Consider the following model of a competitive labour market where both firms and workers have perfect foresight and symmetric information about the price level (that is, no misperceptions). Firms' technology is given by the production function

y = a N (production function)

where a is a positive constant representing total productivity, N is employment and the elasticity of production to employed labour is 1/2. The government requires firms to pay pension contributions to the fiscal authority: the contribution is a small fraction x of the wage paid to each employed worker. Therefore, firms profits equal

P y - W N - x W N

and they are maximized taking the price level P, the nominal wage W, and the pension contribution rate x as given. Labour supply is given by:

W = P b N

where b is a positive constant. Answer all the following questions. a) Derive the labour demand schedule by solving the profit maximization problem of firms.