Question

A change in a season has resulted in to a store reducing the prices of jeans. A pair of jeans which cost R1600 has been reduced it's price by R700. A consumer has a budget of R10000 to spend. Calculate the substitution and income effect given the following demand function

D=20+I/8(Pj)

Where. I is the income
Pj is the price of Jeans.

Answer 1

Let us consider two factors - change in price and change in real income.

Nominal income is 10,000.

$Real Income=\frac{Nominal Income}{CPI}$

$CPI=\frac{1600-700}{1600}=0.5625$

$RealIncome=\frac{10,000}{0.5625}=17,777.77$

Substitution effect is the change in demand when the purchasing power remains constant, so suppose that real income hasn't changed.

$(20+\frac{10,000}{8*1,600})-(20+\frac{10,000}{8*900})=0.607$

Income effect is the change in demand due to the change of real income.

$(20+\frac{10,000}{8*900})-(20+\frac{17,777.77}{8*900})=1.08$

Overall effect is $0.607+1.08=1.687$