1. Rick consumes 2 goods, Chicken McNuggets (M) with Szechuan sauce (S). His utility function is U(M, S) = M2/3 S1/3 and his income is m. The price of Chicken McNuggets is p, and the price of Szechuan sauce is 1. a. Write down Rick's budget constraint. What is the slope of his budget constraint? (1 point) b. Find Rick's marginal utilities of each good, and find his marginal rate of substitution (MRS). (2 points) c. Write down an equation showing the relationship between Rick's MRS and the slope of his budget constraint that must hold if Rick is maximizing utility. (1 points) d. Use the equation from part (c) and the budget constraint from part (a) to find Rick's demand for each of the two goods. (3 points) e. Suppose m=100 and p=1. How much of each good does Rick consume? Draw a graph showing Rick's budget constraint and indifference curve passing through his chosen consumption bundle. (1 points) f. Suppose m=100 and p=2. How much of each good does Rick consume? On the same graph from part (e), show Rick's budget constraint and indifference curve passing through his new chosen consumption bundle. (2 points) g. On the same graph, show the (hypothetical) budget constraint that is tangent to the indifference curve from part (e) but parallel to the budget constraint in part (f). (3 points) h. On the same graph, show the income and substitution effects of the increase in p from 1 to 2 on Rick's consumption of Chicken McNuggets. Are Chicken McNuggets a normal or inferior good for Rick? Explain your answer. (2 points) i. Find the equation representing the (hypothetical) budget constraint drawn in part (g). Hint: you know this budget constraint has the same prices as in part (f), so you need to find the income level m that makes the budget constraint just tangent to the indifference curve passing through Rick's chosen consumption bundle in part (e). (4 points) j. Find the amount of each good that Rick would consume if is his budget were the one found in part (i). What are the numerical values of the income and substitution effects shown graphically in part (h)? (4 points)