Cowflop, Wisconsin, 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 Cowflop are all pretty much the same. In fact, they have identical utility functions. The utility function of each citizen i is U_i(x_i, g) = x_i + √g/20, where x_i 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. 

(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 Cowflop.