Equilibrium and surplus labor market

[goldiecr12]

Hello !
I have the following question in my public economics class : Suppose the labor demand is

and that the labor supply is where N is number of workers and w is the salary. Suppose also that the market for labor is competitive. 1) Find the values of N and w at equilibrium 2) Find the surplus of workers

I don't know how to find the values of N and w when i equalize demand and supply. Do i need to derive the supply equation and the demand equation ?

 

[HallsofIvy]

Since this is a mathematics forum and not economics, I think you will need to say more! What do "\(\displaystyle N^D\)" and \(\displaystyle N^O\) mean? I would guess that \(\displaystyle N^D\) is "the number of workers demanded" but I am not clear on \(\displaystyle N^O\).

 

[goldiecr12]

Thanks for your attention. I will try to be more clear.

In the labor market, Nd is the number of worker demanded by the firms in relation with the hourly wage (w). No is the number of worker who wants to work in relation with the hourly wage (w). So the equilibrium is when number of worker demanded equal the number of worker who want to work. What i don't understand is how to isole w when i equalize w^η = w^λ . The objectif is to find the w who equalize demand of worker and supply of worker.

 

[HallsofIvy]

Given \(\displaystyle w^\eta= w^\lambda\), divide both sides by \(\displaystyle w^\lambda\): \(\displaystyle \frac{w^\eta}{w^\lambda}= w^{\eta- \lambda}= 1\).

Now take the "\(\displaystyle \eta- \lambda\)" root of both sides:
\(\displaystyle w= (1)^{\frac{1}{\eta- \lambda}}= 1\).

1 to any power is 1.

 

[goldiecr12]

thanks for your help Hallsoflvy !