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.

Survey Of Economics
10th Edition
ISBN:9781337111522
Author:Tucker, Irvin B.
Publisher:Tucker, Irvin B.
Chapter1: Introducing The Economic Way Of Thinking
Section1.A: Applying Graphs To Economics
Problem 2SQP
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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 $1 increase in price, sales of this type of cell phone decrease by
million units.
Transcribed Image Text:The following table shows worldwide sales of a certain type of cell phone and their average selling prices in 2012 and 2013. Year 2012 2013 Selling Price ($) 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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