QuestionGiven cell phone sales and prices for Q1 2009 and 2010, find the demand function $q(p)$ . Predict sales at \$156. Also, determine the sales decrease per \$1 price increase.

Studdy Solution

STEP 1

Assumptions1. The wholesale price and sales data for Q12009 and Q12010 are accurate and can be used to model a linear demand function. . The relationship between price and demand is linear.
3. The demand function is in the form $q(p) = mp + b$ , where $q(p)$ is the quantity demanded at price $p$ , $m$ is the slope of the demand function, and $b$ is the y-intercept.

STEP 2

We can find the slope of the demand function by using the formula for the slope of a line, which is the change in y divided by the change in x. In this case, y is the quantity demanded (sales in millions) and x is the price.
$m = \frac{\Delta q}{\Delta p}$

STEP 3

Substitute the given values for the change in quantity demanded and the change in price into the slope formula.
$m = \frac{214 -175}{153 -163}$

STEP 4

Calculate the slope of the demand function.
$m = \frac{214 -175}{153 -163} = -39$

STEP 5

Now that we have the slope of the demand function, we can find the y-intercept by rearranging the demand function to solve for $b$ .
$b = q - mp$

STEP 6

Substitute the given values for the quantity demanded, price, and slope into the y-intercept formula.
$b =175 - (-39 \times163)$

STEP 7

Calculate the y-intercept of the demand function.
$b =175 - (-39 \times163) =6522$

STEP 8

Now that we have the slope and y-intercept of the demand function, we can write the demand function.
$q(p) = -39p +6522$

STEP 9

Use the demand function to predict sales to the nearest million phones if the price was set at $156.
$q(156) = -39 \times156 +6522$

STEP 10

Calculate the predicted sales.
$q(156) = -39 \times156 +6522 =95$ So, if the price was set at $156, the predicted sales would be95 million phones.

STEP 11

For every $ increase in price, sales of cell phones decrease by the absolute value of the slope of the demand function, which is39 million units.
So, for every $ increase in price, sales of cell phones decrease by39 million units.

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QuestionGiven cell phone sales and prices for Q1 2009 and 2010, find the demand function $q(p)$ . Predict sales at \$156. Also, determine the sales decrease per \$1 price increase.

Studdy Solution

STEP 1

STEP 2

We can find the slope of the demand function by using the formula for the slope of a line, which is the change in y divided by the change in x. In this case, y is the quantity demanded (sales in millions) and x is the price.
$m = \frac{\Delta q}{\Delta p}$

STEP 3

Substitute the given values for the change in quantity demanded and the change in price into the slope formula.
$m = \frac{214 -175}{153 -163}$

STEP 4

Calculate the slope of the demand function.
$m = \frac{214 -175}{153 -163} = -39$

STEP 5

Now that we have the slope of the demand function, we can find the y-intercept by rearranging the demand function to solve for $b$ .
$b = q - mp$

STEP 6

Substitute the given values for the quantity demanded, price, and slope into the y-intercept formula.
$b =175 - (-39 \times163)$

STEP 7

Calculate the y-intercept of the demand function.
$b =175 - (-39 \times163) =6522$

STEP 8

Now that we have the slope and y-intercept of the demand function, we can write the demand function.
$q(p) = -39p +6522$

STEP 9

Use the demand function to predict sales to the nearest million phones if the price was set at $156.
$q(156) = -39 \times156 +6522$

STEP 10

Calculate the predicted sales.
$q(156) = -39 \times156 +6522 =95$ So, if the price was set at $156, the predicted sales would be95 million phones.

STEP 11

For every $ increase in price, sales of cell phones decrease by the absolute value of the slope of the demand function, which is39 million units.
So, for every $ increase in price, sales of cell phones decrease by39 million units.

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QuestionGiven cell phone sales and prices for Q1 2009 and 2010, find the demand function q(p)q(p)q(p). Predict sales at \$156. Also, determine the sales decrease per \$1 price increase.

Studdy Solution

STEP 1

STEP 2

We can find the slope of the demand function by using the formula for the slope of a line, which is the change in y divided by the change in x. In this case, y is the quantity demanded (sales in millions) and x is the price.m=ΔqΔpm = \frac{\Delta q}{\Delta p}m=ΔpΔq​

STEP 3

Substitute the given values for the change in quantity demanded and the change in price into the slope formula.m=214−175153−163m = \frac{214 -175}{153 -163}m=153−163214−175​

STEP 4

Calculate the slope of the demand function.m=214−175153−163=−39m = \frac{214 -175}{153 -163} = -39m=153−163214−175​=−39

STEP 5

Now that we have the slope of the demand function, we can find the y-intercept by rearranging the demand function to solve for bbb.b=q−mpb = q - mpb=q−mp

STEP 6

Substitute the given values for the quantity demanded, price, and slope into the y-intercept formula.b=175−(−39×163)b =175 - (-39 \times163)b=175−(−39×163)

STEP 7

Calculate the y-intercept of the demand function.b=175−(−39×163)=6522b =175 - (-39 \times163) =6522b=175−(−39×163)=6522

STEP 8

Now that we have the slope and y-intercept of the demand function, we can write the demand function.q(p)=−39p+6522q(p) = -39p +6522q(p)=−39p+6522

STEP 9

Use the demand function to predict sales to the nearest million phones if the price was set at $156.q(156)=−39×156+6522q(156) = -39 \times156 +6522q(156)=−39×156+6522

STEP 10

Calculate the predicted sales.q(156)=−39×156+6522=95q(156) = -39 \times156 +6522 =95q(156)=−39×156+6522=95So, if the price was set at $156, the predicted sales would be95 million phones.

STEP 11

For every $ increase in price, sales of cell phones decrease by the absolute value of the slope of the demand function, which is39 million units.So, for every $ increase in price, sales of cell phones decrease by39 million units.

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionGiven cell phone sales and prices for Q1 2009 and 2010, find the demand function $q(p)$ . Predict sales at \$156. Also, determine the sales decrease per \$1 price increase.

We can find the slope of the demand function by using the formula for the slope of a line, which is the change in y divided by the change in x. In this case, y is the quantity demanded (sales in millions) and x is the price.
$m = \frac{\Delta q}{\Delta p}$

Substitute the given values for the change in quantity demanded and the change in price into the slope formula.
$m = \frac{214 -175}{153 -163}$

Calculate the slope of the demand function.
$m = \frac{214 -175}{153 -163} = -39$

Now that we have the slope of the demand function, we can find the y-intercept by rearranging the demand function to solve for $b$ .
$b = q - mp$

Substitute the given values for the quantity demanded, price, and slope into the y-intercept formula.
$b =175 - (-39 \times163)$

Calculate the y-intercept of the demand function.
$b =175 - (-39 \times163) =6522$

Now that we have the slope and y-intercept of the demand function, we can write the demand function.
$q(p) = -39p +6522$

Use the demand function to predict sales to the nearest million phones if the price was set at $156.
$q(156) = -39 \times156 +6522$

Calculate the predicted sales.
$q(156) = -39 \times156 +6522 =95$ So, if the price was set at $156, the predicted sales would be95 million phones.

For every $ increase in price, sales of cell phones decrease by the absolute value of the slope of the demand function, which is39 million units.
So, for every $ increase in price, sales of cell phones decrease by39 million units.