A small town has 3,000 people. The citizens are interested in watching fireworks. Each fireworks cost $5. Each citizen is identical and the utility function for citizen i is given by Uᵢ(xᵢ,g) = xᵢ + √g/20
where xᵢ is the income spent on other goods, and g is the number of units of fireworks. (a) Find the absolute value of the marginal rate of substitution between fireworks and the income for citizen i. (Hint: visualize the indifference curve between fireworks and income, in which fireworks is on the horizontal axis and income is on the vertical axis.) (b) Find the socially optimal number of fireworks in this town.