Skip to main content
Log in

Financial exclusion and inflation costs

  • Research Article
  • Published:
Economic Theory Bulletin Aims and scope Submit manuscript


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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Data availability

Data is available under request.


  • Bailey, M.: The welfare cost of inflationary finance. J. Polit. Econ. 64(2), 93–110 (1956)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • 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)

    Book  Google Scholar 

  • Dotsey, M., Ireland, P.: The welfare cost of inflation in general equilibrium. J. Monet. Econ. 37(1), 29–47 (1996)

    Article  Google Scholar 

  • Erosa, A., Ventura, G.: On inflation as a regressive consumption tax. J. Monet. Econ. 49(4), 761–795 (2002)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Guiso, L., Sapienza, P., Zingales, L.: Role of social capital in financial development. Am. Econ. Rev. 94(3), 526–556 (2004)

    Article  Google Scholar 

  • Imrohoroglu, A.: The welfare cost of inflation under imperfect insurance. J. Econ. Dyn. Control 16(1), 79–91 (1992)

    Article  Google Scholar 

  • Jeong, H., Townsend, R.M.: Sources of TFP growth: occupational choice and financial deepening. Econ. Theor. 32(1), 179–221 (2007)

    Article  Google Scholar 

  • Liu, F.: Macroeconomic effects of microsavings programs for the unbanked. J. Econ. Behav. Organ. 154, 75–99 (2018)

    Article  Google Scholar 

  • 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).

  • Lucas, R.E.: Inflation and welfare. Econometrica 68(2), 247–274 (2000)

    Article  Google Scholar 

  • Lucas, R.E., Stokey, N.L.: Optimal fiscal and monetary policy in an economy without capital. J. Monet. Econ. 12(1), 55–93 (1983)

    Article  Google Scholar 

Download references


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



Author information

Authors and Affiliations


Corresponding author

Correspondence to Diogo Baerlocher.

Ethics declarations

Conflict of interest

The author declares that he has no Conflict of interest

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


Steady states

1.1 Pure exchange economy

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

$$\begin{aligned} c^B_{1} + c^B_{2} + \pi m^B = w^B +\frac{1-\beta }{\beta }b^B \\ c^B_{1} + \pi m^B = w^B + \frac{1-\beta }{\beta }b^B \\ c^B_{1} = m^B \\ c^B_{1} = m^B \\ \lambda ^B(c^B_{1} + c^B_{2}) + \lambda ^Bc^B_{1} = w^B + w^B \\ \lambda ^Bb^B+\lambda ^Bb^B = 0 \\ c_{2}^B = \frac{1}{\beta }(1+\pi )c^B_1 \end{aligned}$$

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

$$\begin{aligned} K(s^B) = \left( \frac{\alpha \beta }{1-\delta \beta }\right) ^{\frac{1}{1-\alpha }}n^g(s^B) \quad \text {and}\quad w(s^B) = (1-\alpha )\left( \frac{K(s^B)}{n^g(s^B)}\right) ^\alpha . \end{aligned}$$

The system of equations that characterize the steady state is:

$$\begin{aligned} c^B + w(s^B)\int _0^{s^B}{\gamma (j)dj} + \pi m^B = w(s^B) +\frac{1-\beta }{\beta }k^B \\ c^B + \pi m^B = w(s^B) + \frac{1-\beta }{\beta }k^B \\ c^B(1-s^B) = m^B \\ c^B = m^B \\ \lambda ^B(c^B + \delta k^B) + \lambda ^B(c^B+\delta k^B) = K(s^B)^\alpha n^g(s^B)^(1-\alpha ) \\ \lambda ^Bk^B+\lambda ^Bk^B = K(s^B) \\ w(s^B)\gamma (s^B) = [(1+\pi )/\beta - 1]c^B. \end{aligned}$$

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:

$$\begin{aligned} c^{B0}_t(j)&= u^{-1}_c(\lambda _t + \phi _t) \end{aligned}$$
$$\begin{aligned} c^{B1}_t(j)&= u^{-1}_c(\lambda _t) \end{aligned}$$
$$\begin{aligned} \xi _t^B(j)&= {\left\{ \begin{array}{ll} 1&{}\quad \text { if } u(c^{B1}_t) - \lambda _t[c^{B1}_t + q_t(j)] \ge u(c^{B0}_t) - (\lambda _t+\phi _t)c^{B0}_t \\ 0&{}\quad \text { otherwise}. \end{array}\right. } \end{aligned}$$

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

$$\begin{aligned} \xi _t^s(j) = {\left\{ \begin{array}{ll} 1&{}\quad \text { if } q_t(j) \ge w_t\gamma (j) \\ 0&{}\quad \text { otherwise}. \end{array}\right. } \end{aligned}$$

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

$$\begin{aligned} q_t(j) = w_t\gamma (j), \end{aligned}$$

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:

$$\begin{aligned} \gamma (s^B_t) = \frac{u[u^{-1}_c(\lambda _t)] - \lambda _tu^{-1}_c(\lambda _t) - u[u^{-1}_c(\lambda _t + \phi _t)] + (\lambda _t+\phi _t)u^{-1}_c(\lambda _t + \phi _t)}{\lambda _tw_t},\nonumber \\ \end{aligned}$$

which defines \(s_t^B\).

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Baerlocher, D. Financial exclusion and inflation costs. Econ Theory Bull 12, 87–105 (2024).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


JEL Classification