Understanding Social Discount Rate in Economics

1. Social Discount Rate • See Boardman et al. Chapter 10 • Consumers (Savers): Marginal Rate of Time Preference (MRTP) • Producers (Investors): Marginal Rate of Return on Investment (MRRI) • Under appropriate assumptions: • Social Discount Rate (SDR) = MRTP = MRRI • Equals “market” interest rate

2. Consumers-Savers “budget line” – shows combinations of current consumption and savings. Slope = -i X1 x1 At x0: MRTP = i x0 I0 I1 X0

3. Producers-Investors X1 “PPF”: future production possibilities with current savings At x1: MRRI = i x1 “income line”: shows all combinations of current and future expenditures equal to a specific level of current income x0 X0

4. Slope =equilibrium interest rate X1 I0 Demand for investment > supply of savings S0 I1=S1 X0

5. Social Discount Rate But in reality not a single interest rate for all savers and investors • Many factors affect interest rates. • What factors? • Transactions costs • Differences in risks • Different time horizons • Expectations of future - inflation • Policies – controls on interest rates • Direct interventions in credit markets – Federal Reserve Bank (0pen market operations)

6. Transactions Costs

7. Transactions Costs of Financial Intermediation Si r Ss ri’ ri Costs of intermediation rs’ rs New project increases investment demand Di’ Di K ∆I ∆S ∆K

8. Blended Rate • Capital for project is combination of additional savings and reduced investment in private sector (crowding out) • ∆K = ∆S - ∆I • SDR = (∆S/∆K)*rs + (∆I/∆K)*ri • Harberger: Empirical studies show savings rates insensitive to interest rates (S/ r  0), so ∆S  0 • SDR  ri = MRRI

9. Ss = SI r ri’ ri rs Di Ds K ∆I = ∆K ∆S = 0

10. “Small” Investments • In the previous examples, we have examined the effects of “large” investments • The amount of capital needed for the new investment is enough to affect market interest rates • But many investments are not so big, will not affect interest rates • For these scale of investments, the supply of savings may be considered to be perfectly elastic

11. r ri Si rs Ss Di ∆S = ∆K K ∆I = 0

12. “Small” Investments • ∆K = ∆S - ∆I • SDR = (∆S/∆K)*rs + (∆I/∆K)*ri • But now ∆I = 0 • SDR = rs • So, for “Small” investments, the social opportunity cost of capital should be consumers marginal rate of time preference (MRTP), which is < MRRI