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

by OC332523

Department

Economics for Management StudiesCourse Code

MGEB02H3Professor

A.MazaheriStudy Guide

FinalThis

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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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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

10

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