The following table shows worldwide sales of a certain type of cell phone and their average selling prices in 2012 and 2013.
Year
2012
2013
Selling Price ($)
385
325
Sales (millions)
837
1,173
(a) Use the data to obtain a linear demand function for this type of cell phone. (Let p be the price, and let q be the demand).
q(p) =
Use your demand equation to predict sales if the price is lowered to $285.
x million phones
(b) Fill in the blank.
For every $1 increase in price, sales of this type of cell phone decrease by
million units.
Solution:
Given,
The following table shows worldwide sales of a certain type of cell phone and their average selling prices in 2012 and 2013.
Year | 2012 | 2013 |
Sellling price($) | 385 | 325 |
Sales (millions) | 837 | 1173 |
he general form of linear demand function can be written as
y = a x + b
Where, ‘a’ is slope
‘b’ is intercept
Now, the demand equation is
For 2012,
Demand:
837 = 385a + b
b = -385a + 837 ___________(i)
For 2013,
Demand:
1,173 = 325a + b
b = -325a + 1,173 ___________(ii)
a) Equating (i) and (ii)
-385a + 837 = -325a + 1,173
-385a + 325a = 1,173 - 837
-60a = 336
a = -5.6
Putting a = -5.6 in (i)
b = -385a + 837 ___________(i)
b = -385(-5.6) + 837
b = 2156 + 837
b = 2,993
Therefore,
q(p) = −5.6p + 2,993
If the price is lowered to $285,
q = −5.6(285) + 2,993
q = -1,596 + 2,993
q = 1,397 million
b)
The slope of the demand function is -5.6.
For every $1 increase in price, sales of this type of cell phone decrease by 5.6 million units.
Result:
- The demand linear equation is q(p) = −5.6p + 2,993
- The quantity demanded when the price is lowered to $285 is q = 1,397 million
- For every $1 increase in price, sales of this type of cell phone decrease by 5.6 million units.