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Jalen is a professional athlete who carefully manages his diet to boost his on field performance. He diet consists exclusively of smoothies, s , and fish, f . Suppose his preferences are described by the utility function U ( s , f ) = s 1 f , where 0 < < 1 and > 0 . The price of smoothies is p s , the price of fish is p f , and Jalen has a monthly budget Y to spend on food. a. Draw a graph illustrating Jalen's budget constraint with smoothies on the x -axis and fish on the y -axis. Give expressions that represent the intercepts and slope. In no more than two sentences, describe how the budget constraint would change if the price of fish fell (be sure to reference each of the intercepts and slope in your answer). b. Sketch two of Jalen's indifference curves in the same diagram; just the rough shape, no need to plot the exact curves. Draw one that is just tangent to the budget line at a point E ; and draw a lower one that intersects the budget constraint twice at points denoted by C (where MRS < MRT) and D (where MRS > MRT ). c. Concisely explain why the bundle (in part b) where the budget line is tangent to an indifference curve is the optimal bundle for Jalen. You should reference MRS and MRT in your answer. d. In no more than two sentences, explain how Jalen, at the margin, could improve his standard of living at point C. You should reference MRS and MRT in your answer. e. Find the formulas for Jalen's utility maximizing quantities of smoothies and fish, s and f , respectively. Before you solve, simplify the utility function to make the algebra easier, for example, you could take the natural log of the utility function like we did in class. Briefly explain why the change you make to the utility function will lead to the same answer as the original utility function. f. Jalen's spending on smoothies and fish per month ends up being p s s and p f f , respectively. Plugging in your results for s and f , find expressions for how much he spends on each good as a function of income. What do these expressions tell you about the meaning of the and ( 1 ) parameters of the utility function? What is special about the way that the optimal bundle varies with a change in one of the prices, when a consumer has cobb-douglas utility? .

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Jalen is a professional athlete who carefully manages his diet to boost his on field performance. He diet consists exclusively of smoothies, s , and fish, f . Suppose his preferences are described by the utility function U ( s , f ) = s 1 f , where 0 < < 1 and > 0 . The price of smoothies is p s , the price of fish is p f , and Jalen has a monthly budget Y to spend on food. a. Draw a graph illustrating Jalen's budget constraint with smoothies on the x -axis and fish on the y -axis. Give expressions that represent the intercepts and slope. In no more than two sentences, describe how the budget constraint would change if the price of fish fell (be sure to reference each of the intercepts and slope in your answer). b. Sketch two of Jalen's indifference curves in the same diagram; just the rough shape, no need to plot the exact curves. Draw one that is just tangent to the budget line at a point E ; and draw a lower one that intersects the budget constraint twice at points denoted by C (where MRS < MRT) and D (where MRS > MRT ). c. Concisely explain why the bundle (in part b) where the budget line is tangent to an indifference curve is the optimal bundle for Jalen. You should reference MRS and MRT in your answer. d. In no more than two sentences, explain how Jalen, at the margin, could improve his standard of living at point C. You should reference MRS and MRT in your answer. e. Find the formulas for Jalen's utility maximizing quantities of smoothies and fish, s and f , respectively. Before you solve, simplify the utility function to make the algebra easier, for example, you could take the natural log of the utility function like we did in class. Briefly explain why the change you make to the utility function will lead to the same answer as the original utility function. f. Jalen's spending on smoothies and fish per month ends up being p s s and p f f , respectively. Plugging in your results for s and f , find expressions for how much he spends on each good as a function of income. What do these expressions tell you about the meaning of the and ( 1 ) parameters of the utility function? What is special about the way that the optimal bundle varies with a change in one of the prices, when a consumer has cobb-douglas utility? .

- 1. Jalen is a professional athlete who carefully manages his diet to boost his on field performance. He diet consists exclusively of smoothies, s , and fish, f . Suppose his preferences are described by the utility function U ( s , f ) = s 1 f , where 0 < < 1 and > 0 . The price of smoothies is p s , the price of fish is p f , and Jalen has a monthly budget Y to spend on food. a. Draw a graph illustrating Jalen's budget constraint with smoothies on the x -axis and fish on the y -axis. Give expressions that represent the intercepts and slope. In no more than two sentences, describe how the budget constraint would change if the price of fish fell (be sure to reference each of the intercepts and slope in your answer). b. Sketch two of Jalen's indifference curves in the same diagram; just the rough shape, no need to plot the exact curves. Draw one that is just tangent to the budget line at a point E ; and draw a lower one that intersects the budget constraint twice at points denoted by C (where MRS < MRT) and D (where MRS > MRT ). c. Concisely explain why the bundle (in part b) where the budget line is tangent to an indifference curve is the optimal bundle for Jalen. You should reference MRS and MRT in your answer. d. In no more than two sentences, explain how Jalen, at the margin, could improve his standard of living at point C. You should reference MRS and MRT in your answer. e. Find the formulas for Jalen's utility maximizing quantities of smoothies and fish, s and f , respectively. Before you solve, simplify the utility function to make the algebra easier, for example, you could take the natural log of the utility function like we did in class. Briefly explain why the change you make to the utility function will lead to the same answer as the original utility function. f. Jalen's spending on smoothies and fish per month ends up being p s s and p f f , respectively. Plugging in your results for s and f , find expressions for how much he spends on each good as a function of income. What do these expressions tell you about the meaning of the and ( 1 ) parameters of the utility function? What is special about the way that the optimal bundle varies with a change in one of the prices, when a consumer has cobb-douglas utility?