In an economy, there is a consumer who consumes a consumer good. Its utility 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 where "l_y" is the amount of labor used directly in the production of the consumer good and "E" the total amount of energy expended in the production of this good. The total energy production is given by: Y_E = l_E,

where "l_E" is the total amount of work spent on energy production. The total work allocation is 20.

(a) Formulate the Pareto problem (which generates the efficient allocations). (b) Get an efficient allocation.