A two-person society has a utilitarian social welfare functionU=u₁(c₁) +u₂(c₂) defined over the utilities of the two citizens.c_iis the consump tion of citizeni. Supposeu₁(c₁) =c₁,u₂(c₂) = 2c^0.5

₂. The society has 200

units of consumption and initially all of them belong to citizen 1. Each unit the government takes away from citizen 1 to give to citizen 2 results in a dead weight loss of 0.25 units. How much should the government take from citizen 1 to give to citizen 2? (An approximate solution rounded to the nearest integer is fine.) Explain why this is the government's optimum given its social welfare function