help with question 4 please

4. [30 points total] In an economy. fraction a of people are productive. They can produce to with labor disutility m if they want. By contrast. fraction 1 a of people are totally unproductive. All people have identical consumption utility 111 c. The planner chooses CH, consumption for a productive person. and (3,, consumption for an unproductive person. to maximize social welfare: W=g{lncHn:}+(1g)lncL, 0