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Taxation and Risk-TakingVenture Capital, Risky Investments
o Right Anser
No consensus on whether or not taxing capital gains and losses,
or business gains/losses
o Increases the extent to which business people and investors
are prepared to take risks/decrease it
Conclusions we get depends on the assumptions we make
concerning
oThe structure of the tax system
oThe extent to which investors are averse to risk
iminishing "arginal #tility o$ %ealth & Again
!odels in which "rrow#s coe$cient of relative risk aversion play
a large role , but these are extremelyinvolved and we#ll leave them
alone
%sing a decreasing marginal utility of wealth function &von
Neumann'!orgenstern(
oCan illustrate the ambiguity concerning whether taxes
increase/decrease risk'taking
"aking Risky Investments
)st* recogni+e that no one makes a risky investment expecting to
lose money
opossibility is there, but each investor has some su'(e)tiveidea
of the probability of gaining, and will o
invest if the expected gain is positive
suppose individual has diminishing utility of wealth original
wealth -.
oconsiders risky investment
can gain0 or lose1
undertakes it if she believes that the prob f gain is 2 the prob
of loss
xpe)ted "onetary Value o$ investment
diagramshow expected gain, expected utility of gain
de3ning 4. as prob of gain expected dollar value of
investment
*+gain ./% 0 12 0 /3-.2/%-12
xpe)ted #tility
expected utility of the gamblederived same way
increase of dollar value expected value of utilities
if investment makes money, she has the utility of -50
if investment fails, ends up with -'0
expected utility*
*+# .+#/%012 0 /3-.2+#/%-12
avora'le Investment
illustrate utility of di6erent outcomes 7oining 5ve and 8ve
outcomes
expected utility of gamble depends on the sub7ective prob of
gain
if investor believes that gamble has 99: prob of paying o6
expected utility will be very near the upp
amount
as prob of gains falls expected value of gains moves down and to
left along the line
avora'le 5am'le ithout Tax
supposed expected valueof investment ; 5ve sub7ective prob of
gain is high
investor expects post'investment utility of wealth to be higher
than utility of wealth with no investmen
no taxes on incomeinvestment will be undertaken
kinds o$ Tax 7ystems
assume all are proportional
ax I8 Tax on other in)ome only 9 no tax on spe)ulative
gain:loss
if individ takes no risk obtains utility of after'tax employment
income
takes risk income if investment pays o6 ; &wage income after
tax( 5 gain on investment
investment doesn#t succeed income ; &wage income after tax(
8 the loss
expected utilitywith tax on employment income but no tax on
either investment gains/losses will lie
somewhere along purple straight line &exactly where depends
on her sub7ective expectation that theinvestment pays o6(
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ogains trigger tax at higher marginal rates
amount of loss o6set in event of a loss will be less than the
amount of the tax imposed in the event of
gainxample*
investor stands to gain enough to put her into a marginal tax
bracket of H:
eFuiv to applying uniform >: tax with full loss o6set 5
addition )>: tax on gains with no o6set
proportional tax &with o6set( acts to increase risk takingo
extra tax on gains will have the opposite e6ect
she#ll take fewer risks because of the progressivity of the tax
system that she would have taken had the system been
proportiona
on)lusion
extent to which income tax system increases/decreases risk
depends onowhether or not most investors in risky pro7ects have
other Fualifying income against which losses can b
deductedoprogressivity if income tax system
o relative risk aversion of investors &illustrated by degree
of curvature of the utility'of'wealth f&x(
