Assignment: Show that Price Elasticity of demand (Ep) changes from 0 to -∞ as we move along the linear demand curve.

Solution:

Demand Curve: Relationship between the quantities of a good that consumers are willing to buy and the price of the good.

Linear Demand Curve: Demand Curve that is a straight line.

In mathematical form, it can be defined as

Q = a – bP

Where Q = Quantity demanded;

P = Price per unit of the good; and

a, b = constants

Elastic range

Price Ep = -∞ (PerfectlyElastic) Q = a- bP

. Ep = -1(Unitory elastic)

Inelastic range

Ep = 0 (Perfectly inelastic)

Quantity

Price Elasticity of Demand: Percentage change in quantity demanded of a good as a result from a 1- percent increase in its price.

In mathematical form, it can be defined as

Ep = ΔQ/Q = (P/Q) (ΔQ/ΔP) …………..(1) ΔP/P

Where Q, P = same as above

ΔQ = Change in quantity demanded

ΔP = Change in Price per unit of the good

Consider the Linear demand curve Q = a-bP

Differentiating the above equation w.r.t. price, we have change in quantity w.r.t change in price

ΔQ/ΔP = -b …………….(2)

Substituting (2) in equation (1), we have,

Ep = (P/Q) (-b) = (-Pb)/Q …………………..(3)

From Equation (3), when P 0, than Ep 0 (Perfectly inelastic). This condition is denoted on the graph by point no. 1.

If P/Q=1/b, then Ep =-1 (Unitary elastic). Hence for P/Q between 0 and 1/b, Ep will vary from 0 to -1 (inelastic range) and for P/Q between 1/b and ∞, Ep will vary from -1 to -∞ (elastic range).

And similarly, when Q 0, than Ep -∞ (Perfectly elastic). This