where q(st) is the price of a unit of consumption goods at st in an abstract unit of
account, x(st) is investment at st, and w(st) is the aggregate real wage at st. The producer’s
problem can be stated in two parts. First, the producer chooses sequences
for capital k(st−1), investment x(st), and aggregate labor l(st) subject to (1) and (6).
Second, the demand for labor of type i by the final goods producer is