THE UNIVERSITY OF BRITISH COLUMBIA
Managerial Econ: Class 14
Pre-Midterm Review
1.
Utility Maximization
2.
Perfectly Competitive Markets
3.
Two-Part Pricing
4.
Bundling
5.
Cournot Oligopoly
6.
Additional Comments
Much of today’s review will be based on the posted review
questions.
THE UNIVERSITY OF BRITISH COLUMBIA
Announcements
Midterm Exam on Wednesday, Oct. 27 at 6:30 pm (to 8:30).
If your last name begins with letters A – H go to Woodward 1.
If your last name begins with letters I – Q go to Woodward 4.
If your last name begins with letters R – Z go to Woodward 6.
No class on Thursday.

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THE UNIVERSITY OF BRITISH COLUMBIA
1. Utility Maximization
2 of 4
1. Sally consumes two goods, X and Y. Her utility function is given by U =3XY
2
.
The current market price for X is $10, while the market price for Y is $5.
Sally's current income is $500. Determine the X, Y combination which maximizes
Sally's utility, given her budget constraint. Draw the diagram.
Recall that to maximize utility MRS = price ratio. This is equivalent to saying that
the marginal utility per dollar must be the same for each good consumed.
MU
x
/P
x
= MU
y
/P
y
MU
x
= dU/dX = 3Y
2
.
MU
y
=dU/dY = 6XY
Therefore 3Y
2
/10 = 6XY/5 or 3Y/6X = 10/5
or Y/2X = 2 or Y = 4X.
Also, from the budget line, 10X + 5Y = 500 so 10X + 5(4X) = 500 or 30X = 500.
It follows that X = 50/3 = 16.67
THE UNIVERSITY OF BRITISH COLUMBIA
Clicker Question 1
2 of 4
Suppose Lisa has utility function U = XY
1/2
. The price of X is 5 and
the price of Y is 1. Lisa maximizes utility.
a.Lisa will consume more
than twice as much X as Y.
b.Lisa will consume more X than Y but less than twice as much.
c.Lisa will consume more Y than X but less than twice as much.
d.Lisa will consume more than twice as much Y as X.
e.There is not enough information to determine the relative amounts
of the two goods Lisa will consume.