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, it would be correct to say that demand is:

Question

Quizplus · Accepted Answer

To determine the elasticity of demand, we need to calculate the price elasticity of demand (Ep). Using the information given, we can calculate Ep as follows:

Ep = (% change in quantity demanded) / (% change in price)

Since we are trying to determine the elasticity at a specific point, we will use point elasticity. Point elasticity is represented as:

Ep = (dQ / Q) / (dP / P)

where dQ is the change in quantity demanded, Q is the original quantity demanded, dP is the change in price, and P is the original price.

Using the values given, we can calculate Ep as:

Ep = [(dQ / Q) / (dP / P)]
   = [(240 - Q) / 240] / [(Pe - 10) / 10]
   = [(-dQ / 240) / (Pe - 10) / 10]
   = - (dQ / Q) * (10 / (Pe - 10))

Since Q is given as 240 and Pe is given as 10, we can plug in these values to get:

Ep = - (dQ / 240) * (10 / 10)
   = - dQ / 240

Now we can use the midpoint formula to calculate the percentage change in quantity demanded:

% change in quantity demanded = (dQ / ((Q1 + Q2) / 2)) * 100

Let's say that the price of erasers increases from 10 to 12. Using the demand equation, we can solve for the new quantity demanded:

Q = 240 - 4Pe + 2I + Pb + A
Q = 240 - 4(12) + 2I + 10 + 2
Q = 218 + 2I

So when Pe = 12, Q = 218 + 2I.

Now we can calculate the percentage change in quantity demanded:

% change in quantity demanded = [(218 + 2I - 240) / ((240 + (218 + 2I)) / 2)] * 100
% change in quantity demanded = [(218 + 2I - 240) / (459 + 2I)] * 100

If we plug in I = 0 (i.e. no change in income), we get:

% change in quantity demanded = [(218 - 240) / 459] * 100
% change in quantity demanded = -4.79%

Now we can plug in the values for dQ and Q to get:

Ep = - (-4.79% / 100) / (12 - 10 / 10) 
Ep = 0.2395 or 24%

Since Ep is between 0 and 1, demand is inelastic, but not completely inelastic, and the best choice is D.

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