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.

(a) Suppose now that the government gives a subsidy to energy production, paying 10% more for the amount of energy produced (thus, the energy producing firm's revenue is 1.1*P_E*y_E, where P_E is the energy price). This subsidy is financed by a consumer lump sum tax. Get the new competitive balance.

(b) Is the competitive balance obtained in (a) efficient? What theoretical result is behind your answer?