TRENT UNIVERSITY

DEPARTMENT OF ECONOMICS

Dr. M. Arvin Econ-Admin 2250H 2015-2016

Assignment #2

Date Given: Beginning of class on October 9, 2015.

Due Date: Beginning of class on November 6, 2015.

As page 3 of your course outline states: “the penalty for late assignments is 20 percentage points

for each day or part thereof.” To be fair to all students, the late penalty will be applied to all late

assignments, even if they are late by an hour. You have four (4) weeks to complete this

assignment.

Notes: Please make sure that your answers are neat and legible. Also ensure that your assignment is

securely held together and contains your name and student number. The numbers in the margin

refer to the mark for each part. Please type your answers or use a pen. Do not use a pencil.

(15) 1. Suppose the advertising decisions of two firms are inter-related. Firm 1 always spends $2 million plus 33?% of

what firm 2 spends on advertising. And firm 2 always spends $7 million plus 12.5% of what firm 1 spends on

advertising.

i) Draw the reaction functions for the firms in this problem (in the same diagram). Be sure to

label each curve and the axes.

ii) Use the inverse matrix method to find the Nash equilibrium in this problem.

iii) Now use Cramer’s rule to verify your answer in part ii).

2. Suppose an inflationary economy can be described by the following equations representing the goods and

money markets:

C = 20 + 0.7Yd

M = 0.4Yd

I = 70 – 0.1r

T = 0.1Y

G = 100

X = 20

Ld = 389 + 0.7Y – 0.6r

Ls = 145

where G represents government expenditure, M is imports, X is exports, Y is national income, Yd is

disposable income, T is government taxes (net of transfer payments), I is investment, r is the rate of

interest, C is consumption, Ld is money demand, and Ls is money supply.

(15) i) Use the inverse matrix method to solve for the equilibrium level of national income and the

equilibrium rate of interest in this economy. (Note: ½ of the marks in this part are given for

the correct set up of the equations. Explain what you are doing, including how equilibrium

is established in each market.)

(5) ii) Now use Cramer’s rule to find your answer.

3. There are three types of life insurance policies that a sales representative can sell: term, whole life,

and universal life. The following matrix gives the number of policies sold by three different

representatives during a recent month:

Whole Universal

Term Life Life

?

?

?

?

?

?

?

?

?

?

34 6 38

24 10 32

30 8 40

representative C

representative B

representative A

Assume representatives A, B, and C earned $4400, $4060, and $4160, respectively, in

commissions for these sales. The commission earned depends only on the type of policy sold and

is the same for all representatives.

(10) i) Use the inverse matrix method to find the commission that is earned for selling a policy of

each type.

(10) ii) Now use Cramer’s rule to find your answer.

(15) 4. You are the distributor for a certain brand of wine. The manager of a local liquor store has just

called, wanting to know why this week’s order had not come in. You try to explain that your route

driver called in sick this morning, but the manager demands the usual order and wants its delivered

within the hour. Unfortunately, you do not know what the usual order is and you cannot reach the

driver. A quick check of the account shows that during the months of April, May, and June, this

customer was billed for $456, $474, and $499, respectively. The following matrix gives the price

per case of each of your three kinds of wine during those months. Using Cramer’s rule find how

many cases of each kind of wine constitute this store’s usual order.

Rose Burgundy Rhine

June

May

April

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?

?

?

?

?

?

?

?

?

25 24 21

20 24 21

20 24 18

(30) 5. Fast Finance offers new and used car loans, and quick cash loans each at a different monthly interest

rate. The totals for loans of each type made last month at Fast Finance’s three branch offices are

recorded (in thousands of dollars) in matrix below.

New Used Quick

Car Car Cash

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?

?

?

?

?

70 80 80

50 60 40

80 60 50

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?

?

South Branch

Central Branch

North Branch

The interest earned on these loans during the month branch by branch is as follows. North Branch:

$2,700; Central Branch: $2,200; and South Branch: $3,500. Determine the monthly interest rate for

each type of loan using both the inverse matrix method and Cramer’s rule. Now calculate the

annual interest rates this company is charging. Show your work for all the subparts of this question.