Figure 2.6.2
-When demand is written as Q = a - bP, and P* and Q* are the equilibrium values for price and quantity, which of the following is the value of the price elasticity of demand, E_D?

Question

Quizplus · Accepted Answer

The price elasticity of demand (ED) is defined as the percentage change in quantity demanded (Q) divided by the percentage change in price (P):

ED = (%ΔQ / Q) / (%ΔP / P)

In this case, we want to find the value of ED at equilibrium, so we can use the midpoint formula:

ED = (ΔQ / ((Q1 + Q2) / 2)) / (ΔP / ((P1 + P2) / 2))

At equilibrium, there is no change in quantity or price, so ΔQ = ΔP = 0. Therefore:

ED = (0 / ((Q* + Q*) / 2)) / (0 / ((P* + P*) / 2))
   = 0 / ((2Q*) / 2(P*))
   = 0

Now, we know that Q = a - bP, so we can solve for P* and Q*:

Q* = a - bP*
P* = (a - Q*) / b

We can substitute these values into the formula for ED:

ED = (-bP* / Q*) / (1)
   = -bP* / Q*

Therefore, the value of the price elasticity of demand at equilibrium is -b(P*/Q*), which corresponds to answer choice B.

Figure 2.6.2 -When Demand Is Written as Q = a - BP