(a)_Suppose we have preferences U(X, Y) = X² Y2.. What is the utility at the bundle X = 5 and Y = 20? Create a table then graph/sketch the indifference curve through (5, 20). Interpret the MRS (with MRS = Y/X) at this bundle. < (b)_Let prices be Px = $5, Py = $5 and income M = $1000. Draw/sketch the budget constraint. Explain what the slope of the budget line means in economic terms.< (c) State the consumer's utility maximization problem and express this in words. What are the two conditions (equations) that identify the optimum? Sketch this in a figure and explain.

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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(a)_Suppose we have preferences U(X, Y) = X² Y².. What is the utility at the bundle X = 5 and Y = 20?
Create a table then graph/sketch the indifference curve through (5, 20). Interpret the MRS
(with MRS = Y/X) at this bundle. <
(b) _Let prices be Px = $5, Py = $5 and income M = $1000. Draw/sketch the budget constraint.
Explain what the slope of the budget line means in economic terms.<
(c) State the consumer's utility maximization problem and express this in words. What are the two
conditions (equations) that identify the optimum? Sketch this in a figure and explain.<
(d) Use the information in (a) and (c) to show that demands are: X = ½ M/PX and Y = ½ M/PY.<
(e) For the income and prices in (b), what is optimal X, Y, and utility? Show your work.
(f) Suppose Px falls to $4 and Py rises to $7 but income stays at $1000. Does consumer utility rise
or fall? Show and explain. <
(g) Calculate the Compensating Variation that ensures the consumer is no worse off nor better off
with these price changes. Show and explain your work.
Transcribed Image Text:(a)_Suppose we have preferences U(X, Y) = X² Y².. What is the utility at the bundle X = 5 and Y = 20? Create a table then graph/sketch the indifference curve through (5, 20). Interpret the MRS (with MRS = Y/X) at this bundle. < (b) _Let prices be Px = $5, Py = $5 and income M = $1000. Draw/sketch the budget constraint. Explain what the slope of the budget line means in economic terms.< (c) State the consumer's utility maximization problem and express this in words. What are the two conditions (equations) that identify the optimum? Sketch this in a figure and explain.< (d) Use the information in (a) and (c) to show that demands are: X = ½ M/PX and Y = ½ M/PY.< (e) For the income and prices in (b), what is optimal X, Y, and utility? Show your work. (f) Suppose Px falls to $4 and Py rises to $7 but income stays at $1000. Does consumer utility rise or fall? Show and explain. < (g) Calculate the Compensating Variation that ensures the consumer is no worse off nor better off with these price changes. Show and explain your work.
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