Question

Suppose the wage of an industrial worker follows a path given by S $=x^2$ and inflation rate during the same time is given by $I=e^x$ where x is the time in months. What can you say about his standard of living provided all other factors remain constant? Give reasons behind your observations.

• A. His standard of living will improve with the increase in real wage
• B. His standard of living will remain the same with no change in his real wage
• C. His standard of living will deteriorate with decrease in real wage
• D. It cannot be determined

Answer 1

The correct option is C

His standard of living will deteriorate with decrease in real wage

Let us consider a function $f\left(x\right)=e^x-x^2$. Differentiating f(x) with respect to x, we get $f^{\prime }\left(x\right)=e^x-2x>0$ for $x\ge 0$ which means f(x) is a strictly increasing function for $x\ge 0$ i.e. $f\left(x\right)>0\Rightarrow e^x>x^2$. Hence, the worker’s standard of living will never be able to catch up with inflation. In other words, he won’t be able to maintain his standard of living.