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Consider an economy where every household lives for 60 periods. For the first 45 periods, households...

Consider an economy where every household lives for 60 periods. For the first 45 periods, households participate in the labour market. For the remaining 15 periods they are retired. Working-age households earn a labour income of $40 per period. Retired households get no such income. Households can borrow and save as much as they want; the interest rate is zero. Households want their period consumption to be constant and as high as possible. They do not want to leave any assets or debt after their deaths.

b) What is the working and retired households' saving per period? What is their peak-level of wealth?

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Answer #1

For the entire lifespan : Total income = 45*40 (given no interest rates) = $1800

For an equal amount of consumption at every period: 1800/60 = $30

So, for Working years, Savings = Income - Consumption = $40-$30 = $10

For retirement, Savings = 0( Entire savings of working years goes entirely into consumption)

Peak level of wealth = Total Savings at the start of last working year + salary of working year = 44*10 + 40 = $480

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