# Mathematical Model to Analyze Effect of Demonetization

Nita H. Shah (Department of Mathematics, Gujarat University, Ahmedabad, India), Bijal M. Yeolekar (Department of Mathematics, Gujarat University, Ahmedabad, India), and Zalak Ashvinkumar Patel (L. D. College of Engineering, India)
DOI: 10.4018/978-1-7998-3741-1.ch012
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## Abstract

Demonetization is a fundamental regulatory act of stripping in which a currency unit's status as an exchange is professed worthless. Generally, it is done whenever there is a change of national currency, often to be replaced of the old notes or coins with a new one. Sometimes, a country totally replaces the old currency with new currency. For example, in India recently the government demonetized RS. 500 and 1000 notes. So, one has to deposit their cash within limited time in the banks. The demonetization affects individuals mildly or potentially, which in turn affects banking sector. So, SMPB-model is proposed and analyzed for demonetization. The SMP-model is formulated with the system of nonlinear differential equations. The effect of demonetization is studied by calculating threshold using next generation matrix. The local and global stability for demonetization free equilibrium and demonetization equilibrium is worked out. The existence of the equilibrium is investigated. The model is validated with numerical simulation.
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## Introduction

Demonetization is the act of banning a specific form of currency notes from circulation by the government. Due to demonetization, a currency is blocked or the old currencies changed by the new currency. There are several reasons for demonetizing currency for nations: some reasons include combating the inflation, to control the corruption and crime, to discourage a cash-dependent and to promote the cashless economy for getting transparency in all the modes of legal transaction in the country.

In India, the first time in 1946 that the government demonetized of high value currency notes of Rs. 1000 and Rs. 10000 and then introduced higher quantity bank note of Rs. 1000, Rs.5000 and Rs. 10000 currency notes in 1954. After that in 1978, Prime Minister Shri Morarji Desai demonetized these high value notes. After 38 years again demonetization of currency note bans of Rs. 500 and Rs. 1000 in November 8, 2016 and this time old currency of Rs. 500 notes were replaced with new designed and Rs. 1000 notes vanished and the first time introduced Rs. 2000 value note. The objective of the demonetization was to curb the disease of corruption and black money and curtail the circulation of fake notes in the system.

Demonetization is the interruption of current currency and replaces the old currency units with new currency units. It is a significant decision and it disappointed all the individuals as unexpectedly all the money individuals have become a piece of paper. The old money has no value if one cannot exchange it with new currency units or deposited it in the banks within a given time by the government and use maximum the online services at that time. Online banking mentioned as using internet for different banking amenities extending from bill payments to savings [Pikkarainen et al. (2014)]. Previously banks used to deliver information for their products on respective bank websites and with time they have given chance to the clients for making monetary transaction like bill payments and money transfers etc. [Chong et al. (2010)]. Online banking is classification into an online account with direct money transfer in the account [Chiles (2013)]. From mid ninety’s internet banking had started in India. ICICI was implemented internet banking in 1998 [Kesharwani and Sainti (2012)]. The several reasons like compatibility, importance, involvedness, ability, apparent risk and were measured customer attitude towards internet banking [Ndubisi et al. (2006)]. For understanding internet banking usage Yoon and Steege (2013) observed some features like usability, personality, security and social stimulus of internet banking which are beneficial for banks as well as customers and also it made possible cost savings and ease. Internet banking adoption professed some factors like usefulness, ease of use, social influence and self-efficacy have an influence on customer’s attitude in urban area [Sharma and Govindaluri (2014)]. According to survey of Internet and Mobile Association of India (IAMAI), the safety apprehensions and less knowledge about online transactions are the main blocks to adopt online or internet banking. Rathore (2016) studied that digital wallets are speedily becoming conventional approach of e-payment. Sellers and buyers both are accepting digital wallets at rapid pace, because of its handiness and ease of usability. These all suggested studying the demonetization effect and net banking.

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