ECON 4P14 Assignment 2b: Consumer Choice

| November 24, 2016

Question
ECON 4P14 Assignment 2b: Consumer Choice
(1 mark)
F. Martinello

Fall 2015

Due: Monday, November 2, 2015 Wednesday, November 4, 2015 in class, or in my mailbox
(Plaza 451), or in the Economics assignment box (outside Plaza 451) before 16:00. Late
reports will not be accepted.
1. Jane’s preferences are described by the utility function (1 , 2 ) = 51 + 22 .
Currently, Jane’s income = 120 and the price of 2 is 8.
1a. Derive graphically (don’t try to use a Lagrangian) Jane’s Marshallian demand curve for 1 ,
and show it in a diagram.
Calculate and show all points of interest (intercepts, breaks, coordinates…) on your diagram.
1b. Jane’s preferences are convex but not strictly convex. What does that tell you about:
– the second order condition for Jane’s utility maximization problem, and
– the uniqueness of its solution?
Just a few words for each is sufficient.
0.5
Joy’s preferences over goods are expressed by the utility function (1 , 2 ) = 1 2 , so
she has homothetic preferences
Use a diagram to show Joy’s income consumption curve (ICC) if 1 = 12 and 2 = 9.
Calculate and show on your diagram:
– the amounts of 2 in the bundles of goods on the ICC when 1 = 3 and 1 = 6
– the indifference curve and budget lines going through those bundles
– the slopes of the indifference curve and budget lines at those bundles
Hint: just use the equation for the MRS of the indifference curves, no Lagrangians required.

2.

0.5
3. Bob’s preferences are described by the utility function, (1 , 2 ) = 1 + 2
Bob’s income is 128 and 2 = 2. Calculate Bob’s MRS and use it to derive :
the range of 1 where Bob wants to consume zero amounts of 1
the range of 1 where Bob wants to consume positive amounts of 1
Illustrate with a diagram showing Bob’s indifference curves, MRS and budget constraints.

4. In the previous assignment you derived the Marshallian demand curves



1 = 1 (1 , 2 , ) = ⁄2 + 2.5 and 2 = 2 (1 , 2 , ) = ⁄2 − 2.5( 1⁄ 2 )
1

2

If 1 changes, are 1 and 2 gross substitutes or complements?
If 2 changes, are 1 and 2 gross substitutes or complements?
Give the definition of gross substitutes or complements to show how you know.

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