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QUESTION:
A retail store has
noticed that over the past several months, sales of a particular product X has
typically been close to 200 units per week.
On two occasions, however, sales declined to 120 units per week. The retailer notes that during these periods,
the store was running a special on product Y and has reduced Y price from N5 to
N4.
i.
What is Arc Cross Price Elasticity of demand?
ii.
What Level of sales for X would you
predict if the price of Y is increased to N6?
SOLUTION:
First
of all, let’s bring out the figures on a table like this;
|
Price (Y)
|
Quantity
Demanded (X)
|
|
N5
N4
|
200
120
|
Arc
Cross Price Elasticity of Demand; Arc Exy = ∆Qx Py1
+ Py2
∆Py X Qx1 + Qx2
Arc
Exy = 80 5 + 4___
1 X
200 + 120
Explanation:
How did we get the 80? It 200 – 120=80.
Then the 1 is N5, - N4 = N1. Then
5 is the first price while 4 is the second price. 200 is the first quantity and 120 is the
second quantity.
So
let’s continue:
Arc
Exy = 80 9___
1 X
320
Arc
Exy = 720
320
Explanation:
we got 720 when you multiply 80 x 9=720. Then 1 x 320 is still 320.
Arc
Exy = 2.3
That
is your final answer for (i). Then without the explanation, the answer should
look like this:
SOLUTION:
|
Price (Y)
|
Quantity
Demanded (X)
|
|
N5
N4
|
200
120
|
Arc
Cross Price Elasticity of Demand; Arc Exy = ∆Qx Py1 + Py2
∆Py X Qx1 + Qx2
Arc
Exy = 80 5 + 4___
1 X
200 + 120
Arc
Exy = 80 9___
1 X
320
Arc
Exy = 720
320
Arc
Exy = 2.3
Solution
to (ii) of the question:
First,
we have to bring down our figures if we wish, then develop equation of straight
line:
|
Price (Y)
|
Quantity
Demanded (X)
|
|
N5
N4
|
200
120
|
Formula
for Equation of straight line:
Y – y1 y2-y1
X-x1 = x2-x1
Above
is the formula for the straight line equation and we will use it to solve. Just substitute the figures.
Y
– 5 4-5____
X-200 = 120-200
Y
– 5 -1____
X-200 = -80
Y
– 5 1____
X-200 = 80
Cross
multiply now:
X-200 = 80
(y-5)
X-200 = 80y
-400
X= 80y +200 -400
X= 80y -200
This
is just the straight line equation. We just derived it now.
X,
when Y = N6:
X
= 80 (6) – 200
X
= 480 – 200
X
= 280
280 is the sales
of X that we have predicted as Y is N6.
You
can always contact theotherwomaninmarraige@gmail.com
in any area you don’t understand or comment directly on the blog and the grey
areas will be cleared.
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