ISI 2015 PEB Sample Question 5

[Zen]

I tried to write down the profit function for the firm only in terms of elasticity of supply of male labor using the facts given and tried to differentiate it w.r.t that, but the equation is too messy. Can anyone help me in doing this?

[onionknight]

I could only solve the first part. Just minimize the cost subject to Q=LM+LF and you would get elasticity of male labor supply=εM=2.
I face the same problem as you do while solving the second.

[onionknight]

Have you tried problems from all previous test papers? Or anyone else who'd like to discuss?

[Zen]

I am trying to solve all the problems. But so far I haven't gone very far into the past (pun intended).

[onionknight]

So am I. I've only just started and done for a couple of years and I'll try and finish all those available online. I can't really find the answers anywhere so I thought it'd be a good idea to discuss with someone.

[L]

For second part, I did something like this:
TL = total labor income , TLm = male labor income
we need to calculate TLm/ TL =Z
TLm = Wm*Lm
TL = Wm*Lm + Wf*Lf = Wm(Lm+Lf/2) as Wm=2Wf

So, Z = 2Lm/ (2Lm+Lf)
from first order conditions, you get:

A- Lm - Lf - Wm - Wm/ Em = 0            Em- epsilon for male
Lm+Lf = A-3/2Wm

So, Z = Lm/ (2Lm + Lf)
 = 2Wm^2 / (A -3/2 Wm + sqrt (Wm/2))

So, If A increases then  Z decreases.

[onionknight]

How can you be sure that the equilibrium values of Wm and Wf won't be affected by changing A. To conclude anything about the relation between A & Z, you must have a relation that doesn't have other variables like Wm and Wf in this case.