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Technological progress has transformed the payment industry. Although alternative payment instruments such as bank cards share some characteristics with banknotes, they are not direct competitors to cash. First, cash possesses unique attributes—its functionality without electrical power and its inherent anonymity. Second, statistical data indicate that the ratio of cash to M1 has stabilized at approximately 10% in recent years, primarily due to its substitution with demand deposits. In this paper, we model the demand for banknotes by incorporating technology-related characteristics alongside conventional theories of money demand. Our approach has important implications for central bank, particularly in liquidity management, currency issuance, effective management of physical currency, and continued investment in digital payment infrastructures. We adopt a macroeconomic perspective that considers banknote demand from both transactional and asset viewpoints. To this end, we estimate an autoregressive distributed lag (ARDL) model, which allows us to analyze both short-term and long-term coefficients within a framework of model uncertainty. A key focus of our study is the estimation of a payment system development index using logistic growth and Gompertz models, through which we assess its impact on cash demand. Our empirical evidence supports the notion of S-shaped growth in the adoption of payment technologies. The findings demonstrate that advancements in the payment sector have led to a significant decline in cash demand. Moreover, while increased real economic activity exerts a positive and significant influence on cash demand, a higher opportunity cost of holding cash has a pronounced negative impact.

The implementation of an effective tax system requires specific conditions, among the most critical being equity and efficiency. Taxation on income must align with the principle of the ability to pay; therefore, governments strive to set tax rates appropriately and impactfully. An disproportionate increase in income tax rates can lead to significant social repercussions on income distribution and public welfare. Consequently, calculating the optimal tax rate to maximize social welfare is deemed essential. This paper models the strategic interaction between taxpayers and the tax authority to achieve an optimal tax rate and identifies the factors influencing this rate. By designing a game among taxpayers, assumed to be uniformly distributed within the interval [0, 1], and evaluating the revenue generation of the tax authority, the paper delves into the game formulation and analyses the results. Findings indicate that the optimal tax rate exhibits an inverse relationship with the assessment rates set by investigating groups. Additionally, under specific conditions, the optimal performance tax rate has been determined to be 18%.