Lateley, i have become interested in the question of the utility of the cryptocurrency bitcoin, especially in relation to traditional currencies like USD or EUR, which I will call fiat currency in the remainder, signifying a currency wich is not commodity based, as is the norm.

TL, DR: Compared to a fiat money economcy, gdp growth in a bitcoin economy is limited by the constant growth rate of the money supply.

In the following, I want to compare the market mechanism of bitcoin in relation to the money market mechanism of a fiat currency.

The analysis is based on following assumptions, first regarding supply and demand of bitcoin

• Bitcoins are mined by solving mathematical puzzles, which have no further value, the creation of bitcoin is the only source of income for the miners
• The cost of mining results solely from hardware and energy costs, whose prices move proportionally to the general price index of the economy. Demand from miners is assumed to have no influence on the general price index.
• The difficulty of the puzzles is instantly adjusted, so that the global increase in the stock of bitcoin is constant.
• Consumers can freely borrow or save bitcoin at the nominal interest rate
• The bitcoin is the sole currency used in a small closed economy.

With regard to the fiat currency, I make the following assumptions:

• Fiat currency is generated by the central bank, which adjusts the supply of money in accordance with a constant rate of inflation.
• Consumers can freely borrow or save fiat currency at the nominal interest rate
• The fiat currency is the sole currency used in a small closed economy.

With regard to money demand, I make the following assumptions:

• Money demand changes proportional to economic activy as measured by gdp growth rate
• The nominal interest rate increases with an increase in excess money demand.
• Interest rates adjust instantaniously, price index adjustments are sluggish
• The price index increases with a increase in excess money supply, and an excess in goods demand.
• The gdp growth rate increases with a decrease of the real interest rate

Both economies are assumed to be in steady state before an exogene shock to the economy, both money stocks increase at the current gdp growth rate. This shock is an increase in the gdp growth rate following an increase in government spending.

First, the reaction in the bitcoin economy:

1. Excess goods demand lead to an increase in the demand for bitcoin.
2. The increase in bitcoin supply is insufficient to satisfy the excess demand, leading to an increase in the nominal interest rate and a decrease of the price index.
3. Both effects lead to an increase in the real interest rate, leading to a decrease of the gdp growth rate, which leads to a decrease of excess bitcoin demand. This continues until the excess demand for bitcoin is zero, and gdp growth is back to steady state.

Now, the reaction in the fiat currency economy.

1. Excess godds demands lead to an increase in money demand and increase in price index
2. Increase in money demand leads to rising nominal interest rates. Increase in price index leads to central bank increasing money supply undtil the excess money demand is zero.
3. Relative to the starting point, the real interest rate is higher than before, leading to a decrease in gdp growth rate.

In contrast to the bitcoin case, there is no necessety for the gdp growth rate to return to the old steady state, which depends on constant growth of money supply.