DEPARTMENT OF ECONOMICS
Econ-Admin 2250H 2015-2016
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
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
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
2. Suppose an inflationary economy can be described by the
following equations representing the goods and
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
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:
Term Life Life
34 6 38
24 10 32
30 8 40
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
(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
Rose Burgundy Rhine
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
70 80 80
50 60 40
80 60 50
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.