We prove that the consumption functions in income fluctuation problems are asymptotically linear if the marginal utility is regularly varying. We also analytically characterize the asymptotic marginal propensities to consume (MPCs) out of wealth and derive necessary and sufficient conditions under which they are 0, 1, or are somewhere in between. When the return process with time-varying volatility is calibrated from data, the asymptotic MPCs can be zero with moderate risk aversion. Our results potentially explain why the saving rates among the rich are positive and increasing in wealth .
We prove that the consumption functions in optimal savings problems are asymptotically linear if the marginal utility is regularly varying. We also analytically characterize the asymptotic marginal propensities to consume (MPCs) out of wealth . Our results are useful for obtaining good initial guesses when numerically computing consumption functions, and provide a theoretical justification for linearly extrapolating consumption functions outside the grid .
R
income fluctuation
optimal savings
R
and derive necessary and sufficient conditions under which they are 0, 1, or are somewhere in between. When the return process with time-varying volatility is calibrated from data, the asymptotic MPCs can be zero with moderate risk aversion. Our results potentially explain why the saving rates among the rich are positive and increasing in wealth
. Our results are useful for obtaining good initial guesses when numerically computing consumption functions, and provide a theoretical justification for linearly extrapolating consumption functions outside the grid