1. Assume that an individual has an income of $450,000 which is spent entirely on
the consumption of good X and good Y, and the price ofX is $82 and the price of
Y is $70. Utilizing the given equations answer the following questions. (100
Points)
0 U=X’2>*<Y’8 I=(Px*X)+(Py*Y)
o MUX = .2X”8Y’8
o MUY = X’2.8Y”2
1. Calculate and graph the consumer’s optimal bundle and utility.
11. Assuming that the government imposes a subsidy of $29 per unit on X,
calculate and graph the consumer’s new optimal bundle.
Ill. Using indifference curves and the compensated demand functions calculate
the CV, EV, & excess burden of the subsidy.
IV. Derive the individuals, ordinary, compensated and equivalent demand
curves, and calculate the EV, CV, and consumer surplus from the change in
surpluses.
V. Using the ordinary demand curve, graphically show the deadweight loss and
revenue of the taX.
2. Assume that two consumers have incomes of $250,000 and face prices of PX:$23
and Pyz$7. Assuming that the price ofX increases to $31, use the following
ordinary and compensated demand functions to derive the ordinary demand
curves and compensated demand curves. (Graph both consumer’s ordinary
demand curves on one graph and both consumer’s compensated demand curves
on a separate single graph). In addition, calculate the ordinary price elasticity of
demand, the compensated price elasticity of demand, and cross price elasticity of
demand for the two consumers. What do the elasticities say about the
consumer’s preferences for the two goods? (30 Points).
0 Both consumers have the same CES utility function; however, consumer 1
has a value of cc: -4. (p = .8), and consumer 2 has a value of oc=
O.4737 (p = -.9)
0 U : gXP+yP25
O – L C _ CC CC é-l OC-l
0 Y – (Px’x+PyO<) 0 Y – U(Py + Px )1 Py
Xe = _ – X6 = mm“ + Px“>¥‘1px°<-1
(Pxoc’l’PYoc)