Logarithimic form? Also other questions, need help asap

[GoBlue85]

Hey everyone, collge student, I'm currently taking labor economics, and need some help on this somewhat basic algebra question. I realize this is a math board, not econ, but this is pretty simple math, but I don't think I did this right.

Question:
Demand for labor is known to be: LD(the D is superscrippted) = kW^-2
Supply for labor is known to be: LS(the S is superscrippted) = cW^.5

Write the supply and demand formulas in logarithimic form.

Here is what I came up with:

Demand: logwLD/k = -2
Supply: logwLS/c = .5

The w's are subscrippted, and then of course the D and the S are superscrippted. I divided the c and the k to leave W^-2 and then proceeded to take the log as I wrote it, not sure if thats how it is done. The reason this is so important is b/c their are three more parts to the problem after this, and all are contigent on this being correct. Confused

I'm not sure if I'm doing this right since I don't remember the rules for logs that well, and if I'm forgetting anything.

The next part of the question, which I'm not really expecting an answer from since this is a math board and not economics, but I'll give it a shot anyways. The question states, suppose the government imposes a 5% payroll tax collected from employers, what are the new demand and supply curves (sticking with logs)? I seriously read the book and notes, but cannot figure this out, the book uses set payroll taxes and not percentage, so I have no idea how to go about this. I realize the demand and supply curves will shift, but with a percentage, not sure by how much.

Thanks for any help that you all can provide.

 

[arthur ohlsten]

let D be demand and S supply

D=KW^-2 or
D=K/W^2

S=CW^.5

S/D=[ CW^.5]/[K/W^2]
S/D= [CW^.5W^2] /K
S/D=[CW^2.5]/K take log

log[S/D]= log C +2.5 log W - log K answer or
log S - log D = log C +2.5 log W - log K answer

sorry I can't do second part
Arthur

 

[GoBlue85]

let D be demand and S supply

D=KW^-2 or
D=K/W^2

S=CW^.5

S/D=[ CW^.5]/[K/W^2]
S/D= [CW^.5W^2] /K
S/D=[CW^2.5]/K take log

log[S/D]= log C +2.5 log W - log K answer or
log S - log D = log C +2.5 log W - log K answer

sorry I can't do second part
Arthur

thank you for the reply. I *think* their may have been a misunderstanding, due to the way I wrote the problem. The problem doesn't call for dividing the supply function by the demand, rather it wants to take the supply function and put it into logarthimic form, and then separatly take the demand function and put that into logarthimic form. So sorry for not typing it out correctly, I had written it as "supply/demand", I just meant supply and demand, my mistake.

With THAT said, how does it look now?

 

[skeeter]

Demand for labor is known to be: LD(the D is superscrippted) = kW^-2
Supply for labor is known to be: LS(the S is superscrippted) = cW^.5

\(\displaystyle \L L_D = kW^{-2}\)
\(\displaystyle \L \log{(L_D)} = \log{(kW^{-2})}\)
\(\displaystyle \L \log{(L_D)} = \log{(k)} + \log{(W^{-2})}\)
\(\displaystyle \L \log{(L_D)} = \log{(k)} - 2\log{(W)}\)

find the log form for supply the same way.

 

[GoBlue85]

Demand for labor is known to be: LD(the D is superscrippted) = kW^-2
Supply for labor is known to be: LS(the S is superscrippted) = cW^.5

\(\displaystyle \L L_D = kW^{-2}\)
\(\displaystyle \L \log{(L_D)} = \log{(kW^{-2})}\)
\(\displaystyle \L \log{(L_D)} = \log{(k)} + \log{(W^{-2})}\)
\(\displaystyle \L \log{(L_D)} = \log{(k)} - 2\log{(W)}\)

find the log form for supply the same way.

thanks for the help.

Ok i'm still a little confused though, as I was reading that step for step, it made sense. But my only question is, why can't you do it the way I did? Basically I divided out the k and the c to isolate the wage (W) in each the supply and the demand, and then took the log of W^-2. OR did we do the same thing except I did not take the log of the other side, which would have been LD/K for the demand. I think if you take the log of LD/K for the demand and set it equal to the log of W^-2, then that equation would be the same as what you came up with correct?

I was primairly trying to figure this problem out based of the common example of: 2^x=8, and that turned into log(2 subscript)8 = x, so I didn't really understand why you take the log of the other side as well when I didn't see that happen in this problem.

Sorry for what seems to be a bunch of stupid questions, it seems like I learned logs YEARS ago and don't remember a thing.

 

[GoBlue85]

Ok plugging in values for k and W did not work. (Random numbers)

When I plugged in k = 15 and W = 6 in the original formula, non-log, Labor demanded equaled .416667.

When I plugged in k = 15 and W = 6 into the log form -- log D = log(k) -2log(W), i get log D = a negative number, and when I try to take the log of that to finish the problem, I have a domain error. Am I entering all this into my calculator wrong? Because these two formulas should be equal correct? The log and nonlog formula that is. I am entering into my calculator EXACTLY the following: LOG key (15) - 2 * LOG KEY (6), and then trying to take the log of that answer, the number is negative.

:?