Scenario 4.3:
The demand for erasers (Q) is given as follows:
Q = 240 - 4Pe + 2I + Pb + A
where Pe is the price of erasers
I is the level of income
Pb is the price of another good
A is the level of advertising
Suppose that Q = 240, Pe = 10, Pb = 10, and A = 2.
-Given the information in Scenario 4.3, what is the point price elasticity of demand?

Question

Quizplus · Accepted Answer

To calculate the point price elasticity of demand, we use the formula:
E = (%ΔQ / %ΔPe) = (ΔQ / Q) / (ΔPe / Pe)
We are not given the percentage changes, but we are given specific values for Q and Pe. To find the percentage change in Q, we use the initial value of Q (240) and the given value of Q (240):
%ΔQ = (Q2 - Q1) / Q1 = (240 - 240) / 240 = 0%
To find the percentage change in Pe, we use the initial value of Pe (10) and the new value that gives a 1% decrease in Q:
Q = 240 - 4Pe + 2I + Pb + A
240 - 4(10) + 2I + (10) + (2) = 220 - 4(9) + 2I + (10) + (2)
240 - 40 + 2I + 12 = 220 - 36 + 2I
I = 2
Q = 220 - 4Pe + 2(2) + (10) + (2) = 234 - 4Pe
To get a 1% decrease in Q, we need to decrease Pe by 1/6 of its initial value:
%ΔPe = -1/6 = -16.67%
Now we substitute these values into the elasticity formula:
E = (%ΔQ / %ΔPe) = (0 / -16.67%) / (-1/6) = 0 / (-0.1667) / (-0.1667) = 0.6
Therefore, the point price elasticity of demand is -1/6 or B.

Scenario 4.3: The Demand for Erasers (Q) Is Given as Follows