The profit-maximizing firm's demand for labour, L, is contributed to by the wage paid to labour, w, the price of the output, P, and the level of...

1. The profit-maximizing firm's demand for labour, L, is contributed to by the wage paid to labour, w, the price of the output, P, and the level of output itself, Q, which is a function of labour. Specifically,

Q(L) = L, P(Q) = α − βQ, T C = F + wL,

whereα>0,β>0,F >0,andw>0.

(a) Derive the firm's demand for labour,

(b) Derive the elasticity of labour demand with respect to wage.

(c) What effect does F have on the demand for labour?

(d) Is this firm a monopsonist?