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Hi Mauli :)
This is how I did the first part.
The firm is a monoponist in the labour market.
L=w/2 -20
On rearranging we get w= 2L + 40
Now, the total labour cost to the employer is - wL = 2L^2 + 40L
Marginal expenditure (ME) = 4L + 40
Now, from the production we find that MPL =4
TR=py= y(100-y) = 100y - y^2
MR = 100 - 2y
MRPL = MR x MPL = 4(100-2y) = 400 - 8y => (Since the firm is a monopolist in the output market)
y = 4L, so MRPL = 400 - 32L
On equating ME and MRPL,we get L =10.
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