Question: Suppose a consumer's preferences can be represented by the utility function: \(U\left( X,Y \right)={{X}^{3/5}}{{Y}^{1/4}}\)

a. Derive the function for the marginal rate of substitution holding utility constant: \({{\left. \frac{\Delta Y}{\Delta X} \right|}_{{\bar{U}}}}\)

b. Derive the demand curves for the two goods, X and Y.

c. Confirm that both demand curves slope downward.

d. Calculate the price elasticity for each of the goods.

e. Calculate the income elasticity for each of the goods.