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 ($) 395 325 Sales (millions) 741 1,133 (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 $255. million phones (b) Fill in the blank. For every $1 increase in price, sales of this type of cell phone decrease by million units.
The following table shows worldwide sales of a certain type of cell phone and their average selling prices in 2012 and 2013. Year 2012 2013 Selling Price ($) 395 325 Sales (millions) 741 1,133 (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 $255. million phones (b) Fill in the blank. For every $1 increase in price, sales of this type of cell phone decrease by million units.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:The following table shows worldwide sales of a certain type of cell phone and their average selling prices in 2012 and 2013.
Year
2012
2013
Selling Price ($)
395
325
Sales (millions)
741
1,133
(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 $255.
million phones
(b) Fill in the blank.
For every $1 increase in price, sales of this type of cell phone decrease by
million units.
Expert Solution
Step 1
a)
When price = P1 = $395, the quantity sold = Q1 = 741 million
When price = P2 = $325, the quantity sold = Q2= 1,133 million
The demand function can be written in form,
Q = a +b P
Here, a = intercept and b = Inverse of slope of demand function.
b = ΔQ/ ΔP
b = Q2- Q1/ P2- P1
b = 1,133 – 741/325 – 395
b = 392 /-70
b= -5.6
Put the value of b in demand function.
P = a -5.6 Q
If P = $395, Q = 741 million, the demand function is
395 = a -5.6 (741)
a = 2953
So, the demand function,
Q = 2953 - 5.6 P
If the price is lowered to $ 255, the sale of phones is
Q = 2953 - 5.6 (255)
Q = 1525 million
If the price decreases to $255, sales increase to 1525 million phones.
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