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
Consumers-Savers
“budget line” – shows combinations of
current consumption and savings.
Slope = -i
X1
x1
x0
At x0: MRTP = i
I0
I1
X0
Producers-Investors
X1
“PPF”: future production
possibilities with current savings
x1
At x1: MRRI = i
“income line”: shows all
combinations of current and future
expenditures equal to a specific
level of current income
x0
X0
Slope =equilibrium interest rate
X1
I0
S0
Demand for investment
> supply of savings
I1=S1
X0
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)
Transactions Costs
Transactions Costs of Financial
Intermediation
r
Si
Ss
ri’
ri
Costs of
intermediation
rs’
rs
New project increases
investment demand
Di’
Di
∆I
∆S
∆K
K
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
Ss = SI
r
ri’
ri
rs
Di
Ds
∆I = ∆K
∆S = 0
K
“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
r
ri
Si
rs
Ss
Di
∆S = ∆K
∆I = 0
K
“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