2 Labor market

Consider an economy in which the labor market is competitive. There is a large number of firms each with technology given by the following production function

Y = AKa N1-a where Y denotes the (unique) consumption good, K denotes capital stock, and

N denotes labor input (in hours) in production.

There is also a large number of agents who supply labor, with preferences given by

u (c, l) = log (c) + ? log (l) where l denotes leisure and c denotes consumption. Each of these agents has T hours of time (monthly) to allocate between leisure and labor. The only source of income for the agents is labor income.

Assume that the price of the consumption good (denote it by P) is exogenously given and equal to 2. Use W to denote the hourly nominal wage in the economy