Question

How do we calculate income and substitution effect and please explain the formula for calculating it

Answer 1

Consider a simple quasi-linear utility function of the form $U(x,y)=x+ln(y)$ . For this problem, assume that you have “enough” income, so that the optimal consumption bundle is where: $x,y>0$ .using Lagrange function to derive that $y=PxPy$ , (price of x over the price of y) and $x=MPx−1$ (M is income). In general, for preferences that are quasi-linear in $x(y)$ it holds true that:

Overall effect = Substitution effect, if in the initial situation both goods or if only good $y(x)$ are consumed.

Overall effect = Income effect, if in the initial situation only good $x(y)$ is consumed.

Substitution effect= $x(p(x)′,m′)−x(p(x),m)$

Income effect= $x(p(x)′,m)−x(p(x)′,m′)$