# Classical Theory of Money

## Summary

Although markets can operate without money, money is a beneficial and efficient social institution. Although there are short-run effects to the real economy in the long-run money is neutral.

## Assumptions

### Walrasian System

1. All trade takes place on specific market days where transactions are settled at the end of the trading period.
2. Traders enter with goods either endowed or produced in the previous period. This is market supply.
3. An auctioneer coordinates the market place, groping towards a set of relative prices that ensure all goods clear
4. Prices are such that D=S in all goods and there is market equilibrium following which the market closes.

All goods are perishable except money which is a safe non-interest-bearing asset.

### Quantity Theory of Money

• US version = V is assumed to be constant where causality ran from money to prices P=f(M,V,1/T). And the Chicago (Fisher) School as a flow approach.

• UK version where M=kPY, with causality from prices to money. Cambridge (Marshall) School as a stock approach.
• M_s is assumed to be exogenous.

### Thorton Model

• Includes a loans market with banks and an interest rate which is a real variable determined by real forces of saving and investment

• There is a natural rate of return that is the interest rate which the loans market readjusts to.

## Model/Theory

• Walras's Law proves that it is possible to find a set of relative prices that equilibriates all market simultaneously, and the market will not clear until the auctioneer does so.

### Monetary economy

• By introducing an nth good - money which allows purchasing power to be held from one market day to the next by holding money, and thus allows individuals to defer purchase or if there is a loans market make purchases in advance.

• If the monetary side of the economy is not in equilibrium, then by Walras' Law although there has to be general equilibrium there does not need to be equilibrium in the real economy. Σ(1-->n)p_i*D_i=Σ(1-->n)p_i*S_i
• However, such conditions would be temporary as the value of the money demanded would be sufficient to cover the purchases of goods and the supply of money would be enough to cover the value of the demand for goods. p_n*D_n=Σ(1-->n-1)p_i*S_i and p_n*S_n=Σ(1-->n-1)p_i*D_i
• Walras' Law says that when n-2 equations are in equilibrium the n-1th will also be in equilibrium.

Quantity Theory of Money

• ### MV=PT where M=money supply, V= velocity of money, P= general price level, T = volume of transactions in the economy.

• Transmission mechanism
• Direct effect - M_d=kPY and M_s is vertical and everything is proportional
• Indirect effect (using Thorton model) - Increase in M_s --> increase in deposits --> increase in supply of loans --> fall in price of loans (interest rate) below the natural rate --> increase in borrowing and higher demand for loans until back to natural rate & increase in demand for goods --> raising prices (inflation)

## Predictions

### Monetary economy

• Homogeneity postulate: As all prices are relative, where p_n is the denominator of all the relative price terms, money is neutral only influencing prices in a one for one fashion.

## Evidence

• Dominant monetary theory from 1790-1936

## Evaluation

• Complications with the Quantity Theory of Money arise from 1. differences in opinion about how to define M, V, P and T. 2. differences in opinion about causality of the different varialbes.
• Even though neither Marshall or Fisher thought of velocity as constant (the former as a f(confidence, credit market conditions)
• Two schools of thought around the indirect mechanism:
• Currency School - if the bank interest rate is artificially low --> inflation. Rather than the BoE the foreign exchange markets should determine the value of the currency.
• Banking School - argued that low interest rate kept the currency and credit be stable.
• Thorton's loan market can be modelled as the demand (I - investors) and supply  (S - savers) of bonds. where changes in the Money supply are matched by changes in the demand for bonds such that the real interest rate does not change in the long-run.

### Patinkin's Critiques

• Classical model flawed because the Walrasian market and the quantity theory are incompatible. He argued that in a Walrasian system the monetary and real sectors cannot be kept apart as money-holding and trading of good decisions are made simultaneously. Thus need to correct the classical system to include real money balances.
• Patinkin argued that the two excess demand equations is
1. Indeterminate in the absolute price level - excess demand functions depend only upon these relative prices and not on the absolute price level in the barter model.
2. Overidentified in the number of equations and unknowns and is inconsistent in its treatment of the excess demand for money.
• If you include the monetary economy Patinkin's invalidity hypothesis, excess demand for money does not depend upon on relative prices at all (just the absolute price level), excess demand for money from the real side is a function of just relative prices (and not the absolute price level)

Real Balance effect

• Real balance effects is that M/pn gives utility and is included as part of a utility function.
• This makes the excess demand equations no longer homogenous and therefore consistent with the monetary equations.
• The work of Archibald and Lipsey shows that an increase in M_s and the wealth effect is offset by an increase in Pn restoring price stability and neutrality to the model and returning to original utility.
• Evaluation - real money balances effect of tying down the price level could also be done by an interest rate.

Interest bearing assets

• Liviatin however showed that a permanent equilibrium is not a foregone conclusion by introducing interest-bearing securities (B/pn with a rate of return r every period) which means the endowment is no longer fixed and thus the long-term equilibrium points are no longer vertical (see p.86).
• Potentially S-R equiilbrium curve could be steeper than the L-R equilibrium curve and thus the system is unstable where deviations from equilibrium do not return to eq. Potentially there may not even be an initial equilibrium at all.
• However, we only observe the first case so it seems these are nothing more than theoretical possibilities.