Money Supply Model

Money supply is an integral part of monetary policy as it reflects the types and sizes of liquidity in an economy. Although the U.S. Federal Reserve no longer sets targets for money supply given its dissociation from the economy and inflation starting in the 1990s, useful lessons prior to this period can still be learnt. In the Kelp ecosystem, the money supply framework will be built around the business cycle, whereby, the money supply adjustment mechanism mirrors that of the U.S during the historical expansion and peak phases of its business cycle. The traditional Money Supply Model is:

$$M = C + D \tag{20}$$ $$R = RR + ER \tag{21}$$ $$RR = rd + R \tag{22}$$ $$rd = \frac{R}{D} \tag{23}$$ $$ER = (1 - rd)R \tag{24}$$

Where:
$M$ = Money Supply
$C$ = Currency (coins & bills)
$D$ = Demand Deposit (checking account)
$R$ = Reserves (deposits)
$RR$ = Required Reserves: banks required by law to hold a percentage of all deposits with the Central Bank (CB) to be able to return the deposits
$rd$ = Reserves/Deposit ratio: a percentage determined by the Central Bank
$ER$ = Excess Reserves: reserves used by the banks for lending and investment purposes

Banks create money, a multiplier effect, through lending & investment of ER. Monetary Base (B) is money held by the public in currency and by banks as reserves R

$$B = C + R \tag{25}$$

The currency-deposit ratio (cd) is the amount of currency held by the people as a fraction of the demand deposit.

$$cd = \frac{C}{D} \tag{26}$$

Dividing M by B, we have,

$$\frac{M}{B} = \frac{(C + D)}{(C + R)} \tag{26}$$

Dividing the numerator by D, we have:

$$\frac{M}{B} = \frac{(\frac{C}{D} + 1)}{(\frac{C}{D} + \frac{R}{D})} \tag{27}$$ $$\frac{M}{B} = \frac{(\frac{C}{D} + 1)}{(cd + rd)} \tag{28}$$ $$M = [\frac{(\frac{C}{D} + 1)}{(cd + rd)}]B \tag{29}$$ $$M = m * B \tag{30}$$

Thus, Money multiplier

$$m = \frac{(cd + 1)}{(cd + rd)} \tag{31}$$

For any $1 increase in monetary base B, M increases by $m. Money supply is proportional to the monetary base. An increase in B causes M to increase by m-fold. The lower the reserves-deposit ratio, the more money banks make, and the higher the money multiplier. The lower the currency-deposit ratio, the fewer the amount of the monetary base held by the public as currency, the lower the money multiplier.

The mechanism will mirror the proportion of the currency in circulation and deposits relative to the size of the economy. Our assumption is that these are the optimal proportions, particularly during the expansion and peak phases of the business cycle. The Kelp money supply model is specified as:

$$M = X + K \tag{32}$$

Where:
$M$ = Kelp Supply
$X$ = Adjustment Mechanism
$K$ = $KELP in Circulation

Since the $KELP already in circulation is outside the remit of the Kelp Protocol to alter, 𝑋 becomes the adjustment mechanism. The optimal value for 𝑋, and invariably 𝑀 at the inception is determined as:

$$X = \frac{1}{n} \sum^n_{i=1} Qi \tag{33}$$

Where:
$Q$ = Proportion of deposits relative to Nominal GDP during the expansion and peak phases of the U.S. business cycle. As the ecosystem expands and actual Kelp ecosystem data is generated, the aforementioned models that capture the relationship and sensitivities between these macroeconomic variables will be applied.