In an economy, there is a consumer who consumes a consumer good. Its usefulness is given by U(C)=C, where C is its consumption. The production of this consumer good is given by:

Y_c = (l_y)^0.3*E^0.7

l_Y being the amount of labor used directly in the production of the consumer good and E the total amount of energy spent in producing this good. Total energy production is given by:

Y_E = l_E,

l_E being the total amount of work spent on energy production. The total workload is 20.

Formulate the problem of firms and state the conditions that characterize competitive balance.