Question

Amy has income of $M and consumes only two goods: composite good y with price $1 and chocolate (good x) that costs $px per unit. Her util- ity function is U(x,y) = 2xy; and marginal utilities of composite good y and chocolate are: MUy = 2x and MUx = 2y.

(a) State Amy’s optimization problem. What is the objective function? What is a constraint?

(b) Draw the Amy’s budget constraint. Place chocolate on the horizontal axis, and ”expenditure all other goods” on the vertical axis. What is the opportunity cost of the chocolate? How it is related to the slope of the budget constraint? Why?

(c) Derive Amy’s ordinary (Marshallian) demand for chocolate.

Assume that Amy’s income is $1000 and that chocolate costs $5 per unit.

(d) What is the utility-maximizing choice of composite good and choco-

late?

(e) What is the level of utility at optimal basket from the part d)? Show your result in the optimal choice diagram.

The price of chocolate increases from $5 to $10 per unit (while the price of composite good remains $1 and income remains constant of $1000).

(f) Calculate the new optimal basket for Amy. On the optimal choice diagram (from part e), illustrate this new optimal basket for Amy re- flecting lower price of chocolate. Is Amy better off or worse off at this new optimal basket than on the basket found in part d)? Explain.

(g) Decompose graphically the total effect of chocolate price change into income and substitution effects (calculation is not required).

(h) Based on the ordinary demand function you derived in part c), is chocolate normal or inferior good? Explain. Based on the income / substitution effects from part (g), is chocolate normal or inferior good? Explain.

(i) Is it possible that Amy’s demand for chocolate is upward-sloping? Ex- plain.

(j) What is the compensating variation associated with the increase in the price of the chocolate? Explain by words, and show in the graph you drew in part (g).

(k) Calculate the income and substitution effect for part (g).

Answer #1

Brian consumes units of electricity (E) and a composite good
(Y), whose price is always 1. he likes both goods. in period 1 the
power company sets the price of electricity at $7 per unit, for all
units of electricity consumed. Brian consumes his optimal basket,
20 units of electricity and 70 units of the composite good. in
period 2 the power company then revises its pricing plan, charging
$10 per unit for the first 5 units and $4 per...

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MUX= 0.8X-0.2Y0.2
MUY= 0.2X0.8Y-0.8
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