Money (Medium of Exchange)

See also Monetary Policy

Motivation. We will only discuss money as a medium of exchange in here. For other roles of money, see Money (Disambiguation)

• $P$: Price level
• $\pi :=\frac{P_{t+1}-P_t}{P_t}$: inflation rate
• $R=r+{\pi }^e$: real interest rate (Fisher Identity)

Transaction (Medium of Exchange) §

Motivation. To solve the problem of the double coincidence of wants, we need a medium of exchange. This can be solved by credit or money.

1. Credit is when people keep track of how much one ows another, and by doing so without any medium of exchange, can transact.
2. Money is when people exchange actual paper bills during transaction. We consider credit first, because it is simpler and more natural.

Credit Market §

• $q$ is the cost of credit, e.g. transaction costs, Information Asymmetry, technology costs,…
• $X$: the amount of credit in circulation

1. Credit demand:
   • if $R<q$, credit is expensive, use cash (pay now)
   • if $R>q$, credit is cheap, use credit (pay later, unused cash earns interest $R$, but cost increases by $q$)
   • ! ⇒ In reality, most people use credit and money both, which means $R\approx q$
2. Credit supply:
   • $\propto$ competitiveness, information friction, fintech
   • $\propto 1/$aggregate risk (=Market Risk), regulation

Money Market §

Motivation. It’s hard to find credit-worthy counterparties, e.g. you don’t know if a stranger will pay you back, or if a Escrow will still exist in the future. A strong institution that can issue a medium of transaction you can trust is essential for larger transactions. Thus we have money.

$$\begin{array}{rl}\text{Money Quantity }v\cdot M& :=P\cdot (Y-\stackrel{\text{ Q credit in circ. }}{\overbrace{X^{\ast }(R)}})\\ \text{Inflation Identity }\pi & :=\hat{P}=\hat{v}+\hat{M}-\widehat{(Y-X^{\ast })}\\ \text{Money Demand }{M}^d& :=P\cdot \underset{\text{ liquidity func. }}{\underbrace{L(Y,R)}}\\ \text{Money Supply }{M}^s& \equiv M^{\ast }\end{array}$$

• $v$ is the velocity, i.e. “how many times $1 bill gets used per year”
• $X^{\ast }$ is the amount of credit in circulation
• $L(\cdot )$ is the liquidity function, i.e. how easy it is to convert into cash
• Money supply is just the fixed amount the central bank prints.
• Money demand is the amount of money people want to hold:
  • $\propto$ $Y$, since more goods means more transactions occurring (rotates clockwise)
  • $\propto 1/R$, as $R$ risers just use credit with cost $q$ and get interest on cash → credit demand increases → cash demand decreases (rotates counter-clockwise)

Neutrality Vs Non-Neutrality of Money §

def. Monetary Neutrality is a hypothesis of classical macroeconomists that suggest changing the money supply has no effect on the Intertemporal Consumption-Leisure Optimization (Full General Equilibrium) model. Consider the case where the central bank increases money supply:

As the money supply is increased, prices are simply increased to match. Intution. This is equivalent to central banks saying “we will put another zero at the end of every dollar bill starting next month.” All prices and businesses will be ready to also put another zero at the end of their prices and contracts, and nothing will really change. This assumption is challenged by John Meynard Keynes who suggested firms are not always free to change prices at will. This is modeled in the New Keynesian Business Cycles Model.