The daily inverse demand curve for pet grooming is P=20-0.1Q. 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=20-0.2Q 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.

Question

The daily inverse demand curve for pet grooming is P=20-0.1Q. 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=20-0.2Q 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.

Answer 1

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)

Answer 2

Thanks for the input.

Answer 3

I think it is 10, is that correct?

Answer 4

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 = 400-4Q
As I stated before, we can translate Q into labors needed: Q=L/20. Substitue this into the equation above.
So: w = 400-4(L/20)
w = 400 -.2L
So:
L = 2000 - 5w

Answer 5

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(20-0.2Q) => 400-4Q => 400-4(20L) => 400-80L

Then VMP has to equal wage. VMP=w => 400-80L=w => 400-w=80L => (400/80)-(w/400)=L
L=5-0.0125w.

that is the labor demand curve.

Answer 6

To find the labor demand curve as a function of the daily wage (w), we need to determine the number of workers the pet store would hire at different wage levels.

Given that each worker can groom 20 dogs per day, we can calculate the number of groomings (Q) as the product of the number of workers (L) and the number of dogs groomed per worker (20): Q = 20L.

Now, let's combine this equation with the inverse demand equation for pet grooming: P = 20 - 0.1Q. Since we know that P = w, we can substitute P with w and Q with 20L:

w = 20 - 0.1(20L)
w = 20 - 2L

This equation represents the labor demand curve as a function of the daily wage (w) for the pet store. It states that the daily wage (w) equals 20 minus twice the number of workers (L).