EC2065 - Introduction of Macroeconomics - University of London

Assignment Task

1. Consider the two-period model of consumption choice (with two time periods representing the present and the future). An individual receives income y in the first period and income y in the second period, and can save or borrow at real interest rate r. The individual chooses a plan for current consumption c and future consumption c to maximize utility. The government collects tax revenue to in the current period and t in the future period.

(a) Write down an equation for the individual's life-time budget constrain t and interpret the equation. Draw a diagram illustrating how the optimal consumption plan is found and justify your answer. 

(b) Consider an economy where the real interest rate r rises. What is the effect of a higher interest rate on the life-time budget constraint in the diagram from part (a)? Assuming an individual was initially a saver, use the diagram to deduce whether the rise in interest rates increases or decreases the savers's utility. Explain whether a saver would ever find it rational to start borrowing when interest rates rise. 

(c) In a newspaper report discussing the consequences of high interest rates, a man is quoted as saying that his retirement savings are earning such a high return that I am actually reducing how much I contribute to my pension. Draw indifference curves to illustrate that the man is not being irrational by saving less when interest rates rise. Explain your answer in terms of income and substitution effects and discuss whether all savers would be expected to behave in this way.

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