Life-cycle models

The following questions look at Modigliani syle life-cycle models

5.1 Visualizing life-cycle models A household will live for T years, and will work from the present time period until they retire at year R. The household earns Y per year while working, and earns nothing once retired. In the present period they have W= 0 (i.e they have no initial money in the bank). Assume the household's = 0 and the the interest rate is zero (r = 0), or in other words, the household wants to perfectly smooth its consumption over their lifetime.

1. Draw a figure to show how income, consumption, and money in the bank evolve over time for this scenario.

5.2 Life-cycle model with changing income

In the discussion of the life-cycle hypothesis in the text, income is assumed to be constant during the period before retirement. For most people, however, income grows over their lifetimes until they retire. For this question, assume the same T, R, W, , and r as before, but now assume that Y is zero in the present and increases linearly to Y from the present until retirement at R.

1. Draw a figure like the one above, but with this increasing Y. (Assume there are no borrowing constraints i.e. households can have negative bank balances if they wish.)

2. Explain in words the intuition behind why this figure looks different from your previous figure in Section 5.1.

5.3 Life-cycle model with Students

Our discussions of life-cycle models we often assume households are earning income, Y, from the present until time R. However, as we all know, often households spend time in school before entering the workforce.

Assume now the household is in school until their graduation at time G. (We assume they have a full-ride scholarship, but no time for a part-time job, so school costs the household noting but also they earn nothing while in school). Once they are done school they earn income Y each period until retirement at time R. The household still lives T years, and W, , and r, all equal zero as before.

1. Draw a figure like the ones above, but with this time with the household in school between the present and time G. (Again, assume there are no borrowing constraints i.e. households can have negative bank balances if they wish.)

2. Explain in words the intuition behind why this figure looks different from your inital figure in 5.1