Real money demand in the economy is given by L = 0.3Y - 600 i,where Y is real income and i is the nominal interest rate.In equilibrium,real money demand L equals real money supply M/P.Suppose that Y equals 2000 and the real interest rate is 5%.At what rate of inflation is seignorage maximized?

Question

Quizplus · Accepted Answer

Seignorage is the revenue that a government earns by printing money. It is equal to the difference between the nominal value of money and the cost of producing it. 
In order to maximize seignorage, the government wants to increase inflation as much as possible without causing people to reduce their real money balances. This means that the real money demand and real money supply should be equal. 
Given that Y=2000 and i=5%, real money demand can be calculated as: L = 0.3(2000) - 600(0.05) = 540. 
Real money supply is equal to M/P. Since we don't know the value of M, we can use the quantity equation: M*V = P*Y, where V is the velocity of money (assumed to be constant). Solving for P, we get: P = (M*V)/Y. 
Substituting the given values, we get: P = (M*V)/2000. 
Equating real money demand and supply, we get: M*V = 540*P = 540*(M*V)/2000. 
Solving for M, we get: M = (540/2000)*V. 
Now, seignorage is equal to the difference between the face value of money and the cost of producing it. Since the cost of producing money is negligible, seignorage is essentially equal to the nominal value of money. This means that the government wants to increase the nominal value of money (i.e., the price level) as much as possible. 
Plugging in the expression for M into the equation for P, we get: P = (M*V)/2000 = [(540/2000)*V*V]/2000 = (0.27/1000)*V^2. 
Thus, the rate of inflation is given by the percentage change in the price level: 
Inflation rate = (P - P0)/P0 * 100%, where P0 is the initial price level. 
Assuming that the initial price level is 100, we get: 
Inflation rate = (P - 100)/100 * 100% = (0.27/10)*V^2. 
To maximize seignorage, we want to maximize the inflation rate without causing people to reduce their real money balances. This means that the real money demand should be equal to the real money supply. Since real money demand depends on real income and the nominal interest rate, we want to find the inflation rate that makes real income and the nominal interest rate such that real money demand is equal to the expression we derived for M. 
Here's how: 
Real income is given by Y = P * Y/P = (M*V)/P. Substituting the expression for P and M, we get: Y = (540/2000)*V. 
Nominal interest rate is equal to the real interest rate plus the inflation rate: i = r + pi. 
Since r = 0.05, we get: pi = i - r = 0.475. 
Now, we can plug in these values for Y and pi into the expression for real money demand: 
L = 0.3Y - 600i = 0.3[(540/2000)*V] - 600(0.05+0.475) = 0.162V - 309. 
Setting L equal to (540/2000)*V (which is the expression for M), we get: 
0.162V - 309 = (540/2000)*V 
0.2952V = 309 
V = 1047. 
Therefore, the inflation rate that maximizes seignorage is: 
Inflation rate = (0.27/10)*V^2 = (0.27/10)*(1047)^2 = 47.5%.

Real Money Demand in the Economy Is Given by L