# What will be the effect on velocity of money when demand for real money increases?

Suppose that a change in government regulations allows banks to start paying interest on checking accounts. The money stock is the sum of currency and demand deposits, including checking accounts. (a) How does this change affect the demand for money? (b) What happens to the velocity of money? (c) What will happen to the LM curve? (d)If the price level is fixed, what will happen to the output and interest rate? Use the IS-LM framework to explain your answer.

This was the question given. According to my understanding: (a) interest on checking accounts means lower cost of holding money so money demand goes up. (c)Since demand for money has gone up interest rate will go up, hence LM curve shifts to the left. (d) due to the leftward shift of LM curve interest rate go up and output goes down. Are my answers correct? How do I insert velocity of money in ISLM model?

• In this model you're probably required to think of money demand as coming from a transaction motive and a speculative motive. If cash (checking deposits) earn interest rates than the opportunity cost of holding cash disappears and there would no longer be a speculative motive to hold cash. This affects the interest elasticity of demand for money. I think that should be the starting point for you answer. Commented Apr 19, 2021 at 13:59

(a) The effect of this policy change sounds theoretically ambiguous to me. It ultimately depends on the consumers' preferences.

An increase in interest payments lowers the opportunity cost of having cash, which might make some consumers better off by saving more and some might see this is a relief and hold more cash. We need an utility function in order to know how consumers would react to the policy change.

(b) Again, ambiguous. It depends on the liquid effect of the policy change on money demand. Let's first remember the Equation of Exchange:

$$MV=PQ$$

If consumers deposit more money on checking accounts, money supply goes up. Given the price level and output are fixed (we're in the short run), an increase in $M$ makes the money velocity $V$ decrease. On the other hand, if consumers deposit less on checking accounts, money supply goes down and velocity of money increases.

(c) The correct answer - at least in my understanding - is that it's ambiguous. If the money supply increases, the LM shifts to the right and if it decreases, to the left.

(d) If the LM shifts to the right and the price level is fixed, output goes up and interest rates go down, if it shifts to the left, output goes down and interest rates go up.

Velocity of money is nothing but number of times the nominal money is changing hands. Suppose the GDP (aggregate expenditure) of a country is \$1,000. The amount of money in circulation is \$500. So money should change hands two times for expenditure worth $1000 to occur which makes velocity of money = 2. $$MV=PY$$ => $$M = (1/V) PY$$ Now coming to your question, suppose the GDP increases to \$1500. If money supply and prices remain constant, then velocity of money must increase to 3 to sustain an expenditure worth \\$1500.

This is a completely classical case and output is assumed to be at the full employment level of equilibrium.

But in real economy, the things are not as simple since money itself becomes an asset whose price is the rate of interest.