Demand and Supply for Money : A Detailed Discussion - The Speculative Motive

• People can hold their wealth in the form of landed property, bullion, bonds, money, etc.
• For simplicity, all non-money assets are treated as bonds.
• Bonds are tradable papers issued by governments or firms that promise a future stream of monetary returns.

A firm raises ₹100 by issuing a bond with:

• Face Value: ₹100
• Maturity Period: 2 years
• Coupon Rate: 10%

Returns:

• End of Year 1: ₹10
• End of Year 2: ₹110 (₹10 interest + ₹100 principal)

Present Value (PV)

At 5% market interest rate,

\[X=\frac{10}{1+\frac{5}{100}}\]

\[Y=\frac{110}{\left(1+\frac{5}{100}\right)^2}\]

\[\boxed{PV=X+Y}\]

Present Value (PV) ≈ ₹109.29

The bond price equals its Present Value (PV) in equilibrium.

• Price < PV: Bond is attractive → demand rises → price increases.
• Price > PV: Bond is unattractive → supply rises → price falls.

• When the market rate of interest increases, the Present Value (PV) of the bond falls.
• Therefore, bond price and market rate of interest are inversely related.

Example:

• Interest rate 5% → PV ≈ ₹109.29
• Interest rate 6% → PV ≈ ₹107.33

People form expectations about future interest rates.

• Expected rise in interest rate → Expected fall in bond price → Capital loss → Sell bonds and hold money.
• Expected fall in interest rate → Expected rise in bond price (capital gain) → Buy bonds.

Thus, speculative demand for money arises from expectations about future interest rates and bond prices.

• High interest rate → People expect interest rates to fall → Buy bonds → Speculative demand for money is low.
• Low interest rate → People expect interest rates to rise → Sell bonds and hold money → Speculative demand for money is high.

Hence, speculative demand for money is inversely related to the market rate of interest.

\[M_d^S=\frac{r_\max-r}{r-r_\min}\]

where
\[M_d^S\] = speculative demand for money,
r = current market rate of interest,
r_max⁡ = upper limit of r,
r_min⁡ = lower limit of r.
As r falls towards r_min⁡, \[M_d^S\]→∞ (liquidity trap).

An increase in money supply enables people to buy more bonds.

Money supply ↑ → Bond demand ↑ → Bond price ↑ → Interest rate ↓

Thus, interest rate is the opportunity cost of holding money.

Liquidity Trap

Occurs when interest rate reaches rminr_{min}rmin​.

• Everyone expects interest rate to rise.
• Bond prices are expected to fall.
• People hold only money.
• Additional money is held as cash instead of buying bonds.
• Interest rate cannot fall further.
• Speculative demand becomes infinitely elastic (∞).

Speculative Demand Curve

• Horizontal Axis: Speculative Demand for Money
• Vertical Axis: Market Rate of Interest
• At r = rₘₐₓ, speculative demand for money is zero.
• At r = rₘᵢₙ, the economy is in a Liquidity Trap, and speculative demand becomes infinite.

Total demand for money consists of:

• Transaction Demand
• Speculative Demand
• Transaction demand is directly related to Real GDP (Y) and Price Level (P).
• Speculative demand is inversely related to the Market Rate of Interest (r).

\[\boxed{M_d=M_d^T+M_d^S}\]

or

\[\boxed{M_d=kPY+\frac{r_{max}-r}{r-r_{min}}}\]

\[M_d^T=kPY\]

where k>0, PP = price level, Y = real GDP.

\[M_d=M_d^T+M_d^S\quad\Rightarrow\quad M_d=kPY+\frac{r_\max-r}{r-r_\min}\]

• Bonds are tradable securities promising future monetary returns.
• Bond price = Present Value (PV) in equilibrium.
• Bond price and interest rate are inversely related.
• Rising interest rates cause capital loss on bonds.
• Speculative demand for money depends on expectations and is inversely related to interest rates.
• A liquidity trap occurs at rminr_{min}rmin​, where speculative demand becomes infinite.
• Total money demand = Transaction Demand + Speculative Demand.