(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…

ate a table and graphs (a) Suppose we have preferer 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 calculate and then interpret what the value of the MRS means.< (c) Cobb-Douglas preferences are strictly convex. What does this imply about the 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 the consumer's budget constraint? Sketch this in a figure and explain.<

ate a table and graphs (a) Suppose we have preferer 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 calculate and then interpret what the value of the MRS means.< (c) Cobb-Douglas preferences are strictly convex. What does this imply about the 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 the consumer's budget constraint? Sketch this in a figure and explain.<

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.14P

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