Answer:
(a) The linear demand function is q = 2962 - 5.80p; and sales is expected to be 1,488.80 millions if the price is reduced to $245.
(b) For every $1 increase in price, that sales of this type of cell phone decrease by 5.80 million units.
Step-by-step explanation:
(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).
The form of the linear demand function we are trying to find will as follows:
q = a + bp ........................ (1)
Where;
q = sales = demand
a = constant
b = slope
p = price
From the question, we have the following points:
Point 1 = (price in 2012, demand in 2012) = (p1, q1) = (395, 672)
Point 2 = (price in 2013, demand in 2013) = (p2, q2) = (335, 1020)
We can therefore calculate b as follows:
b = (q2 - q1) / (p2 - p1)
b = (1020 - 672) / (335 - 395)
b = 348 / (-60)
b = -5.80
Substituting for b in equation (1), we have:
q = a - 5.80p ..................... (2)
We can now use any of point 1 or 2 above to find a. Using point 1, we substitute p = 395 and q = 672 into equation (2) as follows:
672 = a - (5.80 * 395)
672 = a - 2291
a = 672 + 2291
a = 2963
Substituting the value for a back into equation (2) gives the demand function as follows:
q = 2962 - 5.80p <-------------- Linear demand function.
if the price is lowered to $245, we substitute p = 245 into the linear demand function as follows:
q = 2962 - 5.80(254)
q = 2962 - 1,473.20
q = 1,488.80
Therefore, sales is expected to be 1,488.80 millions if the price is reduced to $245.
(b) Fill in the blank. For every $1 increase in price, sales of this type of cell phone decrease by ______ million units.
From part (a), b is the slope and it -5.80 in the linear demand function. The slope shows how much q will change when p changes by $1.
Since the sales is in millions and slope is -5.80, it therefore implies for every $1 increase in price, that sales of this type of cell phone decrease by 5.80 million units.
The demand table is an illustration of a linear function
(a) The linear demand function
From the table we have the following points
(p,q) = {(395,672) (335,1020)}
The demand linear equation is calculated using the following:
[tex]\mathbf{\frac{q - q_1}{p - p_1} = \frac{q_2 - q_1}{p_2 - p_1}}[/tex]
So, we have:
[tex]\mathbf{\frac{q - 672}{p - 395} = \frac{1020- 672}{335- 395}}[/tex]
[tex]\mathbf{\frac{q - 672}{p - 395} = -\frac{348}{60}}[/tex]
[tex]\mathbf{\frac{q - 672}{p - 395} = -5.8}[/tex]
Cross multiply
[tex]\mathbf{q - 672 = -5.8(p - 395)}[/tex]
[tex]\mathbf{q - 672 = -5.8p + 2291}[/tex]
Add 672 to both sides
[tex]\mathbf{q = -5.8p + 2963}[/tex]
(b) The quantity when the price is $245
This means that p = 245.
So, we have:
[tex]\mathbf{q = -5.8\times 245 + 2963}[/tex]
[tex]\mathbf{q = -1421 + 2963}[/tex]
[tex]\mathbf{q = 1542}[/tex]
Hence, the quantity demanded when the price is lowered to $245 is 1542 million
(c) Interpret the demand equation
For every $1 increase in price, sales of this type of cell phone decrease by 5.8 million units.
Read more about demand linear functions at:
https://brainly.com/question/2254422
