The following table shows worldwide sales of a certain type

The following table shows worldwide sales of a certain type of cell phone and their average selling prices in 2012 and 2013. (a) Use the data to obtain a linear demand function for this type of cell phone. (Let p be the price, Use your demand). q(p) = Use your demand equation to predict sales if the price is lowered to $245. 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

Consider the given table.

(a)

Let p be the price and q be the demand.

Let q(p) = mp+b.

In the year 2012:

968 = 375m+b     ......(1)

In the year 2013:

1184 = 335m+b      ......(2)

Subtract (2) from (1)

-216 = 40m

m = -5.4

Plug in m = -5.4 in equation (1)

968 = 375(-5.4)+b

b = 968+2025 = 2993

Thus, the demand function is

q(p) = -5.4p+2993

When p = 245:

q(p) = -5.4(245)+2993 = 1670

If the price is lowered to $245 then the sales will be 1670.

(b)

q = 968 when p = 375

When price increases by 1%:

p = 375+0.01(375) = 378.75

Then q(p) = -5.4(378.75)+2993 = 947.75

Decrease in sales = 20.25

Thus, for every 1% increase in price, sales decreases by 20.25 million units.