# Money

## Money commodities

### Money is liquid and information efficient

#### Liquidity of money

Liquidity (don’t always want a goat)

Alice fishes and Bob hunts, and they trade meat and fish with each other. This much fish for that much meat. This all works perfectly well until Carol, Dan and Eve come along, who wants to trade berries, wood and furs. Now agreeing how much of this for that becomes more complicated, for every good there’s a ratio relative to every other good.

So they agree a new system, they collect all of the shells on the island and use these to trade with each other. Now they only have to remember a price for each good.

We want divisibility of money.

#### Information requirements of money

Information requirements $$(n-1)+(n-2)$$ etc v $$(n-1)$$

$$\sum_{i=1}^n n-i$$

$$n^2-\sum_{i=1}^n i$$

$$n^2-\dfrac{n(n+1)}{2}$$

$$\dfrac{n(n-1)}{2}$$

Compared to $$n-1$$ when money is used.

#### Stability

Don’t want to be used for other purposes, demand could fluctuate more, more wasteful.

## The price level

### The equation of exchange

As there’s only so much stuff out there, an increase in the amount of money moving around with cause inflation.

This can be shown as:

$$MV=PQ$$

The amount of money (M) multiplied by the velocity at which money moves (V) must be equal to the average price (P) multiplied by the quantity of stuff (Q). This isn’t a theory, it’s an accounting identity.

### Nominal and real prices

If previously one fish trades for two chunks of meat, we would expect the shell price for fish to be twice as high as the shell price for meat. Relative prices between all goods could be maintained for any price for meat. If all prices doubled, one fish would still get you two chunks of meat.

Nominal prices are those that are actually seen in markets, real prices refer to these prices adjusted for the price level. For example all prices doubling would double all nominal prices but affect no real prices. Doubling only the nominal price of fish would increase the real price of fish, and decrease the real price of other goods.

### The quantity theory of money

The quantity theory of money states that velocity of money is stable and so increases in the money supply cause proportionate increases in prices.

While the supply of money does impact inflation, the velocity of money has a habit of moving around a fair bit. In addition, what we might think of as an increase in the money supply may not in fact be one. For example quantitative easing undertaken in the aftermath of the financial crisis massively pumped massive amounts of base money into the financial system, but at the same time banks were deleveraging and holding more reserves, shrinking the money multiplier. The net effect was modest for the overall supply of money.

## Exchange rates

### Exchange rates

#### Interest rate parity

What determines an exchange rate? Consider someone in the US choosing between investing at home or in the UK. Returns in the US are 4% over the next year and otherwise identical investments in the UK offer 3%.

Is the US investment better? Not necessarily - as the UK bond is valued in pounds, the investor will also consider changes to the exchange rate over the period. If the value of the pound is expected to increase sufficiently over the period then the 3% bond would be a better investment.

If the investor can freely choose between the two –there are no capital controls - expected movements in the exchange rate equal current differences in returns. If the value of pounds was above this level then investors would sell pounds and buy US investments until this relationship was restored. This is known as interest rate parity.

$$Return_USD = Return_GBP /dfrac{Exchange rate_{next year}}{Exchange rate_today}$$

Next, let’s break down what the returns include. If inflation is 1%, then a 3% nominal return only gets you (roughly) 2%.

$$Return \approx inflation + real$$

OK, so now we have a link between changes to the exchange rate and differences in inflation and real (inflation adjusted return).