solve g, h 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.<

From part d: The optimal demand equation for good X is X=2M3Px .....(1) The optimal demand…

Answered: (g) Show that, if M falls to $1034,…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.7P

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solve g, h please

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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 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 the
equilibrium in (e) above. Eg confirm that utility is unchanged but with this new income and
prices.
(h) What do we mean by Compensating Variation (CV)? What is the value of the CV in this
example? Explain.<

Expert Solution

Step 1

From part d:

The optimal demand equation for good X is $X = \frac{2 M}{3 P_{x}}$ .....(1)

The optimal demand equation for good y is $Y = \frac{1 M}{3 P_{y}}$ ..... (2)

Given utility function: $U = 10 X^{2 / 3} Y^{1 / 3}$ .....(3)

To get optimal demand at any price level and income, simply put the values of prices and income in the optimal demand equation, we will get the optimal demand for good x and good Y. Then put the calculated value of X* and Y* into the utility function, we get the maximum utility.

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