of L. basically it means that K=L. if the MRS was 2K/.3L^2 it would mean that 2K = .3L^2.

then you just substitute that into your rate equation as stated.

Jeice

Awesome, that makes things so much clearer now. Thank you.