Suppose that the demand function for a good is
qD(p) = 8000/((p^2) + 1)
where q is the quantity and p is the price in dollars. If the price is decreased from 9 to 8.5, what is the approximate increase in the quantity sold?
qD(9) = 8000/(81+1) = appr 97.56
qD(8.5) = 8000(72.25+1) = appr 109.22
So, what do you think?
To find the approximate increase in the quantity sold, we need to calculate the difference in quantity when the price is decreased from $9 to $8.5.
1. Start by plugging in the initial price, $9, into the demand function to find the initial quantity sold:
qD(9) = 8000/((9^2) + 1)
= 8000/(81 + 1)
= 8000/82
≈ 97.56
2. Next, plug in the new price, $8.5, into the demand function to find the new quantity sold:
qD(8.5) = 8000/((8.5^2) + 1)
= 8000/(72.25 + 1)
= 8000/73.25
≈ 109.25
3. Calculate the difference in quantity sold:
Δq = qD(8.5) - qD(9)
= 109.25 - 97.56
≈ 11.69
Therefore, the approximate increase in the quantity sold when the price is decreased from $9 to $8.5 is approximately 11.69 units.