## Abstract

This paper constructs two models of financial exclusion to assess the welfare costs of inflation. In the first, inflation costs are measured within a classical endowment economy. The second includes a production sector and costly credit. Both models are calibrated to account for inflation costs in a high-inflation economy (developing country) and in a low-inflation economy (developed economy). In an endowment economy, when inflation is reduced from 1.5% to zero in a developed economy, the welfare costs for agents with (without) financial access are 0.38% (0.43%) consumption equivalent variation (CEV). In a model with costly credit, the welfare costs for agents with (without) financial access are 0.87% (1.3%) CEV. For developing countries, when inflation is reduced from 3.2% to zero, the welfare costs for agents with (without) financial access are 0.72% (2.56%) in an endowment economy. In the costly-credit model, the welfare costs for agents with (without) financial access are 0.3% (3.1%) CEV. The main finding is that there is a substantial asymmetry in welfare costs between individuals with and without access to financial services, especially in developing countries.

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## References

Bailey, M.: The welfare cost of inflationary finance. J. Polit. Econ.

**64**(2), 93–110 (1956)Besley, T., Burchardi, K., Ghatak, M.: The gains from financial inclusion: theory and a quantitative assessment. Working paper (2018)

Cavalcanti, T.V.V., Villamil, A.P.: Optimal inflation tax and structural reform. Macroecon. Dyn.

**7**(3), 333–362 (2003)Central Bank of Brazil: Relatório de Inclusão Financeira. Technical Report, Central Bank of Brazil (2011)

Demirgüç-Kunt, A., Klapper, L., Singer, D., Ansar, S.: The Global Findex Database 2021: Financial Inclusion, Digital Payments, and Resilience in the Age of Covid-19. World Bank Publications, Washington, DC (2022)

Dotsey, M., Ireland, P.: The welfare cost of inflation in general equilibrium. J. Monet. Econ.

**37**(1), 29–47 (1996)Erosa, A., Ventura, G.: On inflation as a regressive consumption tax. J. Monet. Econ.

**49**(4), 761–795 (2002)European Commission: Financial services provision and prevention of financial exclusion. Research Report, European Commission (2008)

FDIC: FDIC national survey of unbanked and underbanked households. FDIC Washington, DC (2015)

Gillman, M.: The welfare cost of inflation in a cash-in-advance economy with costly credit. J. Monet. Econ.

**31**(1), 97–115 (1993)Guiso, L., Sapienza, P., Zingales, L.: Role of social capital in financial development. Am. Econ. Rev.

**94**(3), 526–556 (2004)Imrohoroglu, A.: The welfare cost of inflation under imperfect insurance. J. Econ. Dyn. Control

**16**(1), 79–91 (1992)Jeong, H., Townsend, R.M.: Sources of TFP growth: occupational choice and financial deepening. Econ. Theor.

**32**(1), 179–221 (2007)Liu, F.: Macroeconomic effects of microsavings programs for the unbanked. J. Econ. Behav. Organ.

**154**, 75–99 (2018)Liu, F., Villamil, A.: Microfinance in the U. Available at SSRN 4219367 (2021)

Lucas, R.E.: On the welfare cost of inflation. Working Papers in Applied Economic Theory 94-07. Federal Reserve Bank of San Francisco (1994). http://ideas.repec.org/p/fip/fedfap/94-07.html

Lucas, R.E.: Inflation and welfare. Econometrica

**68**(2), 247–274 (2000)Lucas, R.E., Stokey, N.L.: Optimal fiscal and monetary policy in an economy without capital. J. Monet. Econ.

**12**(1), 55–93 (1983)

## Acknowledgements

I’m indebted to Tiago Cavalcanti, George Deltas, Stephen Parente, and Rui Zhao for valuable comments. All remaining errors are mine.

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## Appendices

### Steady states

### 1.1 Pure exchange economy

The system of equations that characterize the steady state in the pure exchange economy is:

where \(r=1/\beta -1\) in the steady state.

### 1.2 Economy with production and costly credit

In the steady state \(r = 1/\beta - \delta \) and \(n^g(s^B) = 1 - \int _0^{s^B}{\gamma (j)dj}\). Therefore we can write aggregate capital and wages as a function of \(s^B\) such that

The system of equations that characterize the steady state is:

### Proof of Lemma 1

This proof is similar to the one found in Dotsey and Ireland (1996). Let \(\beta ^t\lambda _t\) be the Lagrange multiplier on the budget constraint and \(\beta ^t\phi _t\) be the Lagrange multiplier on the cash-in-advance constraint. Then, the first order conditions from the type-*B* agent lead to:

Moreover, profit maximization for the firm in the intermediary sector leads to the following supply choice:

note that Eq. (B4), together with the zero profit condition for the credit service market and the equilibrium for this market implies that

for all *j* demanded by type-B individuals, i.e., \(\xi _t^B(j) = 1\).

Let \(s_t^{B}\in {\mathcal {J}}\) be the good for which type-B individuals are indifferent between buying with credit or money, such that the inequality in Eq. (B3) holds with equality. Substituting Eqs. (B1), (B2) and (B4) into Eq. (B3) at equality yields:

which defines \(s_t^B\).

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Baerlocher, D. Financial exclusion and inflation costs.
*Econ Theory Bull* (2024). https://doi.org/10.1007/s40505-024-00265-x

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DOI: https://doi.org/10.1007/s40505-024-00265-x