Goods Market

Loanable fund theory / Classical theory of interest rates

• $D^{LF}$ is the demand for loanable funds by Firms ($i$)
• $S^{LF}$ is the supply of loanable funds by H.H¹ ($s$)

$$\begin{array}{rlr}s& =s(r_{+})& \to \text{Savings by HH}\\ S& =I& \text{Equilibrated}\\ i& =i(r_{-})& \to \text{Investments by Firms}\end{array}$$

The goods market is equilibrated by interest rates ($r^{\circ }$), equilibrated where $D^{LF}=S^{LF}$

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Equilibrium at markets

• The components of goods market are
  • consumption $C$
  • investment $I$
  • government expenditure $G$
• Consumption and investment are private expenditure whereas $G$ is part of public expenditure
• Expenditure is of two kinds
  1. Autonomous expenditure: which changes on its own.
  2. Induced expenditure which changes due to some macro variable.
• Talking about Goods market. The equilibrium rate of interest is the rate at which the amount of funds that the individuals are desired to lend are just equal to the amount of funds that the others (firms) desired to borrow.
• The bonds here are perpetual bonds where you get a perpetual stream of interest payments with no return of principal amount.²
• Savings depend on rate of interest positively where as investments depend on the rate of interest negatively
  • $s=s(r_{+})$
  • $i=i(r_{-})$
  • Thus savings are upward sloping function and investment is downward sloping function

Effectiveness of Fiscal Policy

$G$ rises the $Y$ and AD remains constant. Therefore, in order to maintain the level, it is adjusted by $C$ & $I$.

Example

$$\begin{array}{rlrlr}\overline{Y}& =& (C& +I)\downarrow & +G\uparrow \\ 1000& =& (700& +100)\downarrow & +200\uparrow \\ 1000& =& (650& +50)\downarrow & +300\uparrow \end{array}$$

It is the rate of interest which guarantees the exogenous changes in particular component of demand do not affect the aggregate demand as a whole.

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Reasoning

$$G\uparrow ⟹D^{LF}\uparrow ⟹(r_0\to r_1)\uparrow ⟹\{\begin{array}{l}(s_0\to s_1)\uparrow \\ (i_0\to i_1)\downarrow \end{array}$$

Increase in Government expenditure, fiscal policy causes the demand for loanable funds by the Firms to increase due to which rate of interests have to increase (firms are willing to borrow, but not enough lenders, HH) due to which the savings increase (as people want to lend more)

Role of Fiscal Policy

$$Y=AD=\underset{\text{Private Exp.}}{\underbrace{C+I}}+\underset{\text{Public Exp.}}{\underbrace{G}}$$

• Increase in Government Expenditure would shift the demand for loaning out fund to the right. $i_0\to i_0+\Delta G$ .
• This would lead to the rise in rate of interest from $r_0\to r_1$ which in turn leads to increase in the savings³ measured by distance A in the diagram, and fall in the investment⁴ measured by distance $B$ in the diagram.
• Thus $\Delta g=A+B$ i.e., increase in government spending balances decreasing the investment and consumption. In other words, rise in public expenditure leads to fall in private expenditure⁵.
• Rise in government expenditure, if financed by selling bonds to the public pushes the rate of interest enough to crowd out and equal amount of private expenditure. Thus, due to Crowding out phenomena the aggregate demand remains same, and therefore fiscal policy becomes ineffective.

Footnotes

1. Supply of loanable funds is nothing but the savings of the individuals (along with the willingness to spend) ↩

2. Coupon Payments = Interest rates, and the price of the bond $P_B=\frac{A}{r}$ ↩

3. Fall in consumption, so that the money can be spend on lending. People leaving money in the banks etc since interest rates are good. So they can as well save some money and be relaxed. ↩

4. Since interest rates are higher, firms would like to withdraw from investments. ↩

5. private: consumption (for HH) and investments (for F) ↩