Question

the demand for ice cream is x=10+m/10p. the income of the consumer is $120 and the price of the ice cream is $3 . now suppose the price of the ice cream falls to $2 . find the income and substitution effect.

Answer 1

$X=10+\frac{m}{10p}$

His demand for ice cream will be;

$10+\frac{120}{30}$

$=10+4=14 dollars$

If the ice cream decreases by 2 dollars then the new price will be;

$10+\frac{120}{20}$

$=10+6=16$ dollars

The total change in demand will be $16-14=2$ dollars

$\Delta$$X$₁⁵$=X$₁$(P$₁$,m)-X$₁$(P$₁$,m)$

$\Delta$$m=X$₁ $\Delta$ $P$₁$=14(2-3)=$ -$14$ dollars

Therefore consumers income will be reduced to 14 dollars in order to hold his purchasing power.

$=m+\Delta$ $m=120-14=106$ dollars.

$\text{With an income of 6 he can still purchase 14 units of the ice cream at a lower price of 2 dollars}$$\text{Consumers demand for the ice cream when he faces the price of 2 dollars and has an income of 106 dollars}$ $=10+\frac{106}{20}$ $=15.3$ dollars.

The substitution effect will therefore be ;

$\Delta$$X$⁵₁$=X$₁$(2,106)-$ $X$₁$(3,120)$

$=15.3-14=1.3$ dollars.This is the substitution effect.

The income effect is;

$\Delta$$X$ⁿ₁$=$$X$₁$(P$₁$,m)-$ $X$₁$(P$₁$,m)$

$\Delta$$X$ⁿ₁$=X$₁$(2,120)-$ $X$₁$(2,106)$

$=16-15.3=0.7$ dollars

Therefore the income effect is $0.7$ $dollars$