Question: Suppose Miranda's preferences for goods 1 and 2 are described by the utility function:

\(U=3x_{1}^{1/3}+3x_{2}^{1/3}\). Suppose additionally that Miranda has a fixed income of 200 and the respective prices of goods 1 and 2 are 6 and 12, respectively.

a. Write Miranda's budget constraint and represent it graphically (hint: represent x₁ on the horizontal axis). What is the maximum quantity of good 1 Miranda could purchase if she spent her entire income on good 1. What is the slope of Miranda's budget line?

b Obtain the marginal utilities for goods 1 and 2. Does the marginal utility of good 2 conform to the law of diminishing marginal utility? Explain. Obtain the MRS of x₁ for x₂

c. Obtain the Marshallian demand functions.

d. What is the most preferred market basket? What. is the highest level of utility Miranda can reach given her incoMeand the prices of both goods? Represent this problem in the diagram from part a. (worth 3 points)

e. Obtain the income elasticity for good 2. Based on this result, what type of good is 2? (2 points)