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MGEB02H3 Study Guide - Final Guide: University Of Toronto Scarborough, Demand Curve, Indifference Curve


Department
Economics for Management Studies
Course Code
MGEB02H3
Professor
A.Mazaheri
Study Guide
Final

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Page 1 of 16
UNIVERSITY OF TORONTO SCARBOROUGH
DEPARTMENT OF MANAGEMENT
MGEB02: Price Theory: A Mathematical Approach
Instructor: A. Mazaheri
Sample Final (Solutions)
Instructions: This is a closed book test. You are allowed the use of a non-programmable
calculator
You have 150 minutes.
Good Luck!

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Page 2 of 16
Answer all following 6 questions in the Exam Paper:
Question-1 [35 Points] Answer the following short questions.
a) (8 Points) A consumer is considering choosing a calling plan for her cell phone. The
plan has a fixed monthly fee of $40, and it gives 200 free minutes per month and charges
$0.1 for each additional minute. The consumer has a monthly income of $100, and she
spend it on cell phone and another composite good y, where p
y
=$1. Her utility function
is given by
2
),( y
xyxU += , where
x
is the minutes of cell phone she uses in a month.
Find her optimal consumption bundle. Graph your solution on a diagram including the
budget line and a representative indifference curve.
Solution:
100
1.0
5.0
5.0 5.0
==>
==
x
x
MRS
This is an interior solution but is not optimal since there is 200 free minutes.
Should expect a corner solution, with x = 200 and y = 60.
Check MRS at this bundle (1/2000.5 < 0.1).
She tries to increase y and reduce x. But this is not feasible.
The corner solution is optimal.
The utility level at the corner solution is 2000.5 + 60/2 = 44.14 > 1000.5 + 50/4.
y
600
60
200
800

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Page 3 of 16
b)
(8 Points)
In a perfectly competitive market, there are 100 firm split equally between
the following short run cost functions:
50 10q 0.5q )(qC
200 10q 2q )(qC
2
2
222
1
2
111
++=
++=
Find the total short run market supply curve and graph it.
Solution:
0)1 P10(ifqP
point) shoutdown10,0(
105.0,10qSRMC
50 10q 0.5q )(qC
0)1 P10(if4qP
point) shoutdown10,0(
102,104qSRMC
200 10q 2q )(qC
2
2
22
2
2
222
1
1
11
1
2
111
+=
===
+=+=
++=
+=
===
+=+=
++=
pqSRAVCSRMC
qSRAVC
pqSRAVCSRMC
qSRAVC
Market supply:
)10( 625-62.5P )10(50)5.2
4
(50
)10( 0
)10((10
)10(5.2
4
2
1
=+=
<=
=
=
PP
P
Q
PQ
ndMarketdema
ifPPq
ifP
P
q
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