solve d,e,f pleaseThank you (a) Suppose we have preferences U(X, Y) = 10X²/³ Y¹/3, Create a table and graph/sketch theindifference curve through the bundle X = 30 and Y = 30.<(b) The Marginal Rate of Substitution is MRSxy=-2Y/X. For the bundle (X= 30, Y = 30),calculate and then interpret what the value of the MRS means.<(c) Cobb-Douglas preferences are strictly convex. What does this imply about the MRS as we movealong the indifference curve? Explain/discuss (you may want to draw a picture). <(d) What are the two conditions (equations) that identify the optimum given these preferences andthe consumer's budget constraint? Sketch this in a figure and explain.<(e)_From (d) we can show that optimal demands are: X=½ M/PX and Y = ½ M/Px. (you do nothave to derive these, just use the equations I have given you.) Calculate optimal demands (X*,Y*) and utility if Px = 10, Px= 5 and income M = 1200. <(f)_Suppose Px falls to Px = 8 but Py and M are unchanged (Px = 5 and M = 1200). Calculate thenew optimal demands and utility. Compare to the original optimal choices in (e) and discuss.(g)_Show that, if M falls to $1034, with Px = 8 and Px = 5, then this has the same utility as theequilibrium in (e) above. Eg confirm that utility is unchanged but with this new income andprices.(h) What do we mean by Compensating Variation (CV)? What is the value of the CV in thisexample? Explain.<

Utility function : U = 10 x2/3 y1/3 Budget Constraint : Px*x + Py*y = M Optimal consumption is…

(a) Suppose we have preferences U(X, Y) = 10X2/3 Y1/3, Create a table and graph/sketch the indifference curve through the bundle X = 30 and Y = 30.< (b) The Marginal Rate of Substitution is MRSxy=-2Y/X. For the bundle (X= 30, Y = 30), calculate and then interpret what the value of the MRS means.< (c) Cobb-Douglas preferences are strictly convex. What does this imply about the MRS as we 100

(a) Suppose we have preferences U(X, Y) = 10X2/3 Y1/3, Create a table and graph/sketch the indifference curve through the bundle X = 30 and Y = 30.< (b) The Marginal Rate of Substitution is MRSxy=-2Y/X. For the bundle (X= 30, Y = 30), calculate and then interpret what the value of the MRS means.< (c) Cobb-Douglas preferences are strictly convex. What does this imply about the MRS as we 100

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.7P

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(a) Suppose we have preferences U(X, Y) = min [X, 3Y]. Graph/sketch the indifference curve through the bundle (X = 30, Y = 30). What is the utility of (30, 30) and explain why the indifference curves look the way they do. (b) What does the Marginal Rate of Substitution tell us about preferences? < (c) Why is the Marginal Rate of Substitution not applicable in this example? < (d) What do we mean by a composite good? What does this composite good look like with these preferences? Show and explain.< (e) State the consumer's maximization problem and express this in words.< (f) Now let Px = 10, Px= 20 and income M = 2000. Find optimal X*, Y*, and the resulting Utility (U*). Show your work. < (g) Now let Py = 15. How does optimal consumption (X*.Y*) and utility (U*) change relative to (e)? Explain in simple terms and show in a diagram.<
solve e, f, and g please Thank you
Number of Sodas per day Total Utility Marginal Utilit 1 20 35 3 47 12 4 10 Refer to the table, The marginal utility of the second soda per day is L. (Answer should be in the form of numerical characters, e.g. 20) Enter your answer here
Donald likes fishing (X1) and hanging out in his hammock (X2). His utility function for these two activities is u(x1, x2) = 3X12X24. (A) Calculate MU1, the marginal utility of fishing. (B) Calculate MU2, the marginal utility of hanging out in his hammock. (C) Calculate MRS, the rate at which he is willing to substitute hanging out in his hammock for fishing. (D)Last week, Donald fished 2 hours a day, and hung out in his hammock 4 hours a day. Using your formula for MRS from (c) find his MRS last week. (E) This week, Donald is fishing eight hours a day, and hanging out in his ham mock two hours a day. Calculate his MRS this week. Has his MRS increased or decreased? Explain why? (F) Is Donald happier or sadder this week compared to last week? Explain.
A consumer finds only three products, X, Y, and Z, are for sale. The amount of utility yielded by their consumption is shown in the table below. Assume that the prices of X, Y, and Z are $10, $2, and $8, respectively, and that the consumer has an income of $74 to spend. (a) Complete the following table by computing the marginal utility per dollar for successive units of X, Y, and Z to one or two decimal places. (b) How many units of X, Y, and Z will the consumer buy when maximizing utility and spending all income? Show this result using the utility maximization formula. (c) Why would the consumer not be maximizing utility by purchasing 2 units of X, 4 units of Y, and 1 unit of Z? Product X Product Y Quantity Utility Marginal Quantity Utility Marginal Utility Utility per$ per$ 1 23 4567 42 82 118 148 170 182 182 1 23 4 5 6 7 14 26 36 44 50 54 56.4 Product Z Quantity Utility Marginal Utility per$ 1 23456 7 32 60 84 100 110 116 120 3..
Ice cream and cakes are perfect substitutes for a child, and 2 units of ice cream is always worth 3 units of cakes (however many ice creams or cakes she might have, she would be willing to give up 2 ice creams to get 3 more cakes to keep the same utility level) . (a) Write down a utility function u(x,y) that represents the child's preferences, where x is the number of ice creams and y is the number of cakes she has. (b) If the prices are px= 8 and py =5, and she has $140 to spend on the two goods this summer, what is her optimal bundle? (c) If the price of ice creams decreases slightly, down to px = 7, what happens to her optimal bundle in this case? Did it change "slightly" compared to (b)?
4 Part Question on Caesar * * PART 1 * * Caesar has preferences that are described by the utility function u = 3x 1 + 5x 2. Caesar strictly prefers the bundle (x 1, x 2) = (0, 6.6) to the bundle A. (3, 3) B. (5, 3.6) C. (0, 8.4) D. (11, 1.8) E. (8, 3.60) * * PART 2 * * What is the functional form of Caesar’s preferences, or indifference curves? A. Linear (perfect substitutes) B. Leontief (perfect complements) C. Satiation D. Concave, but not strictly concave E. Cobb-Douglas * * PART 3 * * Caesar’s preferences are A. strictly convex. B. definitely not well-behaved. C. definitely well-behaved. D. strictly concave. E. neutral. * * PART 4 * * Caesar has been consuming the bundle (x 1, x 2) = (10, 2.4). At this point, what is the marginal rate of substitution? A. – 0.25 B. –0.6 C. – 1.67 D. – 3.0 E. – 5.0.
10) Suppose that the utility function of an individual can be described as U(X,Y) = 4X +2Y. For this utility function the MRSA) is always X*YB) is always constantC) is always X/YD) is always X+YE) is always X-Y.
How does a consumer maximizes their utility given that they experience a budget constraint? Explain with graphical illustrations. Note:- Please avoid using ChatGPT and refrain from providing handwritten solutions; otherwise, I will definitely give a downvote. Also, be mindful of plagiarism. Answer completely and accurate answer. Rest assured, you will receive an upvote if the answer is accurate.
Consider a consumer whose preferences can be represented by the utility function u(x, y) = x + y (a) Originally, px = 1, py = 2 and m = 1. What bundle does the consumer choose, and what is his utility from this bundle? (b) The price of good x then rises to 3. What bundle does the consumer choose after the price change, and what is his utility from this bundle? (c) Calculate the compensating variation. (Hint: at the new price ratio, what good will he spend his income on?) (d) Calculate the equivalent variation.
solve d,e,f please Thank you
It is common for supermarkets to carry both generic (store-label) and brand-name (producer-label) varieties of sugar and other products. Many consumers view these products as perfect substitutes, meaning that consumers are always willing to substitute a constant proportion of the store brand for the producer brand. Consider a consumer who is always willing to substitute four pounds of a generic store-brand sugar for two pounds of a brand-name sugar. Do these preferences exhibit a diminishing marginal rate of substitution between store-brand and producer-brand sugar? Assume that this consumer has $24 of income to spend on sugar, and the price of store-brand sugar is $1 per pound and the price of producer-brand sugar is $3 per pound. How much of each type of sugar will be purchased? How would your answer change if the price of store-brand sugar was $2 per pound and the price of producer-brand sugar was $3 per pound?