For the following utility functions:1. U(X, Y) = XY?2. U(X, Y) =XY+ 10Y3. U(X, Y) = X² + Y sia. Write the general equation of the MRS for each utility function.b. Write the equation for the indifference curve where utility is equal to 100 for each utilityfunction.c. Determine whether these indifference curves for each of the utility functions are convex(that is, whether the MRS decreases as x increases) or are concave (and thus violate anassumption about preferences).3.

Answered: 3. For the following utility functions:…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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?
What information is contained in an indifference curve? Why are such curves (a) downsloping and (b) convex to the origin? Why does total utility increase as the consumer moves to indifference curves farther from the origin? Why can’t indifference curves intersect?
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Donald derives utility from only two goods, carrots (X) and donuts (Y). His utility 0.1 0.9 function is as follows: U(X,Y) =X Y Donald has an income (M) of $900 and the price of carrots (P,) and donuts (P,) are $45 and $90 respectively Based on this information, what does the slope of the indifference curve for Donald tell us. Select one: A. For each additional quantity of carrot consumed, Donald must give up 0.25 of donuts to maintain the same level of satisfaction B. For each additional quantity of donuts consumed, Donald must give up 1/2 of carrots to maintain the same level of satisfaction C. For each additional quantity of carrot consumed, Donald must give up 1/2 of donuts to maintain the same level of satisfaction D. For each additional quantity of carrot consumed, Donald must give up 1/9 of donuts to maintain the same level of satisfaction E. For each additional quantity of donuts constumed. Donald must give up 1/2 of carrots to maintain the same level of satisfaction. F. For…
(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…
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When plotted Sarah's indifference curve for coffee and tea reveals parallel indifference curves that always have a slope of -1. Suppose that Sarah's budget constraint is 20 -1.5C+1.0T where C is the quantity of coffee and T is tea. If Sarah wants to maximize utility, she will buy: a) equal amount of coffee and tea b) coffee only c) tea only d) more coffee than tea e) a combination of coffee and tea cannot be determined from the information given
Suppose you have a $20 gift card and want to buy Blue and Red yarn. The utility function from yards of blue (B) and red (R) yarn can be expressed as follows: U(B,R) = 3B+R Red yarn costs $4 per yard. blue yarn costs $4 per yard. A) Graph the budget constraint and the indifference curves that can be reached. How many yards of each type of yarn will he purchase at these prices with his gift card?
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