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) = 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 move along 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 and the 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 not have 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 the new optimal demands…
(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.<
1. For each of the three utility functions below, find the substitution effect, the income effect, and the total effect that result when prices change from p = (2,1) to p' = (2,4). Assume the consumer has income I = 20. (a) Before doing any calculation, make an educated guess about the relative magnitude of the three substitution effects and the three income effects to be found below. (b) u(x1, x2) = x1 + x2. (c) u(x1, x2) = x1x2. (d) u(x1,x2) = min {x1,x2). (e) Rank the substitution effects and the income effects found above by their magnitude. To what extent do they conform to your guess?
solve g, h please Thank you
solve e, f, and g please Thank you
Give examples by drawing a graph of each of the following. Please draw your graphs neatly using a ruler to draw the axes and label your graphs completely. In each case draw ar least three indiffer- ence curves and indicate clearly the direction of increasing prefer- ence. (i) the preferences being convex but not strictly convex. (ii) the preferences being strictly increasing but not convex.
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
(2) Consider the utility function u(x, y) = Vx+ay. Your budget constraint is P1x+p2y = М. (a) Find the marginal utilities for these goods. (b) Show that these preferences are quasilinicar. (c) Solve the consumer's optimization problem.
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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 4 pounds of a generic store brand for 2 pounds of a brand-name sugar. Do these preferences exhibit a diminishing marginal rate of substitution? 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?
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)?