Question

Suppose the demand for commodity X as the function of its own price and consumer’s money income,

keeping other factors constant is described by the following equation:

X = 100,000 – 2PX + 7M; where M is consumer’s money income in Birr and PX is price of the

commodity X in Birr. If the price is Birr 10,000 and money income is Birr 15,000, then:

a. what is the total demand for X at the prevailing market price and income

b. calculate the income elasticity of demand for the commodity &; comment on the type of elasticity and

type of commodity

c. calculate the price elasticity of demand for the commodity and determine the type of elasticity

Answer 1

$a) X=100000- 2PX+7M$

PX=10000

$M=15000$

$X=100,000-2(10,000)+7(15,000)$ $X=100,000-20,000+105,000$

$X=80,000+105,000=185,000$

b) Income elasticity

$\frac{∆X}{∆I} × \frac{I}{X}$

$\frac{∆X}{∆I} =7$,(change in money income given in the function)

$I=15000 X=185000$

$7×15000/185000=0.567$

A 1% increase in income results in the quantity demanded of good X increasing by 0.567. The elasticity is unit elastic since it is approximately equal to 1 and the commodity is a normal good since the elasticity maintains a positive value.

c) Price elasticity

$\frac{∆Q}{∆P} ×\frac{P}{Q}$

$\frac{∆Q}{∆P}=-2$ (change in price from the function given)

$P=10000$

$-2×10000/185000=-0.108$

Since the value is less than 1, it is inelastic.