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Questions › IIT JAM › IIT JAM 2021 › Q59
2 marksMacroeconomics › Consumption and investment › Relative income, permanent income and life-cycle hypothesesHardabout 3 min

IIT JAM 2021 Question 59: Consumption and investment

Individuals earn and consume from age 18, retire at 60 and die at 90, leaving no debt or bequests. Income at age ttt is 100t−t2100t - t^2100t−t2. The price level is constant and the interest rate is zero. By the life cycle theory, the average annual consumption of an individual is _______ (in integer).

Answer and worked solution

Answer: 1302

Lifetime income is earned from age 18 to 60: ∫1860(100t−t2) dt=93744\int_{18}^{60}(100t - t^2)\,dt = 93744∫1860​(100t−t2)dt=93744. Under life-cycle smoothing this is spread evenly over the consuming years, from 18 to 90, a span of 727272 years.

Average annual consumption is 9374472=1302\dfrac{93744}{72} = 13027293744​=1302. The answer is 130213021302.

Plain-text version

Individuals earn and consume from age 18, retire at 60 and die at 90, leaving no debt or bequests. Income at age t is 100t - t². The price level is constant and the interest rate is zero. By the life cycle theory, the average annual consumption of an individual is _ (in integer).

Also written as: Individuals earn and consume from age 18, retire at 60 and die at 90, leaving no debt or bequests. Income at age t is 100t - t^2. The price level is constant and the interest rate is zero. By the life cycle theory, the average annual consumption of an individual is _ (in integer).

Consumption and investment has come up 74 times in 7 exams since 2005.

What this question tests

This question is on Relative income, permanent income and life-cycle hypotheses, part of Consumption and investment in Macroeconomics.

Why consumption reacts less than one-for-one to temporary income changes.

TestStop has 19 past-paper questions on this subtopic.

Take this paper as a timed mockMore on Relative income, permanent income and life-cycle hypotheses

Question from the IIT JAM 2021 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.