In a scenario where there is a mandated exchange rate, typically enforced by a country's government, this rate dictates the value of the local currency in terms of another currency, such as dollars. However, the actual flow of the market—particularly in the case of an oversupply or undersupply of dollars—may not align with these set rates.

When there is no real supply of dollars, but rather a conversion rate applied to another currency or asset like Bitcoin (BTC), the situation becomes analogous to stating that "$x$ dollars is simply $r*x$ BTC," where $r$ represents the exchange rate between dollars and BTC. This theoretical rate does not necessarily dictate market behavior because traders will act based on the actual availability and demand for dollars versus BTC. If traders are unable to purchase dollars at the government-mandated rate due to a scarcity, they may be willing to pay more, thereby driving up the price above the official rate. Conversely, if dollars are abundant but demand is low, the market value could fall below the mandated rate.

Market forces often reflect the reality of economic conditions, including factors like inflation, confidence in the local currency, and global economic trends, which can all influence whether the free market adheres to or deviates from a government-mandated exchange rate. In essence, while a government can decree a fixed rate of exchange, the free market ultimately responds to the actual supply and demand for currencies involved.