S. R. Aiyagari, Uninsured Idiosyncratic Risk and Aggregate Saving, The Quarterly Journal of Economics, vol.109, issue.3, pp.659-684, 1994.
DOI : 10.2307/2118417

A. Akyol, Optimal monetary policy in an economy with incomplete markets and idiosyncratic risk, Journal of Monetary Economics, vol.51, issue.6, pp.1245-1269, 2004.
DOI : 10.1016/j.jmoneco.2003.09.005

Y. Algan and X. Ragot, Monetary policy with heterogeneous agents and borrowing constraints, Review of Economic Dynamics, vol.13, issue.2, pp.295-316, 2010.
DOI : 10.1016/j.red.2009.05.001

URL : https://hal.archives-ouvertes.fr/hal-01170621

Y. Algan, E. Challe, and X. Ragot, Incomplete markets and the output???inflation tradeoff, Economic Theory, vol.54, issue.1, pp.55-84, 2011.
DOI : 10.1007/s00199-009-0499-0

URL : https://hal.archives-ouvertes.fr/halshs-00654652

T. Bewley, The optimum quantity of money, Models of Monetary Economies, 1980.

A. Berentsen, G. Camera, and C. Waller, THE DISTRIBUTION OF MONEY BALANCES AND THE NONNEUTRALITY OF MONEY*, International Economic Review, vol.22, issue.2, pp.465-487, 2005.
DOI : 10.1016/S0022-0531(03)00132-7

B. Rodriguez, S. Diaz-gimenez, J. Quadrini, V. Rior-rull, and J. , Updated facts on the U.S. distributions of earnings, income, and wealth, pp.2-35, 2002.

V. V. Chari, L. J. Christiano, and P. J. Kehoe, Optimality of the Friedman rule in economies with distorting taxes, Journal of Monetary Economics, vol.37, issue.2, pp.203-223, 1996.
DOI : 10.1016/S0304-3932(96)90034-3

V. V. Chari, P. J. Kehoe, and E. R. Mcgrattan, Sticky-price models of the business cycle: Can the contract multiplier solve the persistence problem?, Econometrica, issue.5, pp.68-1151, 2000.
DOI : 10.3386/w5809

T. Cooley and G. Hansen, The in ?ation tax in a real business cycle model, American Economic Review, vol.79, issue.4, pp.733-781, 1989.

M. Doepke and M. Schneider, Inflation and the Redistribution of Nominal Wealth, Journal of Political Economy, vol.114, issue.6, pp.1069-1097, 2006.
DOI : 10.1086/508379

D. Domeij and J. Heathcote, On The Distributional Effects Of Reducing Capital Taxes*, International Economic Review, vol.3, issue.1, pp.523-554, 2004.
DOI : 10.1016/0304-3932(94)90021-3

A. Erosa and G. Ventura, On inflation as a regressive consumption tax, Journal of Monetary Economics, vol.49, issue.4, pp.761-795, 2002.
DOI : 10.1016/S0304-3932(02)00115-0

M. Friedman, The optimum quantity of money, in The Optimum Quantity of Money and Other Essays, 1968.

J. Heathcote, Fiscal Policy with Heterogeneous Agents and Incomplete Markets, Review of Economic Studies, vol.72, issue.1, pp.161-188, 2005.
DOI : 10.1111/0034-6527.00328

B. Heer and A. Maussner, The burden of unanticipated in ?ation: Analysis of an overlapping generations model with progressive income taxation and staggered prices, 2011.

J. A. Holman, GMM Estimation of a Money-in-the-Utility-Function Model: The Implications of Functional Forms, Journal of Money, Credit and Banking, vol.30, issue.4, pp.679-698, 1998.
DOI : 10.2307/2601124

M. Huggett, The risk-free rate in heterogeneous-agent incomplete-insurance economies, Journal of Economic Dynamics and Control, vol.17, issue.5-6, pp.953-69, 1993.
DOI : 10.1016/0165-1889(93)90024-M

A. Imrohoroglu, The welfare cost of inflation under imperfect insurance, Journal of Economic Dynamics and Control, vol.16, issue.1, pp.79-91, 1992.
DOI : 10.1016/0165-1889(92)90006-Z

T. Jappelli, Who is Credit Constrained in the U. S. Economy?, The Quarterly Journal of Economics, vol.105, issue.1, pp.219-234, 1990.
DOI : 10.2307/2937826

T. J. Kehoe, D. K. Levine, and M. Woodford, The optimum quantity of money revisited, in Economic Analysis of Markets and Games, 1992.

T. Krebs, Growth and welfare effects of business cycles in economies with idiosyncratic human capital risk, Review of Economic Dynamics, vol.6, issue.4, pp.846-868, 2003.
DOI : 10.1016/S1094-2025(03)00030-9

P. Krusell, T. Mukoyama, and A. , Labour-Market Matching with Precautionary Savings and Aggregate Fluctuations, Review of Economic Studies, vol.77, issue.4, pp.1477-1507, 2010.
DOI : 10.1111/j.1467-937X.2010.00700.x

P. Krusell, T. Mukoyama, A. Sahin, and A. A. Smith, Revisiting the welfare effects of eliminating business cycles, Review of Economic Dynamics, vol.12, issue.3, pp.393-402, 2009.
DOI : 10.1016/j.red.2009.01.002

P. Krusell and A. A. Smith, Income and Wealth Heterogeneity in the Macroeconomy, Journal of Political Economy, vol.106, issue.5, pp.867-896, 1998.
DOI : 10.1086/250034

P. Krusell and A. A. Smith, INCOME AND WEALTH HETEROGENEITY, PORTFOLIO CHOICE, AND EQUILIBRIUM ASSET RETURNS, Macroeconomic Dynamics, vol.1, issue.02, pp.387-422, 1997.
DOI : 10.1017/S1365100597003052

V. Quadrini, Entrepreneurship, Saving, and Social Mobility, Review of Economic Dynamics, vol.3, issue.1, pp.1-40, 2000.
DOI : 10.1006/redy.1999.0077

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

X. Ragot, The case for a ?nancial approach to money demand, 2011.

J. A. Scheinkman and L. Weiss, Borrowing Constraints and Aggregate Economic Activity, Econometrica, vol.54, issue.1, pp.23-45, 1986.
DOI : 10.2307/1914155

K. Storesletten, C. Telmer, and A. Yaron, The welfare costs of business cycles revisited: Finite lives and cyclical variation in idiosyncratic risk, European Economic Review, issue.7, pp.45-1311, 2001.

C. Walsh, Monetary Theory and Policy, 2010.

E. Young, Solving the incomplete markets model with aggregate uncertainty using the Krusell???Smith algorithm and non-stochastic simulations, Journal of Economic Dynamics and Control, vol.34, issue.1, pp.36-41, 2010.
DOI : 10.1016/j.jedc.2008.11.010

A. Numerical-algorithm and A. , 1 Overview of the Algorithm The algorithm used to obtain the solution of the model is as follows. 1. Given laws of motion for real money balance and capital, de?ned by (14) and (15), solve the household's problem given by the equations