We consider first the equilibrium in the money market. The portfolio choice of individuals is to decide how much to invest in various financial assets. Suppose, for simplicity, that an investor has to decide how much to invest of her assets into money (cash balances that have a zero interest rate return) and how much to invest into interest bearing assets (short term Treasury bills).
Money (cash) balances have the disadvantage of not offering any nominal return (zero interest rate); they have the advantage that you can use them to do transactions (buy/sell goods). Short term bonds have the advantage that they earn interest; however, they have the disadvantage that they cannot be used to make transactions (you need money to buy goods and services). So, an investor will decide to allocate its portfolio between money and bonds considering the benefits and costs of both instruments.
So the demand for money will depend positively on the amount of transactions made (GDP, Y) and negatively on the opportunity cost of holding money: this is the difference between the rates of return on currency and other assets (bonds):
Asset Real Return Nominal Return
Cash -p 0
T-bill r i = r + p
Difference i = r + p i = r + p
where p is the inflation rate, i is the nominal interest rate and r is the real interest rate.
So the nominal demand for money is:
+ - +
MD = P L( i , Y)
MD is the number of dollars demanded
P is the price of goods
L is the function relating how many $ are demanded to Y and i.
The equation suggests that there are three main determinants of the nominal demand for money:
1. Interest rates. An increase in the interest rate will lead to a reduction in the demand for money because higher interest rates will lead investors to put less of their portfolio in money (that has a zero interest rate return) and more of their portfolio in interest rate bearing assets (Treasury bills).
2. Real income. An increase in the income of the investor will lead to an increase in the demand for money. In fact, if income is higher consumer will need to hold more cash balances to make transactions (buy goods and services).
2. The price level. An increase in the price level P will lead to a proportional increase in the nominal demand for money: in fact, if prices of all goods double, we need twice as much money to make the same amount of real transactions. Since the nominal money demand is proportional to the price level, we can write the real demand for money as the ratio between MD and the price level P. Then, the real demand for money depends only on the level of transactions Y and the opportunity cost of money (the nominal interest rate):
MD/P = L(Y, i*)
