What allocation should the government choose to maximize its social welfare function subject to its equity-efficiency tradeoff?

Learning Goal: I’m working on a international economics multi-part question and need an explanation and answer to help me learn.A three-person society has a utilitarian social welfare function U = u(c1) + u(c2) + u(c3) defined over the utilities of the three citizens. ci is the consumption of citizen i and u(ci) = 2c^0.5i. The society has total 100 units of consumption to divide among the three citizens. Suppose that initially 80 units belong to citizen 1 with 10 units belonging to each of citizens 2 and 3. The government loses $0.50 for each unit it takes away from citizen 1 to give to others. What allocation should the government choose to maximize its social welfare function subject to its equity-efficiency tradeoff? (An approximate solution, rounded to the nearest integer, is fine.
Requirements: 1 page explaination and solution of practical robelm

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