Question

Joana’s monthly income is $5000. She spends 40% of her income on grocery and the rest on buying designer clothes. The Provincial Government thinks it is unfair that people spend more than 35% of their income for grocery. In order to lower the proportion of income going to grocery, the Provincial Government gives Joana $500. Given that Joana’s income elasticity of grocery is 2, does the Provincial Government accomplished its goal? Support your answer.

Answer 1

Joana’s monthly income new$=5000+500=$ $$5500;$

E^d_i $=\frac {\Delta Qx}{\Delta I}×\frac {I}{Qx};$

$\Delta Qx=\frac {(5500-5000)}{5000}×100=$ %$10;$

$I=40×5000/100=$ $ $2000;$

$\frac {10}{\Delta I}×\frac {2000}{5000}=2;$

$\frac {10}{\Delta I}×0.4=2;$

$\frac {10}{\Delta x}=5;$

$\Delta I=$ %$2;$

$I$_new$=2000+\frac {2×2000}{100};$

$I$ _new$=2040;$

% of her income on grocery$=2040/5500×100=$ %$37;$

answer: the government did not achieve its goal, as Joanna will spend on products 37% of its income, rather than 35%.