Question

An employer offers his or her employee the option of shifting x units of income from next year to this year. That is, the option to reduce income next year by x units and increase income this year by x units.

a) Would the employee take this option (use a diagram)?

b) Determine, using a diagram, how this shift in income will affect consumption this year and next year and saving this year. Explain your results.

Answer 1

Suppose t = t' = 0. Initial lifetime wealth is

we₀= y + (1 + r) -1 y^'

Lifetime wealth after the shift is we₁= y + x + (1 + r)^-1 (y^' − x)

= y + (1 + r) ^-1 y^'  + x( 1 − (1 + r)^-1)

we₁ > we₀ whenever r > 0, and so the employee should take the option, provided that interest rate is positive.

(b) The shift in income creates a pure income eect (shifts budget constraint outwards in a parallel fashion).

Thus, both c, c ^' will increase.

Saving will increase: c ^' = y ^' + (1 + r)s Since c ^'increases while y^' decreases, s must increase for the equality to hold.