Inflation and real money balances.
As we know money market equilibrium is represented by LM relation,
m / p = Y L (i) , from this it follows that with higher real income people will hold higher money balances, with higher nominal interest rate people will hold lower money balances.
From fisher effect we know that, i = r + π ^ e
Therefore, we get m / p = Y L ( r + π ^ e )
From this it follows real money balance depends on real income , real interest rate and expected inflation. All these variables will change over time . But during inflation , expected inflation is likely to move much more than other variables. So, it is not a bad approximation to assume that real income and real interest rate remains constant.
Therefore, m / p = Ӯ L ( ṝ + π ^ e )
As expected inflation increases it becomes more and more costly to hold money. So, people try to reduce their money holding and there are many ways to reduce money holdings, they may engage in barter transactions. In addition, as real value of money decreases, they will prefer to hold more foreign currency and this process is called dollarization.
Deficit , seigniorage and inflation
The relation between seigniorage, nominal money growth and real money balance is expressed by the following equation-
Seigniorage = ( dm / m ) ( m / p )
On the other hand relation between real money balance and expected money balance is expressed by the following equation-
m / p = Y L ( r + π ^ e )
COMBING THESE TWO WE GET
Seigniorage = ( dm / m ) [Y L ( r + π ^ e ) ]
This equation show that the need to finance large budget deficit through seigniorage can lead not only to high inflation but also during hyperinflation, it leads to increasing inflation.