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Suppose that an individual with income I cares about two goods,X and Y. The price of the two goods is Px and Py. The individualhas the following utility function:

U(X,Y) = X(2+Y)

a) Find the Marshallian(uncompensated) demand for X and Y.

b) Find the Hicksian(compensated) demand for X and Y.

c) What is the minimumexpenditure necessary to achieve a utility level of U = 100 with Px= 5 and Py = 20 ?

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Yusra Anees
Yusra AneesLv10
28 Sep 2019
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Related questions

Jill buys two goods: X and Y and has the following utility function: U(X,Y) = 2X0.25Y0.75

a. Find the equation for her generalized demand curve for X*(Px,Py,I)

b. Find the equation for her generalized demand curve for Y*(Py,Px,I)

c. Are the above generalized demand functions homogeneous of degree 0? (Show your work)

d. Is X a normal good?

e. Is X a gross substitute or complement to Y?

f. Find the compensated demand curve for Xc(Px, Py, U)

g. Find the compensated demand curve for Yc (Py, Px, U)

h. Are the compensated demand functions homogenous of degree 0 in Px and Py if utility is held constant?

i. Find the expenditure function: E(Px, Py, U)

j. Use Shephard’s Lemma to verify that your compensated demand functions Xc and Yc are correct.

k. Find the indirect utility function: V(Px,Py,I)

Suppose that a consumer's preferences over two goods, x and y, are represented by a Cobb-Douglas utility function:

U(x,y) = x1-i² yi²

a. Find the expenditure function of the consumer, and the compensated demand functions.

b. Suppose that i² = 1/4 and that initially a consumer is in equilibrium with px = 1,py = 1, I = 100. What are the demands for xand y.

c. What is the minimum increase in income necessary for the consumer to be as well offunder price px = 1, py = 2, as she/he was at prices px = 1, py = 1?

Explain why the percentage increase is smaller than the increase inthe CPI for the consumer that you derived in part c.

Jill buys two goods: X and Y and has the following utility function: U(X,Y) = 2X0.25Y0.75

Please show all work

a. Find the equation for her generalized demand curve for X*(Px,Py,I)

b. Find the equation for her generalized demand curve for Y*(Py,Px,I)

c. Are the above generalized demand functions homogeneous of degree 0? (Show your work)

d. Is X a normal good?

e. Is X a gross substitute or complement to Y?

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