Abstract
Small coins, large coins, and ingots circulated in parallel in the metallic currency system, and they were sorted by different mechanisms based on the transaction value of each form. This is the first attempt to model their boundaries. We construct a model of the market mechanism of the mint which derives two models to achieve our goal. The first model derived is a supply-demand model of small coins that determines the demarcation between small coins and large coins, and the second is a game model whose equilibrium solution determines the dividing line between large coins and ingots.
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