Question #108505

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.

Expert's answer

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

E^{d}_{i} "=\\frac {\\Delta Qx}{\\Delta I}\u00d7\\frac {I}{Qx};"

"\\Delta Qx=\\frac {(5500-5000)}{5000}\u00d7100=" %"10;"

"I=40\u00d75000\/100=" $ "2000;"

"\\frac {10}{\\Delta I}\u00d7\\frac {2000}{5000}=2;"

"\\frac {10}{\\Delta I}\u00d70.4=2;"

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

"\\Delta I=" %"2;"

"I"_{new}"=2000+\\frac {2\u00d72000}{100};"

"I" _{new}"=2040;"

% of her income on grocery"=2040\/5500\u00d7100=" %"37;"

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

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