Savings, Investment, and the Financial System

1. Marginal utility is decreasing within a period.
2. Future utility is discounted at rate $0 \lt \delta \lt 1$.
3. Utility over consumption path: $U(c_{0},c_{1},\ldots,c_{T})=u(c_{0})+\delta\, u(c_{1})+\ldots+\delta^{T-1} u(c_{T})$ where $u' \gt 0$ and $u'' \lt 0$.
4. Assumption (1) implies that the consumer prefers to smooth out consumption.
5. Assumption (2) implies that the consumer prefers present consumption to future consumption.

Consumption smoothing drives savings and borrowing during the life cycle:

• Start of career period $\Rightarrow$ borrow,
• High earnings period $\Rightarrow$ save,
• Retirement period $\Rightarrow$ dissave.

• The higher the interest rate $1+r$, the higher the incentives to save (lend money).
• The lower the interest rate $1+r$, the higher the incentives to borrow.
• The equilibrium interest rate is determined so that savings (supply) equals borrowing (demand).

• Banks $\Rightarrow$ transform short-term loans (from depositors) into long-term loans.
• Liquidity = the degree to which a financial asset can be converted into cash.
• Liquidity demand = demand for cash or liquid assets.
• Since depositors' liquidity demands are likely to be uncorrelated, the risk that many depositors will need their money at the same time is low, so diversification (of risk) allows banks to do this.

Firms with high reputation may borrow money directly (from the public) by issuing bonds:

• Face value of the bond = value of the bond to be paid at its expiration date.
• Coupons = regular payments before the bond matures.

Rate of return of the bond between expire date $T$ and date $t \lt T$:

where, $p_T\Rightarrow$ face value and $p_t\Rightarrow$ price of the bond in period $t$.

The rate of return and the price of the bond always move in opposite directions.

How do we evaluate how much a bond is worth? How do we estimate the value of a company's stock?

1. Estimate all future cash flows generated by the bond, company, or asset.
2. Convert those future cash flows into today's dollars using the present value formula.