怎樣決定一個幣值是用紙幣還是硬幣來發行呢？

The use of coins has descended over the past century through the invention of coinage. It is kept in the market for cultural and economical reasons. Coins used to actual gold-excangeable-value of its representing face value. Higher valued coins could be worth up to fractions of an once of pure gold.
As the economy grew and wealth began to accumulate. Coins got less convenient as huge amounts of payment would require many loads of heavy weighted coins. Thus paper based currency was invented by trade companies and financial institutes.
Coins also possed many other problems... such as clipping. The government or some organizations would illegally melt coins and add in other metals to make more coins out of the original, or they would cut off metal from existing coins to make more coins. (That is why coins today have cuts on the rim so no one can clip off metals from the side)

Coin and paper money are both crucial to the economy. The ratio is depenadant on the price of precious metals, living index of the country, spending patterns of the country and the final determinant factor is on the Government's Monetary policy. As different distribution patterns can affect consumer spending (/patterns) easily to achieve different government goals.

Hope this will help you out a bit~