Post on 19-Dec-2015
Lecture Plan Interest rate in 1st best worldThe present value criterionEthical basis for discountingEconomic growth rateDiscount rate in 2nd best worldShadow price-approach
Interest rate in 1st best world
1)( 00 MRTP
P
PMRSslope
ii
C0
C2
Cons in P0
Cons in P1
Opportunity cost of cons - today is loss of available cons next year (MRT)
Interest rate in 1st best world
Transformation curve (PPC)
MRT = MRS
MRTP = MOCR
C0
C1
Indifference
curve
Interest in 1st best world MRT is equal to marginal opportunity costs
of capital (MOCR) plus 1
Efficiency: MRTPs for all consumers equal social rate of time preference (SRTP)
SRTP=SOCR (social opp.cst of capital)
MOCRMRTPMRTMRS 010101 11
Interest rate in a 1st best world
Relevant interest rate = called discount rate
In 1st best world economy the correct discount rate for B/C-analysis is just the market rate
The Present Value-criterion
Thus:
Discounting: calculate the equivalent of C1 in period 0 (C0) (calculated along indifference curve: i.e. consumer is indifferent)
SRTPMRSC
C 101
0
1
SRTP
CC
11
0
Ethical basis for discounting
“Veil of ignorance”-principle
choose a discount rate before knowing to
what generation you will belong to
positive discount rate implies placing more
value on 1 euro in the present generation
than 1 euro in a future generation
Economic Growth Rate
Discount rate effects investment level Investment level determines economic
growth rate What proportion of GNP should be saved? Optimal growth path (max cons): marginal
return to capital should equal the growth rate of the economy due to technical change
Discount rate in 2nd best world Economy is economy with taxes Assume:
corporate profit tax 36%marginal income tax 27%MRTP 8%
Before-tax rate should be 10,9% to end up with 8% after (8 / (1 – 0.27) = 10.9)
Corporation must earn 17% before taxes
%9.1064.017100
)36100(17
Discount rate in a 2nd best world In a 2nd best world (tax) the choice for a discount
rate is no longer obvious
Wedge between rate of return and MRTP causes
biases (underinvestment, favors short-term
projects)
Debate:
MRTP-rate: trade present cons. for future cons.
OCR-rate: public investment displaces private
investment
Discount rate in 2nd best world
But….
SRTP (or MRTP)-approach not yet takes into
account displacement of private investment
Solution: adjust for OCR-effect
NEW: shadow price approach
Shadow Price of Capital
Trick: express both benefits and costs of an
investment in consumption terms
Total capital: K(t)=K(0)esrt
sr: growth factor
s: fraction of proceeds reinvested
r: private rate of return (OCR)
i: social rage of time preference (SRTP)
Shadow Price of Capital
srtsrt
resK
eKrstC )1(
)0(
)0()1()(
Consumption: (1-s)* net capital income
Present value (general rule)
Thus:
itPV Peitsrt eerstCPV )1())((
Shadow Price of Capital
Total cons. stream
with s . r < i (necessary cond.)
Simplifies to
T
t
itsrtresCPV0
)()1()(
sri
rsVSPC
sri
rsCPV
t
)1(
)1()(
Present value of the
consumption from
€1 of private
investment
Shadow price of
private capital
Shadow Price of Capital
Shadow price (SPC):
In 1st best world: i=r and Vt=1
sri
rsVt
)1(
Rationale: convert all benefits and costs to consumption equivalents
and discount by the social rate of time preference (shadow price of private
capital SPC)
Shadow Price of Capital (optional)
: fraction of public spending that displaces
private spending
costs
benefits
c
*)1()( ttctct CCVCPV
*)1()( ttbtbt BBVBPV
Shadow Price of Capital (optional)
Fundamental present value equation for B/C-A in a 2nd best world
with FB and FC conversion terms
T
tt
tctB
T
tttt
i
CFBF
i
CBNPV
0
0
**
)1(
)1(
Shadow Price of Capital (optional)
T
tt
tctB
i
CFBFNPV
0 )1(
Case 1: (multiplier affects size but not sign)
Case 2: (all benefits go to private capital)
Case 3: (all costs from private capital)
FFF cBcb ,
0,1 cb
1,0 cb