Suppose Nick's utility function for shirts (s) and dumplings (d) is U(s,d) = s^0.75d^0.25. Nick's income is $12, the price of a shirt is $6, and the price of a dumpling is $2. Place shirts on the x-axis.

(a) Looking at the utility function and the relative prices of both goods, can you predict if Nick's optimal bundle will contain more dumplings or more shirts? Explain.

(b) Solve for Nick's optimal consumption bundle using the steps from class.

(c) Graph Nick's budget constraint, his optimal bundle, and some indifference curves (one of which is tangent to his optimal bundle, and one that intersects the suboptimal bundle (0.5 shirts, 4.5 dumplings)). As always, make sure your graph is super-well labeled.

(d) What is Nick's MRS at the suboptimal bundle (0.5, 4.5) and what is his MRS at the optimal bundle? Why is one smaller than the other? Explain (in terms of diminishing marginal rate of substitution).