For the following demand function, Q D = 100 – P, answer the following questions
ID: 2496112 • Letter: F
Question
For the following demand function, QD = 100 – P, answer the following questions
a. what is the point elasticity of demand at P = 80?
b. what is the point elasticity of demand at P = 20?
c. at what price is demand unitary price elastic?
d. demand is price elastic for prices between __________ and ___________
e. Consider your answer to part d., what happens to revenues as prices decrease within
this range? Are marginal revenues positive, constant or negative in this range of
prices?
f. demand is price inelastic for prices between __________ and ___________
g. Consider your answer to part f., what happens to revenues as prices decrease within
this range? Are marginal revenues positive, constant or negative in this range of
prices?
h. How many units of this good does a firm facing this demand curve have to produce to
maximize its revenues?
i. What are maximum revenues for this firm?
j. Draw the total revenue curve associated to this demand curve.
Explanation / Answer
(a) Calculate the point elasticity of demand at P = 80 -
QD = 100 - P
P = 80
QD = 100 - 80 = 20
Point elasticity = [dQD/dP] * [P/QD] = [d(100 - P)/dP] * [80/20] = -1 * 4 = -4
The point elasticity of demand at P = 80 is -4.
(b) Calculate the point elasticity of demand at P = 20 -
QD = 100 - P
P = 20
QD = 100 - 20 = 80
Point elasticity = [dQD/dP] * [P/QD] = [d(100 - P)/dP] * [20/80] = -1 * 0.25 = -0.25
The point elasticity of demand at P = 20 is -0.25.
(c) Calculate price at which demand is unitary elastic -
Demand is unitary elastic implies that value of elasticity of demand is -1.
Point elasticity = [dQD/dP] * [P/QD] =
-1 = [d(100 - P)/dP] * [P/QD]
-1 = -1 * [P/QD]
QD = P
QD = 100 - P
P = 100 - P
P = 50
The price at which demand is unitary elastic is 50.
(d) At P = 50, demand is unitary elastic.
So, at each price below 50, demand would be inelastic and at each price above 50, demand would be elastic.
At P = 80, demand is elastic.
So, demand is price elastic for prices between 50 and 80.