求解一道关于帕雷托最优问题和PUblic good 问题

求解一道关于帕雷托最优问题和PUblic good 问题。Galway, Ireland has 1,000 people. Every year they have a fireworks show on the Fourth of July. The citizens are interested in only two things, drinking milk and watching fireworks. Fireworks cost 1 gallon of milk per unit. People in Galway have identical utility functions Ui(xi, g)=xi+(√g)/20, where xi is the number of gallons of milk per year consumed by citizen i, and g is the number of units of fireworks exploded in the town’s Fourth of July extravaganza. (Private use of fireworks is outlawed.)

a.Solve for the absolute value of each citizen’s marginal rate of substitution between fireworks and milk.
b. Find the Pareto optimal amount of fireworks for Galway.
第一题答案是1/40(√g),第二题答案625.谢谢！