5. (12 points) For each of the following utility functions, write the general equation for theindifference curve and the general equation for the MRS. Next graph the indifferencecurve for U= 40 for each of the following utility functions (with x on the horizontal axis).Finally determine whether the indifference curves for each of the utility functions areconvex (that is, whether the MRS decreases as x increases).a. U(x, y) = xyb. U(x, y) =x¹/² + yc. U(x, y) = 3x + y

The objective of this question is to find the general equation for the indifference curve and the…

Answered: 5. (12 points) For each of the…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question 4 Which of the following is NOT true about indifference curves? O They are downward sloping O They do not cross O The one is closer to the origin is preferable to indifference curves further from the origin O They are bowed in toward the origin
9. Income and substitution effects Sean and Yvette Durand live in Edmonton and enjoy going out to fancy restaurants for dinner and to diners for breakfast. On the following diagram, the purple curves I1 and 12 represent two of their indifference curves for fancy dinners and diner breakfasts. They have $800 per month available to spend on eating out. The price of a diner breakfast is always $10. Each labelled point represents the tangency between a budget constraint and the corresponding indifference curve. DINER BREAKFASTS 48 40 26 BC 0 2 5 10 Z H BC FANCY DINNERS (?) The initial budget constraint (BC₁) shows the Durands' budget constraint when the price of a fancy dinner is $160. At this price, Sean and Yvette would choose to consume two fancy dinners. Suppose that the price of a fancy dinner decreases to $40, shifting their budget constraint to BC2, which represents a new relative price of four diner breakfasts per fancy dinner. (Hint: The blue line labelled H is parallel to BC2 and…
Emily is a utility maximizer. Her income is $100, which she can spend on cafeteria meals and on notepads. Each meal costs $5 and each notepad costs $2. At these prices Emily chooses to buy 16 cafeteria meals and 10 notepads. a) Draw a diagram that shows Emily’s choice using an indifference curve and her budget line, placing notepads on the vertical axis and cafeteria meals on the horizontal axis. Label the indifference curve, I1, and the budget line BL1. Make sure you calculate the endpoints of the budget constraint. b) The price of notepads falls to $1; the price of cafeteria meals remains the same. On the same diagram, draw Emily’s budget line with the new prices and label it BL2. c) Lastly, Emily’s income falls to $90. On the same diagram, draw his budget line with this income and the new prices and label it BL3. Is she worse off, better off, or equally as well off with these new prices and lower income than compared to the original prices and higher income?
4. Depict in separate graphs indifference curves for the following utility functions i. U(x1,x2) = min(x1,x2) ii. U(x1,x2) = max(x1, x2) iii. Are the goods in both cases substitutes or complements?
3. Juliette spends $48 each month on Oreo cookies (which cost $2 per package) and salt and vinegar chips (which cost $3 per bag). a) Suppose that the price of chips falls to $2 per bag and Juliette increases her chip consumption to 8 bags each month. Draw Juliette's new budget constraint and indicate her chosen bundle with an appropriately drawn indifference curve. Label her utility-maximizing bundle with the letter B. (Be sure to determine the right quantities of both chips and Oreos!) -LJ-J-1. IIII IIII J-L--- -1-1-L -LJ-J- 1- --+-+ --1-1 - IIII ת - ד -ר IIII III I IIII IIII L -1-L----1-1-L-- L--L- -LJ-J-1- IIII -LJ-J- 1- IIII IIII -+--- --+-+
In your own words, explain what indifference curves are. Give 4 properties of indifference curves.
(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…
4- An indifference curve connects points on a graph representing different quantities of two goods, points between which a consumer is indifferent. Food Clothing a) Danyal is obsessed with food and clothes. Assume you have no knowledge of the budget line, what point would Danyal prefer to be at. b) Why can't two indifference curves not intersect, explain and illustrate your answer. c) As we move from point c to f, who's marginal rate of substitution declines.

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