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## How the interest rate is determined

Think of money as being a good. Just like any other good, it will have a price that is determined by the interaction of supply and demand. The price of money is the interest rate.

The reason the interest rate is the price of money is because it reflects the opportunity cost of holding money. You can simplify this by thinking of your total wealth being divided into two forms, money and savings. In the textbooks you might see this being simplified to saying you can split your wealth into the portion you hold as money and the portion you hold as ‘bonds’. Think of ‘money’ as being both the coins and notes you hold in your pocket and also the balance in your current account. Your current account is basically money because you can access it instantly (it is liquid) for transactions, but it doesn’t pay any interest (in reality it probably pays you a negligible rate of interest).

You can think of ‘bonds’ as being money you hold in a savings account, because your bank will be using your money to hold bonds so they are effectively holding bonds on your behalf – the bank is a financial intermediary allowing you to save by lending your money out to other people (issuers of bonds). But usually you will have to tie up your savings account for a certain amount of years, you don’t have instant access to it, so it is illiquid.

So the concept here is you split your wealth into two parts:
Money – liquid, no interest
Bonds – illiquid, you get interest

The interest rate is basically the interest rate you get on the portion of your wealth you hold as bonds. So every £1 of your wealth that you hold as money rather than saving as bonds, is missing out on the interest it would get if it was tied up in bonds. So you are making a sacrifice here which is kind of your preference for liquidity. You want to keep some of your wealth as money, because its convenient, and you need to use it for transactions, but you want to keep some of it as bonds to earn interest on it. It is a waste if you have a lot of money and let it stack up in your current account, when you are not spending it.

Now obviously if the interest rate is higher, then you are missing out on more interest by holding money, so when the interest rate is higher you are going to hold less of your wealth as money and more as bonds. When the interest rate is low, then you are not missing out on much so you are likely to hold more money because it is more convenient.

This is basically the demand for money curve which is also described as the liquidity preference curve. You draw a graph with nominal interest rate, i, on the vertical axis and $\frac{M}{P}$ which means money divided by prices, on the horizontal axis – this is known as ‘real money balances’. The reason you have prices in there is because a nominal amount of money, M, is pretty meaningless unless you have a price level to judge it against. The demand for money curve is downward sloping and the supply of money is just a vertical line, at whatever level of money and prices we have. Where the two curves intersect gives us the interest rate, it is the price of money that brings the demand and supply for money into equilibrium.

The demand for money then basically depends on 2 things….

1. What the interest rate is for the reasons described above which show why the money demand curve is downward sloping

2. How much total wealth people have. The money demand curve shows us the amount of money which people want to hold at a given level of wealth. It basically tells you at interest rate x, people want to hold y% of their wealth as money and (1-y)% as bonds. But what if wealth rises? Then at the same interest rate, they still want to hold y% of their wealth as money but now their total wealth is bigger, so that y% means they demand more money than they did before. This is basically a shift up of the whole money demand curve on the graph.

So you can play around with moving the money supply and money demand curves and see what the effect is on the equilibrium interest rate where they intersect.

The money demand curve moves up if incomes rise (people have more wealth) and down if incomes fall.

The money supply curve moves right if the nominal money stock, M is increased, (ie the central bank increases the money supply) or left if M is decreased. But this is where prices come into play as well. Because we are really talking about real money balances, (M/P) rather than just the nominal money stock, M, then price changes will have an effect as well. When P rises, then (M/P) gets smaller, so the money supply curve starts going to the left.

The central bank can control the interest rate by controlling M. If for instance it decides to keep an interest rate of say 2.5%, and then incomes start rising, that will mean the money demand curve starts shifting up and it pushes the interest rate up. So they increase M to push the money supply curve to the right, and bring the interest rate back to 2.5%. They will also have to increase M to deal with the effects of inflation. As prices, P, rise, then the money supply curve starts going to the left, so in order to keep it where they want it to be, they will have to increase M again. So the central bank, by controlling the money stock, can respond to upward or downward pressure on interest rates.