Answer to Question #122660 in Microeconomics for Brenda Formin

Question

4. The following is a straight-line demand curve that confronts a single firm.

Quantity
Price demanded (3) (4)
$6 1 _____ _____
5 2 _____ _____
4 3 _____ _____
3 4 _____ _____
2 5 _____ _____
1 6 _____ _____

(a) In column 3, compute total revenue. In column 4, compute the coefficient for the price elasticity of demand at each price using the midpoints formula.
(b) Describe the character of elasticity across the prices based on the total revenue test and the elasticity coefficient.
(c) Does a straight-line demand curve have constant elasticity?
(d) Of what practical significance is your answer to (c)?

Answer 1

(a) In column 3, compute total revenue. In column 4, compute the coefficient for the price elasticity of demand at each price using the midpoints formula.

The price elasticity of demand using the midpoint formula is calculated as:

$$E_d = \dfrac{\Delta Q}{\Delta P}\cdot \dfrac{(P_1 + P_2)/2}{(Q_1 + Q_2)/2}$$

The table below shows the elasticities and the total revenue

(b) Describe the character of elasticity across the prices based on the total revenue test and the elasticity coefficient.

When the demand is inelastic (between P = 1 and P = 3), the total revenue is increasing as the price increases. However, as the demand becomes elastic (between P = 4 and P = 6), the total revenue begins to fall.

(c) Does a straight-line demand curve have constant elasticity?

As we can see from the table (which is a representation of a linear demand curve), the price elasticity of demand is not constant. The elasticity increases as we move upwards along a linear demand curve.

(d) Of what practical significance is your answer to (c)?

This enables any firm to decide where to price its product as setting a price above the midpoint of the demand curve (where the demand is unit elastic) will reduce the total revenue.