Questions: Multiple Choice Question
When the product price falls from 80 to 60, the quantity demanded rises from 500 to 800 units. The slope in this range is:
-0.29.
-0.067
0.46.
-15.
Transcript text: Multiple Choice Question
When the product price falls from $\$ 80$ to $\$ 60$, the quantity demanded rises from 500 to 800 units. The slope in this range is:
-0.29 .
$-0.067$
0.46.
$-15$.
Solution
The answer is the last one: \(-15\).
To find the slope of the demand curve in this range, we use the formula for the slope of a line, which is the change in quantity demanded divided by the change in price:
\[
\text{Slope} = \frac{\Delta Q}{\Delta P}
\]
Where:
\(\Delta Q\) is the change in quantity demanded.
\(\Delta P\) is the change in price.
Given:
Initial price \(P_1 = \$80\)
Final price \(P_2 = \$60\)
Initial quantity demanded \(Q_1 = 500\)
Final quantity demanded \(Q_2 = 800\)
Calculate the changes:
\(\Delta Q = Q_2 - Q_1 = 800 - 500 = 300\)
\(\Delta P = P_2 - P_1 = 60 - 80 = -20\)
Now, substitute these values into the slope formula:
\[
\text{Slope} = \frac{300}{-20} = -15
\]
Explanation for each option:
\(-0.29\): Incorrect. This does not match the calculated slope.
\(-0.067\): Incorrect. This does not match the calculated slope.
\(0.46\): Incorrect. This does not match the calculated slope.
\(-15\): Correct. This matches the calculated slope.
In summary, the slope of the demand curve in this range is \(-15\).