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 Shephardâs Lemma to verify that your compensated demand functions Xc and Yc are correct.
k. Find the indirect utility function: V(Px,Py,I)
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 Shephardâs Lemma to verify that your compensated demand functions Xc and Yc are correct.
k. Find the indirect utility function: V(Px,Py,I)
Related textbook solutions
Related questions
The generalized demand and supply functions for good X are
Qd = 10 -2Px - 4PY + M Qs = 10 + 2PX
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Where: QD = quantity demanded of good X PX = price of good X M = consumer income PY = price of good Y |
QS = quantity supplied of good X PX = price of good X
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A. Are good X and good Y substitutes or complements? Why?
B. Is good X a normal good or an inferior good? Why?
C. What is the demand function when PY = $4 and M = $600?
d. Use the demand function you found in part c. and solve for the equilibrium price (Po) and the equilibrium quantity (Qo).
e. Find the inverse demand function and the inverse supply function.
f. Sketch this market.
