economics
posted by anonymous .
The daily inverse demand curve for pet grooming is P=200.1Q. where P is the price of each grooming and Q is the number of groomings given each day. This implies that the Marginal revenue is MR=200.2Q Each worker hired can groom 20 dogs per day. What is the labor demand curve as a funciton of w, the daily wage the pet store takes as given.

Take a shot, what do you think.
Hint. Set MC=MR. You have MR. Since one worker can groom 20 dogs, MC=w/20.
Hint 2: Q can be translated into number of workers (L). You are given 20Q=L. So Q=L/20.
By substitution, you should be able to get a demand function in the form w=f(L) 
Thanks for the input.

I think it is 10, is that correct?

Not correct. I believe your answer should be in the form L=f(w) where L is the number of laborers. This is a demand function for labor (and is the invers of w=f(L) as i hinted before)
you are given MR=20.2Q. As I stated before MC=w/20. In equilibrium, MC=MR.
So: w/20 = 20.2Q.
So: w = 4004Q
As I stated before, we can translate Q into labors needed: Q=L/20. Substitue this into the equation above.
So: w = 4004(L/20)
w = 400 .2L
So:
L = 2000  5w 
it's not L/20. it's supposed to be 20L. therefore, VMP=MPxMR. MP is the derivative of P=20x0.1Q so MP=20. VMP=20x(200.2Q) => 4004Q => 4004(20L) => 40080L
Then VMP has to equal wage. VMP=w => 40080L=w => 400w=80L => (400/80)(w/400)=L
L=50.0125w.
that is the labor demand curve.
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