In these questions you are in the role of the mayor of a small town. Given the preferences in your town, you are asked to make optimal decisions on how the town should use its resources. Specifically, town revenue can either be used on paying for live concerts or purchasing a generic consumer good (such as toys, food, cars, etc), to distribute to the population of the town.

In the following problems: Let x₁ be concerts held over the year.

Let x₂ be amounts of the consumer good for everyone in the town purchased per year

SA 1 Utility Maximization / Finding the Optimal Bundle.

Suppose the town's preferences are cobb douglas: U(x₁ x₂^1/4 ). The price for a concert is p₁ = 10. The price of consumer goods is p₂ = 10 and town has income: m = 200

a. Find the equations for the marginal utilities of both goods.

b. Find the marginal rate of substitution.

c. Set the MRS equal to the slope of the budget line, solve this equation for x₂.

d. Write down the equation for the budget line

e. Using the two equations in c. and d, solve for the optimal bundle. Show your work. What are the values of the optimal bundle ( x₁^*, x₂^* )