The demand curve for a good is a straight line. At a price of Rs 10 t…

The correct answer is Option (4) → 2

First find the equation of the straight-line demand curve, q = a − bp. Then use the elasticity on a linear demand curve, e_D = −bp/(a − bp).

Given:

p = Rs 10, q = 40

p = Rs 15, q = 30

Elasticity wanted at p = Rs 20

    \( \displaystyle b = \frac{40 - 30}{15 - 10} = 2 \)

    \( \displaystyle a = 40 + 2 \times 10 = 60, \text{ so } q = 60 - 2p \)

    \( \displaystyle \text{At } p = 20: \; q = 60 - 40 = 20 \)

    \( \displaystyle |e_D| = \frac{bp}{q} = \frac{2 \times 20}{20} = 2 \)

The elasticity is 2. On a linear demand curve it is different at each price: here it rises above 1 because p = 20 is above the mid-point price a/2b = 15.