Cash-Flow Business Taxation Revisited:
Bankruptcy and Asymmetric Information
Robin Boadway, Queen’s University<boadwayr@econ.queensu.ca>
Motohiro Sato, Hitotsubashi University<satom@econ.hit-u.ac.jp>
Jean-François Tremblay, University of Ottawa<Jean-Francois.Tremblay@uottawa.ca>

February 25, 2019

Abstract
It is well-known that cash-flow business taxes with full loss-offset, and their present-value
equivalents, are neutral with respect to firms’ investment decisions when firms are riskneutral and there are no distortions. We study the effects of cash-flow business taxation
when there is bankruptcy risk, and financial intermediaries face asymmetric information
problems in financing heterogeneous firms. In these circumstances, investment decisions are
distorted, with investment being less than in the full-information case. Cash-flow taxation
applying to both real and financial cash flows corrects the distortion by inducing moreinvestment in rent-generating projects and increases social welfare.
Key Words: cash-flow tax, bankruptcy, asymmetric information
JEL: H21, H25
Acknowledgments: Earlier versions of this paper were presented at the Public Economics
Theory 2015 Conference in Luxembourg, the International Institute of Public Finance 2015
Congress in Dublin, the Oxford University Centre for Business Taxation 2015 Academic
Symposium, the Canadian Public Economics Group 2015 Conference at UBC Okanagan,
the 2nd Belgian-Japanese Public Finance Workshop at CORE in March, 2017, and theNorwegian Center of Taxation Fall Conference in October, 2017. We are grateful for many
helpful comments from conference participants. Sato acknowledges support from the Japan
Society for the Promotion of Science program of Grants-in-Aid for Scientific Research.
This research did not receive any other specific grant from funding agencies in the public,commercial, or not-for-profit sectors.

1

Introduction

A classic result in the design of business taxes due to Brown (1948) concerns the neutralityof cash-flow taxation. Investment decisions undertaken in a world of full certainty will be
unaffected by a tax imposed on firms’ cash flows, assuming there is full loss-offsetting (andthe tax rate is constant, as shown by Sandmo, 1979). In effect, a cash-flow tax will diverta share of the pure profits or rents from the firm’s owners to the government. This is ofobvious policy interest since it represents a non-distorting source of tax revenue.
In this paper, we revisit the use of cash-flow taxation as a rent-collecting device whenfirms face asymmetries of information in capital markets. We do so in a simple partial
equilibrium model of risk-averse entrepreneurs who vary in their productivity, so that returns to inframarginal entrepreneurs generate rents. We assume that banks can observe
entrepreneurs’ types so there is no adverse selection. Investment outcomes are uncertainand entrepreneurs face the possibility of bankruptcy, which banks can verify only by engaging in costly monitoring. In these circumstances, investment is inefficiently low comparedwith the full-information case.
We study the effects of cash-flow taxation on both the entry decision of potential entrepreneurs (the extensive margin) and on the decision as to how much to borrow and invest(the intensive margin). We assume the cash flow tax is levied on both real and financial cashflows, so applies to both entrepreneurs and banks. The effect of the tax on intensive-margin
decisions turns out to be especially important. Unlike in the full-information case, cash-flow
taxation is not neutral. On the contrary, it tends to encourage rent-generating investment
and improve efficiency thereby acting as a corrective device in a distorted environment.
The Brown neutrality result inspired a sizable literature on neutral business tax design,
much of which generalized his result to taxes that are equivalent to cash-flow taxes in present
value terms. Boadway and Bruce (1984) show that the cash-flow tax is a special case of amore general class of neutral business taxes that have the property that the present value of
deductions for future capital costs (interest plus depreciation) arising from any investment
just equals initial investment expenditures. A special case of this is the Capital AccountAllowance (CAA) tax in which investment expenditures are added to a capital account eachyear, and each year the capital account is depreciated at a rate specified for tax purposes.
Annual deductions for capital costs then consist of the sum of the cost of capital plus thedepreciation rate multiplied by the book value of the capital account.
More generally, neutrality can be achieved by a business tax in which the present valueof future tax bases just equals the present value of cash flows. An example of a cash-flow
equivalent tax system of this sort is the Resource Rent Tax (RRT) proposed by Garnaut and1

Clunies-Ross (1975) for the taxation of non-renewable natural resources. In their version,
firms starting out are allowed to accumulate negative cash flows in an account that rises
each year with the cost of capital. Once the account becomes positive, cash flows are taxed
as they occur. Negative cash flows are carried forward at the interest rate to achieve theequivalent of cash-flow taxation.
These basic results continue to apply if returns to investment are uncertain, provided
firms are risk-neutral. Fane (1987) shows that neutrality holds under uncertainty as long as
tax credits and liabilities are carried forward at the risk-free nominal interest rate, and tax
credits and liabilities are eventually redeemed. Bond and Devereux (1995) show that the
CAA tax remains neutral in the presence of uncertainty and the possibility of bankruptcy
provided that a risk-free interest rate applied to the value of the capital account is used forthe cost of capital deduction, that any unused negative tax credits are refunded in the eventof bankruptcy, and that the valuation of risky assets satisfy the value additivity principle.1
The use of a risk-free discount rate reflects the assumption that there is no risk to thefirm associated with postponing capital deductions into the future (i.e., no political risk).
Boadway and Keen (2015) show that the same neutrality result applies to the RRT in thepresence of uncertainty.
The above results focussed on taxes applied to real cash flows or their equivalent, what
Meade (1978) called R-base cash-flow taxation. Bond and Devereux (2003) show thatneutrality can be achieved using the more general case of cash-flow taxation proposed byMeade, referred to as (R+F)-base cash-flow taxation, in which both real and financial
cash flows are included in the base. They also study the neutrality of the Allowance for
Corporate Equity (ACE) tax, which is a version of the CAA tax that allows actual interest
deductions alongside a cost of capital deduction for equity-financed investment. (Theyassume that there are no rents earned by bond-holders.) Notably, Bond and Devereux
assume full information in the sense that banks can observe incomes of firms that claim to
be bankrupt. As well, they do not allow firms to choose the quantity of investment.
These neutrality results have inspired various well-known policy proposals, some of whichhave been implemented. A cash-flow business tax was recommended by the US Treasury(1977), Meade (1978) in the UK, and the President’s Panel (2005) in the USA. The latter two both recommended additional cash-flow taxation to apply to financial institutions.
The Australian Treasury (2010) (the Henry Report) recommended an RRT for the mining
industries in Australia. Several bodies have recommended an ACE corporate tax system,
1

The value additivity principle implies that the present value of the sum of stochastic future payoffs isequal to the sum of the present values of these payoffs, and is consistent with a no-arbitrage principle in thevaluation of assets.

2

including the Institute for Fiscal Studies (1991), the Mirrlees Review (2011) and Institutd’Economia de Barcelona (2013). ACE taxes have been deployed in a few countries, including Brazil, Italy, Croatia and Belgium. Reviews of their use may be found in Klemm(2007), de Mooij (2011), Panteghini, Parisi, and Pighetti (2012), and Princen (2012). Cashflow-type taxes with full loss-offset are used in the Norwegian offshore petroleum industry(Lund, 2014), and the RRT was applied temporarily in the Australian mining industry.
The neutrality of cash-flow taxation no longer applies when firms’ owners are risk-averse
so that part of the return to investment is compensation for risk. A cash-flow tax applies toboth rents and returns to risk-taking, and these two streams cannot be distinguished. As
Domar and Musgrave (1944) famously show, risk-averse savers faced with a proportional
tax on capital income with full loss-offset would be expected to increase the proportion of
their portfolio held as risky assets, although the results become murkier when the proceedsfrom the tax are returned to savers by the government, as discussed in Atkinson and Stiglitz(1980) and Buchholz and Konrad (2014). These results readily extend to an entrepreneurial
firm, as shown in Mintz (1981). This non-neutrality is not necessarily a bad thing if thegovernment is better able to diversify risk that private savers.
In our analysis, investment is undertaken by entrepreneurs of differing productivity. We
begin with the case where entrepreneurs are risk-neutral, and then extend the analysis toallow for risk-averse entrepreneurs. Our main results are as follows. With risk-neutral
entrepreneurs and the possibility of bankruptcy, the (R+F)-base cash-flow tax is neutral in
the absence of asymmetric information as in Bond and Devereux (1995, 2003), but distorts
investment decisions if banks must incur monitoring costs when firms declare bankruptcy.
Remarkably, the cash-flow tax increases investment while leaving bankruptcy risk and firms’
expected profits unchanged. Expected rents, government expected revenues and social
surplus all increase with the tax rate. In effect, as well as raising revenue the cash-flow tax
serves as a corrective device for the market failure arising from asymmetric information.
With risk-averse entrepreneurs, the cash-flow tax results in some risk-sharing between firms
and the government. The tax induces higher investment but is neutral with respect tobankruptcy risk and expected utility as in Domar and Musgrave (1944).
We begin by outlining the main elements of the model under risk-neutrality. We showthat under-investment occurs in the absence of taxes. We then study the effects of cash-flow
taxation on the entry and investment decisions of entrepreneurs in the basic model. Finally,
we extend the analysis to the case where entrepreneurs are risk-averse.

3

2

The Base Case with Risk-Neutral Entrepreneurs

2.1

Outline of the model

Our model is designed to capture the following key features. Firms’ investments are heterogeneous such that inframarginal investments generate pure profits or rents. The purpose ofprofit taxation is to tax these rents, and in a first-best world cash-flow profits taxation would
do so in a non-distorting way. Our model departs from the first best by assuming that firms,
who rely on the banks to finance their investments, face the possibility of bankruptcy, butthat banks cannot observe without cost the profits of firms that declare bankruptcy. Banks
can learn these profits at a cost by ex post monitoring or verification. The consequence isthat relative to the full-information setting, there are too few loans. In this context, cashflow taxation can actually encourage lending and improve social efficiency. The manner inwhich cash-flow taxation affects efficiency depends on whether the owners of firms, which
we refer to as entrepreneurs, are risk-neutral or risk-averse.
There is a population of potential entrepreneurs with an identical endowment of wealth
who can undertake an investment project. They differ in the productivity of their projects.
We simplify our analysis by assuming there is a single period so we can suppress the entrepreneurs’ consumption-savings decision and focus on production decisions. At the beginning of the period, potential entrepreneurs decide whether to enter a risky industry andinvest their wealth in a risky project. Those who do not enter invest their wealth in a riskfree asset and consume the proceeds at the end of the period. Entrepreneurs who enter therisky industry choose how much to borrow to leverage their own equity investment, which
determines their capital stock. After investment has been undertaken, risk is resolved.
Those with good outcomes earn profits for the entrepreneur. Those with bad outcomesgo bankrupt. Their production goes to their creditors, which are risk-neutral competitivebanks.
There are thus two decisions made by potential entrepreneurs. First, they decide whether
to enter, which is an extensive-margin decision; and second, they decide how much toborrow to expand their capital, which is an intensive-margin decision. For simplicity, wesuppress their labor income: all income comes from profits they earn if they enter the risky
sector, or from their initial wealth if they do not. Adding labor income (as in Kanniainen
and Panteghini (2012)) would make no substantial difference for our result on businesstaxation. Our purpose is to study how cash-flow corporate taxation affects the extensiveand intensive-margin decisions of firms, and as a result the efficiency of firms’ behavior.
We assume that banks know the productivity of entrepreneurs, so can offer type-specificinterest rates. The interest rate offered to a given type of entrepreneur depends on the4borrowing the entrepreneur chooses. More borrowing increases the risk of bankruptcy,
which in turn affects the expected profit of the lending bank. Since banks are competitive,
their expected profits from loans to each type of entrepreneur will be zero in equilibrium,
and this zero-profit condition determines the interest rate. Entrepreneurs know how theirborrowing affects their interest rate, and that influences how much they borrow.
The details of the model with risk-neutral entrepreneurs are as follows. Later we consider
the consequences of entrepreneurs being risk-averse and unable to insure against the risk of
their uncertain incomes.

2.2

Details of the model with risk-neutral entrepreneurs

A continuum of potential entrepreneurs are all endowed with initial wealth E. For simplicity, we assume that the production function is linear in capital K. The average productof capital, denoted R, is constant, but differs across entrepreneurs, and is distributed over[0, Rmax ] by the distribution function H(R). The value of output is subject to idiosyncratic risk, and the stochastic value of a type−R entrepreneur’s output is ε̃RK, where ε̃ isdistributed uniformly over [0, εmax ], with density g = 1/εmax . The expected value of ε is:2
ε ≡ E[ε̃] =

εmax
1
=
2
2g

(1)

We assume that the distribution of ε̃ is the same for all entrepreneurs, so they differ only by
their productivity R. Capital is financed by the entrepreneur’s own equity and debt, anddepreciates at the proportional rate δ per period. Entrepreneurs who do not enter invest all
their wealth in a risk-free asset with rate of return ρ, so consume (1+ρ)E. Since all potential
entrepreneurs have the same alternative income, those with the highest productivity asb denote the productivity of theentrepreneurs will enter the entrepreneurial sector. Let R
marginal entrepreneur.
Entrepreneurs who enter invest all their wealth in the risky firm. Then, E will be
the common value of own-equity of all entrepreneurs. The type−R entrepreneur who hasentered borrows an amount B(R) so his aggregate capital stock is K(R) = E + B(R).
Denote the leverage rate by φ(R), where φ(R) = B(R)/K(R). Then K(R) can be written:
K(R) =

E
1 − φ(R)(2)

We assume that there is a maximum value of the capital stock, such that K(R) 6 Kmax ,and moreover that E < Kmax so the entrepreneur’s wealth is less than the maximum sizeof the capital stock. By (2), this implies that 0 6 φ(R) 6 1 − E/Kmax < 1. Since we
2

A stochastic variable is denoted x̃; its expected value is x; and its cutoff value where relevant is x̂.

5assume that all the entrepreneur’s wealth is invested, the minimum level of capital for
entrepreneurs who enter is E. Allowing entrepreneurs to invest only part of their wealthwould complicate the analysis slightly without adding any insight.3 The entrepreneur’scapital stock is therefore in the range K(R) ∈ [E, Kmax ]. The assumption of a maximal
capital stock reflects the notion that after some point additional capital is non-productive. It
is like a strong concavity assumption on the production function, which precludes extreme
outcomes that would otherwise occur with linear production. In most of our analysis,
entrepreneurs choose an interior solution so K(R) 6 Kmax is not binding.
Since we assume that banks can identify entrepreneurs by type and set a type-specificinterest rate, equilibrium analysis applies separately to entrepreneurs of each type.4 Accordingly, consider a representative type−R entrepreneur and drop the identifier R from allfunctions for simplicity. After the shock ε̃ is revealed, an entrepreneur’s ex post after-tax
profits (or return to own-equity) evaluated at the end of the period is given by:e = ε̃RK + (1 − δ)K − (1 + r)B − TeΠ(3)where Te is the tax paid and r is the interest rate, so (1 + r)B is the repayment of interest
and principal on the borrowing B. The term (1 − δ)K is the value of capital remaining after
production, given the depreciation rate δ. The type-specific interest rate r will depend upon
the leverage φ chosen by the entrepreneur since this affects bankruptcy risk. The mannerin which φ affects r depends upon the behavior of the lending banks as discussed below.
In our base case, we assume the government deploys an (R+F)-base cash-flow tax on
both the firms and the banks. As we show below, this is equivalent to ACE taxation. In
the absence of market failures, these taxes are non-distorting. However, in our asymmetric
information setting, they affect firms’ investment choices and serve partly to correct themarket distortions. Tax liability under cash-flow taxation, again evaluated at the end of
the period after ε̃ is revealed, is given by:
Te = τ ε̃RK − (1 + ρ)K + (1 − δ)K + (1 + ρ)B − (1 + r)B
{z
} |
{z
}
|
F −baseR−base3(4)

If entrepreneurs were to invest part of their wealth in the safe asset, leverage would increase for any given

level of investment. That would increase bankruptcy risk and the interest rate faced by the entrepreneur.
If entrepreneurs face unlimited liability in the case of bankruptcy, there would be no incentive to invest lessthan total wealth in the risky project since the interest rate on borrowing will be higher than the rate of
return on the safe asset. If there is limited liability in the case of bankruptcy, entrepreneurs may choose tohold wealth in the safe asset although that would result in higher interest costs on borrowing.
4
If wealth differed among entrepreneurs, leverage φ and therefore the interest rate could vary with both
R and E. This would not affect the qualitative results of our analysis.

6where τ is the tax rate and, as noted above, ρ is the risk-free interest rate. The realcomponent of the cash-flow tax base (R-base) in (4) consists of three terms. The first is
the revenue of the firm, ε̃RK. The second, (1 + ρ)K, is the end-of-period value of thededuction for investment. Since investment K occurs at the beginning of the period, we
assume that the tax savings from deducting investment are either refunded immediately
or are carried over to the end of the period with interest at rate ρ. Third, the cash-flow
tax is levied on selling or winding-up the depreciated value of business assets, (1 − δ)K, atthe end of the period. Financial cash-flows (F-base) include the end-of-period value of theborrowing B obtained by the firm less the principal and interest repaid, (1 + r)B. Eq. (4)applies whether Te is positive or negative, so implicitly assumes that the tax system allows
full loss-offsetting. The tax liability Te is incurred by the firm as long as it is not bankrupt.
If the firm goes bankrupt, the bank pays taxes on the bankrupt cash flows.
Using B = E − K, (4) may be rewritten as:
Te = τ ε̃RK − δK − rB − ρE = TeACE(5)

where the term in brackets is the ACE tax base. It includes revenues ε̃RK less three
deductions for capital at the end of the period: depreciation δK, interest rB, and the costof equity finance ρE. This verifies that the R+F and ACE bases are equivalent.
Using (3) and (4), ex post after-tax profits under cash-flow taxation can be written:e = (1 − τ ) ε̃RK + (1 − δ)K − (1 + r)B + τ (1 + ρ)EΠ(6)
Entrepreneurs are confronted with bankruptcy when ε̃ is too low to meet debt repaymente < 0. This occurs for entrepreneurs with ε̃ < ε̂, where ε̂ (which
obligations, that is, when Πis specific to type R) satisfies:
0 = (1 − τ ) ε̂RK + (1 − δ)K − (1 + r)B + τ (1 + ρ)E(7)

In what follows, we refer to ε̂ as bankruptcy risk. The higher the value of ε̂, the greater the
chances of the entrepreneur going bankrupt. Combining (6) and (7), we obtain:e = (1 − τ )(ε̃ − ε̂)RKΠfor ε̃ > ε̂Eq. (7) determining ε̂ can be rewritten, using B = φK and E = (1 − φ)K, as:(1 − τ ) ε̂R + (1 − δ) − (1 + r)φ + τ (1 + ρ)(1 − φ) = 0

(8)

(9)

As this expression indicates, bankruptcy risk ε̂ depends on both the leverage chosen by theentrepreneur, φ, and the interest rate, r. The latter is determined by a competitive banking
7sector as follows. Assume that banks are risk-neutral and can observe R and φ for eachentrepreneur, but cannot observe ε̃ or ex post profits. Thus, there is no adverse selection
since banks know entrepreneurs’ types, but there is moral hazard since entrepreneurs may
have an incentive to declare bankruptcy to avoid repaying the loan. Imperfection of thefinancial market due to asymmetric information is addressed by an ex post verification ormonitoring cost in the event a firm declares bankruptcy. Following the financial accelerator
model of Bernanke et al (1999), we assume that the verification cost is proportional to
ex post output so takes the form cε̃RK, for ε̃ 6 ε̂. This might reflect the fact that theverification cost includes the costs of seizing the firm’s output in a default.5 We assume forsimplicity that there are no errors of monitoring. Then, only entrepreneurs with ε̃ < ε̂ will
declare bankruptcy in equilibrium. The expected total monitoring cost incurred by a bankfor a given type of entrepreneur will be:
Z ε̂cε̃RKgdε̃ = cRKg
0

ε̂2
2

(10)

so the expected monitoring cost increases with bankruptcy risk, ε̂. This specific form of themonitoring cost is chosen for analytical convenience and is not critical for our results.
In the event of bankruptcy, the firm no longer repays it debt and interest, (1 + r)B, andits after-tax profits go to the bank. Using (6), these after-tax profits become:
e = (1 − τ ) ε̃RK + (1 − δ)K + τ (1 + ρ)E for ε̃ < ε̂Π

(11)As this expression indicates, we assume that negative tax liabilities owing to bankrupt
firms are refundable to the banks. Competition among banks ensures that expected profits
earned from lending to the representative entrepreneur of each type are zero. We assume
that banks will not go bankrupt, so they pay the risk-free interest rate ρ on their deposits.
We also assume that banks incur no operating costs for simplicity.
The banks pay the (R+F)-base tax on their financial income less monitoring costs plus
any revenues they obtain from bankrupt firms. The expected tax liability of a bank from aloan B to a given type of entrepreneur is: Z εmax TB = τ
(1 + r)B − (1 + ρ)B gdε̃ε̂
5Bernanke and Gertler (1989) introduced a fixed verification cost in a business cycle model where thereis asymmetric information between lenders and borrowers about the realized return on risky projects, while
Townsend (1979) explored the design of debt contracts with verification costs that could either be fixed orfunctions of realized project output. See also Bernanke et al (1996) for an analysis of the implications ofagency costs in lending contracts arising from asymmetric information about project outcome.

8+Z ε̂ 

ε̂RK + (1 − δ)K − (1 + ρ)E − (1 + ρ)B − cε̂RK gdε̂

(12)

0

The first term of the tax base is net financial cash flow when the loan is repaid. The second
includes the net revenues from the bankrupt firms less the unclaimed tax credit owing tothose firms, the deduction for the cost of repaying deposits and the cost of monitoring.
Using (12), the bank’s zero-expected profit condition can be written:
 Z εmax(1 − τ )(1 + ρ)B = (1 − τ )(1 + r)Bgdε̃ε̂+

Z ε̂ ε̃RK + (1 − δ)K +

0


ε̂2
τ (1 + ρ) E gdε̃ − cRKg
1−τ
2

(13)

This zero-profit condition, which applies for each type of entrepreneur, determines the interest rate the entrepreneur of a given type pays, given their bankruptcy risk, or equivalently,
their leverage. Using (13) in (12), expected tax liabilities of the bank simplify to:Z ε̂
TB = −
0τ
(1 + ρ)Egdε̂
1−τ

(14)

Though this is negative in expected terms, the bank’s tax liabilities will be positive if thefirm does not go bankrupt.

2.3

Leverage, bankruptcy risk and the interest rate

The bankruptcy condition (9) and the bank’s zero-profit condition (13) jointly determine
the relations among r, φ and ε̂. By combining these equations, we can eliminate (1 + r)B
and obtain a relationship between φ and ε̂ as shown in the following lemma.
Lemma 1 The leverage rate φ = B/K, for 0 < φ < 1 − E/Kmax , is given by:!
g ε̂ cg ε̂ 1−τ 1−ε̂R + (1 − δ) + τ−φ(ε̂, R, τ, c) =
1+ρ
2
2

(15)

The proofs of all lemmas are given in the Appendix. Routine differentiation of (15) gives
properties of φ(ε̂, R, τ, c) that are useful in what follows:
φε̂ =

1−τ
(1 − g ε̂ − cg ε̂)R;
1+ρ
φτ =

1−φ
;
1−τ

1 − τ Rg ε̂2
;
1+ρ 2

φR =

1−τ
(1 − c)Rg ε̂;1+ρ

φε̂τ = −φc = −

φε̂ε̂ = −91−τg ε̂ cg ε̂ 
1−
−
ε̂;
1+ρ
2
2
1 − g ε̂ − cg ε̂
R
1+ρ

(16)

Eqs. (9) and (15) represent two equations in three unknowns: φ, ε̂ and r. In practice,an entrepreneur chooses leverage φ, and this determines both bankruptcy risk ε̂ and theinterest rate r through (9) and (15). Bankruptcy risk is increasing in leverage by (16),and, as the following lemma states, so is the interest rate. That is, an increase in leverageincreases the probability of the entrepreneur going bankrupt, and that increases the interest
rate that banks must charge if their zero-expected-profit condition is to be satisfied.
Lemma 2 The interest rate r facing an entrepreneur is increasing in leverage φ.
To interpret the role of (15) in our analysis, we assume that entrepreneurs understandhow the leverage they choose affects the probability of bankruptcy and the interest ratethey face through the bankruptcy condition (9) and the bank’s zero-profit condition (13).
Therefore, they know the relationship between φ and ε̂ in (15), and how it implicitly takes
account of the interest rate they face. In what follows, we take advantage of Lemma 1
to suppress the interest rate r from our analysis. While in practice, entrepreneurs choose
leverage φ, it is convenient for us to assume that they choose bankruptcy risk ε̂, which isrelated to leverage via (15). The choice of ε̂ is equivalent to choosing leverage φ because,even though φ is not necessarily monotonic in ε̂, φε̂ε̂ < 0 by (16). We proceed by deriving
an expression for expected profits as a function of ε̂.6

2.4

Entrepreneurs’ expected after-tax profits

Prior to ε̃ being revealed, the expected after-tax profits of a representative entrepreneur ofRεe(Recall that for ε̃ < ε̂, profits are claimed by the bank.)
a given type are Π ≡ max Πgdε̃.
ε̂e in (6), this becomes:
Given the expression for ΠZ εmax Π=(1 − τ ) ε̃RK + (1 − δ)K − (1 + r)B + τ (1 + ρ)E gdε̃

(17)

ε̂

The entrepreneur takes into account the fact that the interest rate r depends on the zeroprofit condition of the bank, which in turn depends upon the bankruptcy risk or leverageRεhe chooses. Using the bank’s zero-profit condition (13) to eliminate (1 − t) ε̂ max (1 + r)Bgdε̃from (17), and using (1) and (2) along with B = K −E, (17) may be written after integration
as:


Π=

6



1−τ
ε̂2 
εR − δ − ρ − cgR+ 1 + ρ E ≡ π(ε̂, R, τ, c)E
1 − φ(ε̂, R, τ, c)
2(18)

We could instead have used (15) to determine ε̂ as a function of φ, and obtained derivatives of ε̂ withrespect to φ and the other variables. We could then use φ as the choice variable of entrepreneurs. While
this would more accurately reflect entrepreneurial choices, it would make the analysis more complicated andwould not change the results.

10where π(ε̂, R, τ, c) is expected profit per unit of own equity. For future use, differentiateπ(·) in (18) with respect to ε̂ to obtain:1−τcRg ε̂2 π ε̂ =− cε̂gR∆(ε̂, R, τ, c) εR − δ − ρ −1 − φ(·)
2where∆(ε̂, R, τ, c) ≡!

φε̂ (ε̂, R, τ, c)
1 − φ(ε̂, R, τ, c)

(19)

(20)

Using the relationship between leverage and bankruptcy risk in (15), Π = π(ε̂, R, τ, c)E
satisfies the following lemma.
Lemma 3Π = π(ε̂, R, τ, c)E =1 − τ Rg(εmax − ε̂)2 E
1 − φ(·) 2(21)The expression for expected profits in (21) takes into account both the endogeneity of
the interest rate r facing the entrepreneur through the bank’s zero-profit condition (13)and the relationship between leverage and bankruptcy risk through (15). Since we assume
risk-neutrality in this basic model, the expected utility of entrepreneurs, and thus theirobjective function, is given by Π = π(ε̂, R, τ, c)E in (18) or (21). We make use of both ofthese in what follows.

3

Behavior of Risk-Neutral Entrepreneurs

Recall that entrepreneurs make two decisions in sequence. First, they decide whether toundertake risky investments, given their productivity R. This is the extensive-margin decision. Then, if they enter, they decide how much to borrow to acquire more capital over
and above their own equity, E. This is the intensive-margin decision. Once their shock ε̃ isrevealed, their after-tax profits and therefore ex post utility are determined. We consider
the intensive and extensive decisions in reverse order for an entrepreneur of a given type,and continue to suppress the type identifier R for simplicity.

3.1

Choice of leverage: intensive margin

Consider a type−R entrepreneur who decides to enter. As mentioned, given (15) the choiceof ε̂ is equivalent to the choice of leverage φ, and we use the former as the entrepreneur’s
choice variable. Differentiating (21) with respect to ε̂, we obtain: (1 − τ )Rg2dΠ= π ε̂ E = ∆(ε̂, R, τ, c) −(εmax − ε̂)2 Edε̂
εmax − ε̂
1−φ
11

(22)

where ∆(ε̂, R, τ, c) was defined in (20).
Let ε̂∗ be the optimal choice of ε̂. It could be in the interior or it could take on
corner solutions at the top or bottom. From (15), ε̂∗ takes on a minimum value of ε̂∗ = 0
when φ 6 φ(0, R, τ, c) = (1 − τ )(1 − δ)/(1 + ρ) + τ . The maximum value of ε̂∗ satisfiesφ(ε̂, R, τ, c) = 1 − E/Kmax , which is assumed to be smaller than εmax for any entrepreneurtype.
If it is in the interior, dΠ/dε̂ = 0, so by (22) the first-order condition on ε̂ can be written:∆(ε̂∗ , R, τ, c) =2>0εmax − ε̂∗(23)Using this, we obtain the following lemma.
Lemma 4 For ε̂∗ in the interior, φε̂ > 0, φR > 0, φε̂R > 0 and, if the second-ordercondition is satisfied, dε̂∗ /dR > 0.
Thus, the probability of bankruptcy increases with the productivity R of the entrepreneur.
This occurs because entrepreneurs with higher productivity choose higher leverage. Although a higher value of R tends to reduce bankruptcy risk directly through the bankruptcy
condition (7), this direct impact on bankruptcy risk is more than offset by the increase inleverage, φR > 0.

3.2

Decision to undertake risky investment: extensive margin

Ex ante, entrepreneurs decide whether to undertake the risky investment or to opt for therisk-free option. In the risk-free option, they invest their wealth E at a risk-free return ρ,
leading to consumption of (1 + ρ)E. They enter if their expected after-tax income as anentrepreneur, given by Π in (18) or (21), is at least as great as their certain income if they
invest their wealth in a safe asset and obtain consumption of (1 + ρ)E, that is,Π = π(ε̂, R, τ, c)E > (1 + ρ)Eor π(ε̂, R, τ, c) > 1 + ρ(24)

Differentiating π(·) in (21) by R and using φR > 0 by Lemma 4, we obtain that π(·) isb willincreasing in R. Given that ε̂ is being optimized, the cutoff value of R, denoted R,b τ, c) = 1 + ρ. Using the expression for π in (18), thebe uniquely determined by π(ε̂, R,
following lemma is apparent.
Lemma 5 The cutoff value of R is determined by:b−δ−ρ−
εR

12

b ε̂2
cRg
=0
2

(25)

b enter the risky sector and earn a rent. Those with R < Rb
Entrepreneurs with R > R
invest their wealth in a risk-free asset, so earn no rent. Moreover, as the following lemmashows, bankruptcy risk is zero for marginal entrepreneurs, and positive for all inframarginalones.
bb chooses ε̂∗ = 0, while all entrepreneurs R > R
Lemma 6 The marginal entrepreneur R
choose ε̂∗ > 0.
This has implications for the effect of the cash-flow tax in what follows. To study this,consider first the social optimum as a benchmark.

4

The Social Optimum

To study the efficiency properties of cash-flow business taxation, it is useful to characterize
the full-information social optimum, that is, the outcome where c = 0 so banks can observe
without cost the output of the bankrupt firms. Social surplus includes only the surplus
of projects of entrepreneurs who invest in the risky sector since no surplus is generated
either by the banks, which earn zero expected profits, or by potential entrepreneurs who
invest in the safe outcome and earn (1 + ρ)E. Expected social surplus can be defined as the
expected value of production by entrepreneurs less the opportunity cost of financing theircapital. Financing costs include the cost of both debt and equity finance, so are given by(1 + ρ)B + (1 + ρ)E = (1 + ρ)K.
For the representative entrepreneur of type−R, end-of-period expected social surplus
S(R) can be written as follows, using K = E/(1 − φ):Z εmax 
S(R) =ε̃RK + (1 − δ)K gdε̃ − (1 + ρ)K = εR − δ − ρ
0where φ(·) satisfies (15) with c = 0 and τ = 0, or:g ε̂ 
1
φ(ε̂, R, 0, 0) =1−
ε̂R + (1 − δ)1+ρ2E
1 − φ(·)

(26)

(27)

and ε̂ satisfies the bankruptcy condition, (7). Note that S(R) includes the surplus earned
by the investments that go bankrupt since this accrues to the banks. This expression for
S(R) applies whether taxes are in place or not.
In a social optimum, both the extensive and intensive margins are optimized. Entry is
optimized if S(R) = 0 for the marginal entrepreneur, or by (26),bo − δ − ρ = 0
εR
13

(28)

bo is marginal entrepreneur in the social optimum. All entrepreneurs R ≥ R
bo enterwhere Rin the social optimum. Changes in leverage, or equivalently in bankruptcy risk, affect S(R)in (26) as follows:

φε̂
dS(R)
=
εR
−
δ
−
ρ
E
dε̂
(1 − φ)2(29)

bo , dS(Rbo )/dε̂ = 0 for the marginal entrepreneur so social surplus
This implies by (28) that R
bo , dS(R)/dε̂ > 0 for all ε̂ since φε̂ > 0
is independent of leverage and K. For R > R
by Lemma 4. Inframarginal entrepreneurs will therefore maximize leverage and choose
K = Kmax .
As expected, when c = 0 so the full-information social optimum is achieved, the cashflow tax has no effect on market outcomes. It simply diverts rents from inframarginal
entrepreneurs to the government. To see this, consider first the extensive-margin decision.
b − δ − ρ = 0 so R
b is independent of τ . Thus, R
b=R
bo by
When c = 0, (25) implies that εR(28) so entry is socially optimal. Next, consider the effect of the cash-flow tax on leverage.
With c = 0, (19) implies:1−τdΠ= π ε̂ E =∆(ε̂, R, τ, c)(εR − δ − ρ)Edε̂
1−φFor the marginal entrepreneur, (28) implies that π ε̂ = 0, so dΠ/dε̂|R=Rb = 0. Therefore,
leverage φ and thus K are indeterminate for the marginal entrepreneur and independentb so π ε̂ has the sameof τ . For inframarginal entrepreneurs, εR − δ − ρ > 0 since R > R,
sign as ∆(·) = φε̂ /(1 − φ), which is positive by Lemma 4. Therefore, ε̂ takes its maximum
value with φ(ε̂∗ , R, τ, c) = 1 − E/Kmax . Since φε̂ > 0 and φτ > 0 by (16), we have thatdε̂∗ /dτ < 0 to keep φ constant. While ε̂∗ changes, τ does not distort φ or the capital stock
K = Kmax = E/(1 − φ).
When banks must incur a monitoring cost c to observe the profits of bankrupt firms,
the social optimum will not be achieved. We saw above in Lemma 6 that ε̂∗ = 0 for themarginal entrepreneur. Therefore by (25), the productivity of the marginal entrepreneurb − δ − ρ = 0, which implies that R
b=R
bo so entry is optimal. At the same time,satisfies εR
since ε̂∗ > 0 for inframarginal entrepreneurs by Lemma 6, ε̂∗ will be in the interior for large
enough values of R, so leverage and therefore investment will be below the maximum levelobtained in the social optimum. Thus, while entry is socially optimal in the presence ofimperfect information, there is too little investment for entrepreneurs that incur bankruptcy
risk.
Before turning to the implications of cash-flow taxation in the imperfect information
setting, it is useful to define constrained social surplus as social surplus less the costs ofmonitoring incurred by the banks since the government confronts the same information14

problem that the banks do. For a type−R entrepreneur, constrained social surplus can be
expressed as follows, analogous to (26):ε̂2  E
S(R) = εR − δ − ρ − cRg
2 1 − φ(·)(30)

Combining the entrepreneur’s expected profits in (17) with the bank’s zero profits expression(13), we obtain:
Π − (1 + ρ)E =Z εmax 0ε̂2(1 − τ ) ε̃RK + (1 − δ)K − (1 + ρ)(B + E) gdε̃ − (1 − τ )cRKg
2= (1 − τ )S(R)(31)

In the absence of taxation, maximizing private surplus Π − (1 + ρ)E maximizes constrainedsocial surplus, but that will no longer be the case with τ > 0. We use (31) below to interpretthe efficiency consequences of cash-flow taxation in an information-constrained setting.
To summarize, in the full-information social optimum, inframarginal entrepreneurs maximize leverage and choose K = Kmax , while marginal entrepreneurs are indifferent to thelevel of K. The cash-flow tax has no effect on entry or leverage, but diverts to the government the rents of inframarginal entrepreneurs. If there are monitoring costs, entry remains
optimal and marginal entrepreneurs assume no bankruptcy risk, while some inframarginal
entrepreneurs underinvest.

5

Cash-Flow Taxation with Risk-Neutral Entrepreneurs

The model discussed in the previous sections includes both bankruptcy, when entrepreneurs
are unable to repay their loans fully, and asymmetric information, in the sense that banks
can only verify bankruptcy with costly ex post monitoring. In this section, we consider theeffect of (R+F)-base cash-flow taxation on leverage and entry as well as on after-tax profits,
tax revenue and social surplus.

5.1

Cash-flow taxation and leverage

The leverage decision for an inframarginal type−R entrepreneur is governed by (22), wheredΠ/dε̂ = 0 if ε̂∗ is in the interior. To determine the effect of taxes on leverage, differentiate
φ ε̂(·), R, τ, c to obtain:
dφ
dε̂∗
(32)
= φε̂
+ φτ
dτ
dτ
where φτ = (1 − φ)/(1 − τ ) by (16). To evaluate (32), we can use the first-order conditionon ε̂, (23), to obtain the following lemma.
15Lemma 7 Assume ε̂∗ is in the interior. Then,
dε̂∗
=0
dτ

Thus, the cash-flow tax does not affect bankruptcy risk for firms with ε̂∗ in the interior.
Using Lemma 7 and (16), (32) reduces todφ
1−φ= φτ =
>0
(33)
dτ
1−τ
While the tax does not affect bankruptcy risk, it does increase leverage and therefore investment. Some explanation for this comes from the following lemma.
Lemma 8 For ε̂ in the interior,
dr
<0
dτ

(34)

The intuition is that the cash-flow tax allows the banks to claim a refund of the opportunity
cost of investment, τ (1+ρ)K, on bankrupt projects. An increase in τ increases the gain thatthe bank can collect from the bankrupt entrepreneurs, which improves its expected profits
and thus leads to a reduction in r. By reducing r, the increase in τ induces entrepreneurs
to borrow and therefore invest more.

5.2

Cash-flow taxation and entry

Consider now the extensive-margin decision. The productivity of the marginal entrepreneurb is determined by (25). Since ε̂∗ is independent of τ by Lemma 7, so is Rb and thereforeR
entry. Therefore, the cash-flow tax is neutral with respect to entry.

5.3

Cash-flow taxation and expected profits

Next, consider the effect of the cash-flow tax on expected profits of a type−R firm. Lemma
3 applies, so π is given by:π=

1 − τ Rg
Rg
(εmax − ε̂)2 ≡ D(εmax − ε̂)2
1−φ 2
2

(35)

Using (33), D ≡ (1 − τ )/(1 − φ) is independent of τ ,7 so expected profits πE are as well.
Therefore, while the tax increases leverage and therefore investment, it leaves expected
7

Proof:
Dτ = −11−τ
11−τ 1−φ+φτ = −+=01−φ(1 − φ)21−φ(1 − φ)2 1 − τ

16after-tax profits unchanged. This is analogous to the Domar and Musgrave (1944) result
albeit for a different reason in this context since entrepreneurs are risk-neutral. We obtaina similar result below for risk-averse entrepreneurs.

5.4

Cash-flow taxation and expected tax revenue

Expected government revenue from the cash-flow tax can be written, using (4), as:Z Rmax ε̂2  ET =τεR − ρ − δ − cRg
dH(R) ≡ τ Y
2 1 − φ(·)
b
R

(36)

where Y is the aggregate expected tax base and H(R) has been defined as the distribution
b nor ε̂ are affected by the tax,of entrepreneur types. Given from above that neither R
differentiating T yields:
dT
=Y +τ
dτ

Z Rmax εR − ρ − δ − cRgbRε̂2  EdφdH(R) > 0
2 (1 − φ)2 dτ(37)

where the inequality follows from (33). The first term is the mechanical effect of an increasein the tax rate on revenues which is positive. The second term is also positive given thatleverage increases with the tax rate as shown above. Since leverage and therefore investment
increase with τ , more rents are created and this induces an increase in the tax base Y .

5.5

Cash-flow taxation and expected social surplus

Finally, consider the effect of the tax on constrained expected social surplus S. UsingΠ − (1 + ρ)E = (1 − τ )S from (31), we have:S=Π − (1 + ρ)E
1−τ

Since a tax increase leaves Π = πE and therefore the numerator unchanged, it will increase
S. In effect, the tax induces the firms to increase leverage while keeping ε̂ constant. Since
investment satisfies K = E/(1 − φ) by (2), introducing the tax increases K, and as can beseen from (30), S increases. Equivalently, the increase in K holding ε̂ constant generates
more pre-tax profits, or rents. The government taxes away those profits, leaving after-tax
expected profits unchanged and improving constrained expected social surplus. Thus, while
the no-tax outcome replicates the constrained social optimum, implementing a cash-flow tax
improves social outcomes without changing firms’ expected profits. It does so by breaking
the connection between leverage and bankruptcy risk. This reflects the fact that levels of
K in the absence of the tax are less than in the unconstrained social optimum for someentrepreneurs as discussed above.
17

The optimal tax rate for a given entrepreneur-type would be that which just induced
the entrepreneur to choose maximum leverage. Since the government cannot observe R, it
cannot implement optimal type-specific tax rates.
The main results of the analysis in the base-case model are summarized as follows.
Proposition 1 With risk-neutral entrepreneurs, equilibrium has the following properties:b enter the risky industry
i. Entrepreneurs with productivity R above some threshold level R
and earn a rent. For those with K in the interior, leverage φ and bankruptcy risk ε̂∗are increasing with R.
ii. In the absence of taxation, entry is socially efficient in equilibrium, but leverage andtherefore investment are below the full information socially optimal levels.
iii. (R+F)-base cash-flow taxation increases leverage, while bankruptcy risk and expected
profits remain unchanged, and expected tax revenues increases. Expected rents andexpected social surplus both increase, so the cash-flow tax act as a corrective device.
We assumed in this section that the government deployed an (R+F)-base cash-flow tax,
or equivalently an ACE corporate tax. In a previous version of this paper (Boadway, Satoand Tremblay, 2016), we considered the case of an R-base cash-flow tax where financial
cash-flows are not taxed. If banks are exempt from the tax, marginal entrepreneurs stillassume no bankruptcy risk and entry is not affected by the tax. However, bankruptcy
risk falls with the tax and the change in leverage is smaller than in the (R+F)-base case.
Leverage may even fall in which case the tax would move the equilibrium away from thesocial optimum. On the other hand, if the real cash-flows of banks were taxable, the same
results as in the (R+F)-base cash-flow tax are obtained.

6

Risk-Averse Entrepreneurs

Assume now that entrepreneurs are risk-averse and unable to insure their uncertain project
outcomes. Assume also that the government deploys an (R+F)-base cash-flow tax to both
entrepreneurs and banks as in our basic model. The key new element in this setting isthat because the tax system cannot distinguish returns to risk from rents, the cash-flow tax
necessarily applies to both.
Recall that all consumption takes place at the end of the period. Entrepreneurs whoenter the risky industry invest all their wealth in their firm at the beginning of the period
e at the end, where the latter are given by (6) or (8). As
and consume the after-tax profits Π18

in the base case with risk neutrality, entrepreneurs get no income in the event of bankruptcy
since that goes to the bank. Let their end-of-period expected utility V be:
Z εmax1e 1−γ gdε̃V =
Π1 − γ ε̂(38)

where 0 < γ < 1, so the entrepreneur’s utility function exhibits constant relative risk
aversion. Using (8), (2) and D = (1 − τ )/(1 − φ) in (38), expected utility becomes:
Z εmax 
1−γ
1−γ
g
1
1 
DRE
(εmax − ε̂)2−γV =D(ε̃ − ε̂)RE
gdε̃ =
1 − γ ε̂
1−γ
2−γ

(39)

As before, the entrepreneur decides whether to enter, and if so, how much to borrowand therefore how much risk to take on. Consider these decisions in reverse order.

6.1

Intensive-margin decision

The choice of leverage φ is again equivalent to the choice of bankruptcy risk ε̂ through (15).
Differentiating (39) with respect to ε̂ and using the definition of ∆(·) in (20), we obtainafter straightforward simplification:2−γ
1dV∝ ∆(ε̂, R, τ, c) −dε̂
1 − γ εmax − ε̂(40)

If the optimal choice of ε̂, ε̂∗ , is in the interior, dV /dε̂ = 0, and (40) gives:∆(ε̂∗ , R, τ, c) =

1
2−γ
>0
1 − γ εmax − ε̂∗(41)

From (41) we obtain the following analogue to Lemma 7.8
Lemma 9 If ε̂∗ is in the interior, then
dε̂∗
=0
dτ

and

dε̂∗
<0
dγ

Note that Lemma 4 applies here as well, so bankruptcy risk and therefore leverage are
increasing in entrepreneurial productivity: dε̂∗ /dR > 0.
8

We have assumed that entrepreneurs who enter invest all of their initial wealth E in the firm. Risk-averse

entrepreneurs may choose to invest only a portion of their wealth, say, α, in the firm to diversify their risk.
Suppose entrepreneurs choose both ε̂ and α. It is straightforward to show that Lemma 9 applies to both αand ε̂ if they are in the interior. We omit α as a choice variable for simplicity.

19

6.2

Extensive-margin decision

The entry decision involves comparing expected utility as an entrepreneur with that obtained from the safe alternative yielding end-of-period consumption of (1 + ρ)E. En1−γ/(1 − γ). From (39), V is increasing in R,
trepreneurs will enter if V > (1 + ρ)Eb
so the cutoff value R will be uniquely determined.
To characterize the extensive-margin decision, we show first that in equilibrium ε̂∗ = 0
b The following lemma indicates when ε̂∗ = 0.
for the marginal entrepreneur, R.
Lemma 10ε̂∗ = 0

if

εR
12−γ
≤
δ+ρ
21−γ

(42)

Let R0 be the value of R such that ε̂∗ just becomes zero. Then, by (42), R0 satisfies thefollowing:
εR0
12−γ
=
δ+ρ
21−γ

(43)

so is increasing in γ. For any R, higher risk-aversion will lead an entrepreneur to choose
lower leverage and bankruptcy risk. Therefore, the value of R at which bankruptcy risk
just becomes zero will increase with the degree of risk aversion.
Next, we can establish the following relationship between R0 and the productivity ofbthe marginal entrepreneur, R.
b 6 R0 as γ > 0
Lemma 11 R
b as long as risk-aversion γ is nonThe implication of Lemma 11 is that ε̂∗ = 0 at R = R
negative, and this applies regardless of the values of c or τ . This result nests what we
found earlier in the risk-neutral model with γ = 0 where the marginal entrepreneur chooseb = R0 , so ε̂∗ > 0 for all inframarginalε̂∗ = 0 as well. However, in the risk-neutral case, R
entrepreneurs.
b R0 ]. In
Lemma 11 implies that with γ > 0, ε̂∗ = 0 for all entrepreneurs with R ∈ [R,that range, there is no risk of bankruptcy, so r = ρ by the banks’ zero-profit condition (13)and ex post after-tax profits in (6) can be written, using B = K − E = E/(1 − φ) − E:e = 1 − τ ε̃R − δ − ρ + 1 + ρ E = D(ε̃R − δ − ρ) + 1 + ρ EΠ
1−φwhere, recall, D ≡ (1 − τ )/(1 − φ). Therefore, expected utility can be written:
V =Z εmax e 1−γ
Z
1−γ
ΠE 1−γ εmax
gdε̃ =
D(ε̃R − δ − ρ) + 1 + ρ
gdε̃
1−γ
1−γ 0
0
20

(44)

b R0 ]. In this range, an entrepreneur
The expression for V in (44) applies for all R ∈ [R,of given R will choose leverage, or equivalently D ≡ (1 − τ )/(1 − φ), to maximize V . The
first-order condition ∂V /∂D = 0 reduces to:Z εmax−γgdε̃ = 0(ε̃R − δ − ρ) D∗ (ε̃R − δ − ρ) + 1 + ρ

(45)

0

where D∗ is the optimal choice of D. This value of D∗ , and therefore φ will be increasingin R. As R → R0 , φ → (1 − τ )(1 − δ)/(1 + ρ) + τ , which is the value of φ that just satisfies(15) when ε̂ = 0.
b where V = (1 + ρ)1−γ E 1−γ /(1 − γ)The extensive margin is determined by value of R
or using (44) with D = D∗ ,Z εmaxb − δ − ρ) + 1 + ρ 1−γ gdε̃ = (1 + ρ)1−γD∗ (ε̃R(46)

0b Those with R < R
b will invest their
Entrepreneurs will enter the risky sector only if R > R.
wealth in a safe asset.

6.3

The effects of cash-flow taxation

We next turn to the effects of (R+F)-base cash-flow taxation on entrepreneurs’ decisions
and equilibrium outcomes when entrepreneurs are risk-averse. We begin with the intensiveand extensive-margin decisions, and then consider the effects on expected profit and on
government revenues.
6.3.1

Intensive-margin decisionb < R0 since γ > 0. Consider first entrepreneurs in the range R ∈ [R,b R0 ].
By Lemma 11, R
As we have seen, for these entrepreneurs, ε̂∗ = 0 and the first-order condition (45) applies.
This yields a unique value of D∗ for each R which is independent of the tax rate. Since
D∗ = (1 − τ )/(1 − φ), leverage will rise by the same amount as an increase in τ . Given thatD∗ is invariant with the tax rate, V will be as well as seen by (44). Thus, for entrepreneursin this range, a result analogous to Domar-Musgrave (1944) applies. Entrepreneurs offset anincrease in τ by increasing private risk-taking, while achieving the same level of expectedutility V . The increase in leverage φ entails more investment and therefore more rent
generation, which accrues to the government in increased tax revenues as discussed below.
For entrepreneurs of type R > R0 , ε̂∗ > 0 so they incur some bankruptcy risk. Theirintensive-margin decision is similar to the base case with risk-neutrality above. Eq. (32)again applies, and since dε̂∗ /dτ = 0 by Lemma 9 (32) simplifies to dφ/dτ = φτ . By (16),21φτ = (1 − τ )/(1 − φ), so τ encourages leverage. However, the increase in leverage does
not translate into an increase in bankruptcy risk ε̂, since dε̂∗ /dτ = 0. As well, as we haveshown in footnote 7, D = (1 − τ )/(1 − φ) is constant when φτ = (1 − τ )/(1 − φ). Therefore,
with D and ε̂ constant, so is expected utility V in (39) as long as leverage φ and K are in
the interior. This again is analogous to the Domar and Musgrave (1944) result on portfolio
investment: a tax on capital income with full loss-offset encourages risk-taking by riskaverse individuals because the government is sharing the risk with them on actuarially fairterms. In our case of an (R+F)-base cash-flow tax on firms, the government is sharing therisk of the entrepreneur, and as a result the tax does not affect private risk ε̂.
6.3.2

Extensive-margin decisionb < R0 we have that ε̂∗ = 0 for the marginal entrepreneur. For a given tax rate τ , theSince Rb chooses leverage such that the first-order condition (45) is satisfied
marginal entrepreneur R
b This leads to a unique value of the optimal D∗ = (1 − τ )/(1 − φ) regardless of theat R = R.
b satisfies (46). Since the choice of D∗ by the marginal entrepreneur
tax rate. Recall that R
b and therefore the extensive-margin decision,is independent of the tax rate, the value of R,
that satisfies (46) is independent of τ .
6.3.3

Expected profits and tax revenues

As well as V being unaffected by the cash-flow tax, so are expected profits Π. To see
this, consider the expression for the expected rate of return on equity, π, in (21). Sinceboth ε̂∗ and D∗ = (1 − τ )/(1 − φ) are independent of τ , π will also be invariant with τ .
Therefore, entrepreneurs are able to offset the effect of the tax on their expected after-tax
profits by increasing their leverage. The increase in leverage will correspond to an increasein borrowing and investment, which in turn will increase expected before-tax profits andtherefore expected tax revenue to the government since after-tax profits are unchanged.
To see that expected tax revenues will rise, note that (36) still applies, and the change
in expected tax revenues will again be given by (37), which is positive since dφ/dτ > 0.
Expected tax revenues rise due both to a mechanical effect and to an increase in the tax basebecause of increased leverage and investment. Social welfare will increase if the increasein expected tax revenues is valuable to the government, and that depends on how thegovernment evaluates the increase in risk that might accompany the tax revenues.
Our findings with risk-averse entrepreneurs are summarized as follows.
Proposition 2 With risk-averse entrepreneurs subject to (R+F)-base cash-flow taxation,equilibrium has the following properties:
22

b R0 ] for whom there is no risk ofi. There is a range of entrepreneurs with R ∈ [R,bankruptcy, so ε̂∗ = 0 and r = ρ.
ii. For all entrepreneurs with ε̂∗ below the maximum, leverage increases with the cash-flow
tax rate, while bankruptcy risk, expected profits and expected utility are unchanged.
iii. The (R+F)-base cash-flow tax is neutral with respect to entry decisions.
iv. Expected tax revenues increase with the tax rate.

7

Concluding Remarks

In this paper, we analyzed the impact of cash-flow business taxation on entrepreneurs’ decision of whether to enter a risky industry and, if so, how much to borrow when entrepreneurs
face bankruptcy risk, and when there is asymmetric information between entrepreneurs andfinancial intermediaries. The neutrality of cash-flow taxation found by Bond and Devereux(1995, 2003) in the absence of asymmetric information and risk-aversion no longer applies
under these features. Moreover, there is too little investment in the information-constrainedsocial optimum compared with the full-information case. The issue is then whether cash-flow
taxation improves social efficiency. We assume that cash-flow taxation is of the (R+F)-basesort so it applies both to entrepreneurs and banks.
With risk-neutral entrepreneurs, cash-flow taxation taxes rents only. When banks must
undertake costly monitoring of firms that declare bankruptcy, the tax does not affect entry
decisions, given that the marginal entrepreneur earns no rent, but it does affect leverageand therefore investment. In particular, the tax will actually increase social welfare. By
inducing firms to increase leverage, and therefore investment, the cash-flow tax leads tohigher pre-tax profits, or rents, without affecting bankruptcy risk. These additional pre-tax
profits are taxed away by the government leading to a higher constrained social surplus. By
inducing more investment, the cash-flow tax is implicitly correcting for the inefficiencies of
the information-constrained outcome.
When entrepreneurs are risk-averse, cash-flow taxation taxes both rents and return
to risk. The cash-flow tax does not affect the entry decision and increases leverage, whileleaving bankruptcy risk unchanged as in the risk-neutral case. In addition, neither expected
profits nor expected utility are affected. Expected tax revenues of the government increase,and the government may incur greater risk if it is unable to pool risk better then the private
sector. This is analogous to the results of Domar and Musgrave (1944) and Atkinson andStiglitz (1980).
23

We have assumed that asymmetric information involved moral hazard rather than adverse selection, so banks can observe firm types but not their profits. If banks cannot observe
the productivity of entrepreneurs ex ante, there will be an adverse selection problem as in
Stiglitz and Weiss (1981) and de Meza and Webb (1987), among others. In this case, ifbanks cannot offer separating contracts, all entrepreneurs face the same interest rate. In
contrast to the case considered here, the equilibrium without taxation will be inefficientalong the extensive margin and cash-flow taxation will generally not be neutral. In particular, there will be excessive entry by the least-productive entrepreneurs to take advantageof the favorable interest rate. A cash-flow tax will discourage entry, thereby improving efficiency. It would be interesting to consider the case where banks are able to offer contracts
in which the interest rate varies with the size of loan, so firms can be separated by type.
There will be informational rents that might influence the effect of cash-flow taxes.

Appendix
Proof of Lemma 1
Using (7) and integrating, (13) can be written:g ε̂2(1−τ )(1+ρ)B = (1−τ )(ε̂R+(1−δ))K+τ (1+ρ)E (1−g ε̂)+(1−τ )RK2
cRKg ε̂2+ (1 − τ )(1 − δ) + τ (1 + ρ) Eg ε̂ − (1 − τ )22cRKg ε̂2g ε̂RK + (1 − τ )(1 − δ)K + τ (1 + ρ)E − (1 − τ )= (1 − τ ) ε̂(1 − g ε̂) +22Using E = K − B, this becomesg ε̂ cg ε̂ 
ε̂RK + (1 − τ )(1 − δ)K + τ (1 + ρ)K(1 + ρ)B = (1 − τ ) 1 −−2
2
Using φ = B/E,g ε̂ cg ε̂ 
(1 + ρ)φ = (1 − τ ) 1 −−ε̂R + (1 − τ )(1 − δ) + τ (1 + ρ)22
Proof of Lemma 2
Differentiate (9) with respect to ε̂ and r, and use φr = 0 to obtain:1
τ (1 + ρ)
0 = Rdε̂ − φdr −ε̂R + (1 − δ) +
φε̂
φ
1−τ
Using φε̂ from (16) gives:1
τ (1 + ρ) 1 − τε̂R + (1 − δ) +1 − (1 + c)g ε̂ R
0 = Rdε̂ − φdr −
φ
1−τ
1+ρ
24

This can be rewritten using (15) as:!

1−τ  1+c τ (1 + ρ) 1 − τ
φ2 dr
=
1−
g ε̂ ε̂R+(1−δ) +τ − ε̂R+(1−δ)+
1−(1+c)g ε̂
R dε̂
1+ρ
2
1−τ
1+ρ
which simplifies to:


1−τ
ε̂ 
φ2 dr
= (1 + c)g ε̂ τ +(1 − δ) + R
> 0
R dε̂
1+ρ
2
Proof of Lemma 3
Rewrite π in (18) as!
1
cRg ε̂2 + (1 + ρ)(1 − φ)π(ε̂, R, τ, c) =(1 − τ ) Rε − δ − ρ −1−φ2
From (15), we obtaing ε̂ cg ε̂ 
(1 + ρ)(1 − φ) = −(1 − τ ) 1 −ε̂R + (1 − τ )(ρ + δ)−22
Substituting this in the expression for π gives, using ε = εmax /2 and εmax = 1/g:π(ε̂, R, τ, c) =1−τ g  1 − τ Rg
R ε − ε̂ 1 − ε̂ =(ε̂ − εmax )2
1−φ
2
1−φ 2

Proof of Lemma 4
Since ∆(ε̂∗ , R, τ, c) > 0 for ε̂∗ in the interior by (23), φε̂ > 0 by (20). Therefore, φR > 0
and φε̂R > 0 by (16). The second-order condition on ε̂ is:∆ε̂ (ε̂, R, τ, c) −2
< 0(εmax − ε̂)2Differentiate the first-order condition (23), and use ∆R = φε̂R /(1 − φ) + φε̂ φR /(1 − φ)2 > 0
and the second order-conditions on ε̂ to obtain dε̂∗ /dR > 0.

Proof of Lemma 6
For the marginal entrepreneur, Lemma 5 implies by (19) that π ε̂ < 0 for ε̂ > 0. Therefore,
the marginal entrepreneur chooses ε̂∗ = 0 and incurs no bankruptcy risk. Then, with ε̂ = 0,b than causes π ε̂ to become positive, so ε̂∗π ε̂ in (19) becomes zero. Increasing R above R
increases above zero.

Proof of Lemma 725

Differentiating ∆(ε̂, τ, c) = φε̂ /(1 − φ), we have ∆τ = φε̂τ /(1 − φ) + φτ φε̂ /(1 − φ)2 . Using(16) for φτ , φε̂ and φε̂τ ,∆τ = −

1−φ1−τ
1
1 − g ε̂ − cg ε̂R+(1 − g ε̂ − cg ε̂)R=0
(1 + ρ)(1 − φ)1−τ 1+ρ
(1 − φ)2(47)

Since ∆τ = 0, the solution of first-order condition (23) for ε̂∗ is independent of τ .

Proof of Lemma 8
Differentiate (9) with respect to τ and use dε̂/dτ = 0 by Lemma 7 to obtain:− ε̂R + (1 − δ) − (1 + ρ) + (1 + r)φτ dτ − φdr = 0
Since φτ = (1 − φ)/(1 − τ ) by (16), this becomes:
dr
1 − φ
1
= − ε̂R − (δ + ρ) + (1 + r)dτφ
1−τUsing (9), this can be written:
dr
1 r−ρ
=−
dτ
φ1−τ
which is negative since r > ρ by the bank’s zero-profit condition.

Proof of Lemma 9
Note that τ enters into (41) through ∆(·) = φε̂ /(1 − φ). Differentiating ∆(·) with respectto τ and using (16), we obtain:φε̂τφε̂
1 − g ε̂ − cg ε̂
1 − τ 1 − g ε̂ − cg ε̂∂∆=+φτ = −
R+Rφτ = 0∂τ
1 − φ (1 − φ)2(1 + ρ)(1 − φ)
1 + ρ (1 − φ)2
Therefore, ∆ remain unchanged when τ changes as long as the solution is in the interior,so ε̂∗ not affected by changes in τ . Then, differentiation of (41) gives ∂ ε̂∗ /∂γ > 0.

Proof of Lemma 10
We have that ε̂∗ = 0 if dV /dε̂|ε̂=0 ≤ 0, or ∆(0, R, τ, c) ≤ (2 − γ)/((1 − γ)2ε) by (40), using(1). By (20) and using (15) and (16), we obtain∆(0, R, τ, c) =(1 − τ )R/(1 + ρ)Rφε̂ (0, R, τ, c)==
1 − φ(0, R, τ, c)
1 − (1 − τ )(1 − δ)/(1 + ρ) − τ
ρ+δEq. (42) follows immediately.

26

Proof of Lemma 11
Using (21) for π(ε̂, R, τ, c), expected utility in (39) may be written:
V =

E 1−γ
21−γ g γπ(ε̂, R, τ, c)1−γ (εmax − ε̂)γ1−γ2−γAt ε̂ = 0 and using εmax = 1/g, this becomes:
V0 =

E 1−γ
21−γ
π(0, R0 , τ, c)1−γ1−γ2−γUsing (21) for π, (15) for φ, and (43), this may be written after manipulation:
V0 =(1 + ρ)1−γ E 1−γ
1
1−γ
1−γ
(1 − γ) (2 − γ)γ(48)bRecall that for the marginal entrepreneur, R,
1−γ

b = (1 + ρ) E
V (R)
1−γ

1−γ

b 6 R0 if V (R)b 6 V0 , or from (48) if (1 − γ)1−γ (2 − γ)γ 6 1, or equivalently
We have that R
γ > 0, where the equality applies for γ = 0.

27

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