Question

41. The demand equation for a product is given by
Q = (20I) / (P), where I is income and P is price.
i) Write an equation for the point price elasticity. For what values of I and P demand is unitary elastic? Explain.
ii) Write an equation for the point income elasticity. For what values of I and P is the good a necessity? Explain.

Answer 1

$$Solution$$

When proportionate or percentage change in quantity demanded is exactly equal to proportionate or percentage change in price, then the demand will be said to be unitary elastic.

i) An equation for the point price elasticity will be

$D_e=\frac{\delta\ Q}{Q}/\frac{\delta\ P}{P}\\ If\ I=\frac{1}{20}p, then\ the\ demand\ is\ unitary\ elastic$

ii)  If the percentage change in quantity demanded is less than the percentage increase in income, the value is less than unity then the good will be termed as a necessity.

Therefore, $I>\frac{1}{20}P, this\ good\ is\ a\ necessity.$