Long-Run Effects of Tax Policies
in a Mixed Market
Joint work with Susumu Cato
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Long-Run Effects of Tax Policies
in a Mixed Market
(1) Mixed Oligopoly at Free Entry Markets (2005,
Journal of Economics)
(2) What Role Should Public Enterprises Play in FreeEntry Markets? (2010, Journal of Economics)
(3) Long-Run Effect of Foreign Penetration on the
Optimal Degree of Privatization (forthcoming in Journal
of Institutional and Theoretical Economics)
(4) Mixed Duopoly, Privatization, and Subsidization with
Excess Burden of Taxation (forthcoming, Canadian
Journal of Economics)
(5) Market Structure and Privatization Policy under
International Competition (forthcoming in Japanese
Economic Review)
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Plan of the Presentation
(1) Two lines of related literature on mixed oligopoly
(a) Free entry mixed market
(b) Privatization Neutrality Theorem
(3) Non-Neutral Results
(4) Model formulation
(5) Results, intuition, and implications
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Related Literature on Mixed
Oligopoly (1)
(1) Free Entry Market
(1-a) Monopolistic Competition
Anderson et al (1997), Matsumura et al (2009)
(1-b) Cournot Competition
Matsumura and Kanda (2005), Brandao and Castro
(2007), Fujiwara (2007).
(1-c) Stackelberg
Ino and Matsumura (2010)←Ino and Matsumura
(forthcoming in IER)
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Ｍａｔｓｕｍｕｒａ and Kanda (2005)
Long-run analysis on mixed oligopoly
(1) Cournot competition, simultaneous-move, no
product differentiation)
(2) No restrictions on the cost differences between
public and private firms.
(3) The objective function of the public firm is the
weight sum of social welfare and its own profits.
U0= (1-θ)W + θπ0
(4) General demand and general cost (increasing
marginal costs).
(5) Free entry of private firms.
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Time Line
(1) The government chooses whether to build a
public firm (firm 0). The set-up cost F0 is sunk if it
chooses to build it.
(2) The government chooses θ.
(3) After observing θ, each private firm chooses
whether to enter the market.
(4) After observing the number of entering firm n,
firms face Cournot competition.
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The equilibrium of the subgame
given α
Given θ, the following four variables are endogenously
derived:
n（the number of firms）,q1（the output of each private
firm）,q0（the output of the public firm）,Ｑ（total output）
from
(1) the first order condition of the public firm
(2) the first order condition of each private firm
(3) zero profit condition of each private firm
(4) Q=nq1+q0
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The equilibrium of the subgame
given θ
Comparative Statistics for these four variables
Question:
(a) q1 and Ｑ are independent of θ.
(b) q0 is (increasing in, decreasing in, independent of )
θ.
(c) n is (increasing in, decreasing in, independent of ) θ.
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P
Free entry equilibrium
private firm's residual demand
private firm's AC
0
private firm's output
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a decrease in θ
P
private firm's residual demand
private firm's AC
0
Y
private firm's output
long run ~ reduction of the number of private firms
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Optimal θ
θ =0 is optimal. ←marginal cost pricing restrict
wasteful entries (excess entry theorem).
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Intuition
Suppose that θ>0. A decrease in θ
(1) does not affect Q.→Consumer surplus remains
unchanged.
(2) increases q0.→ Production cost increases by (firm
0’s marginal cost)・Δq0.
(3) Decreases n.→Production cost decreases by (firm
1’s average cost) ・q1・Δn.
q1・Δn =Δq0 (because Q remains unchanged).
Firm 1’s average cost ＝price ＞firm 1’s marginal cost
⇒An increase in α reduces production cost without
changing the production level. (Welfare-improving
production substitution)
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First stage choice
・The government sets up firm 0 if and only if
π0>0.
～The public firm which has deficit should be
abolished in the ling-run.
Question:
・If the public firm is as efficient as private firms, it
obtains (strictly positive, strictly negative, zero)
profits.
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P
Free entry equilibrium
private firm's
residual demand
AC
MC
0
private firm's output
Y
public firm's output
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Summary
Effect of Privatization
CS
PS
exogenous decrease
increase
number of
firms
free entry
unchanged ambiguous
decrease if
the public
firm’s profit is
positive
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ambiguous
ambiguous
decrease if
the public
firm’s profit is
positive
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Related Literature on Mixed
Oligopoly (2)
(2) Privatization Neutrality Theorem (PNT)
(2-a) Privatization does not affect welfare under simple
optimal subsidy policy, unit production subsidy.
White (1996), Tomaru (2006), Kato and Tomaru (2007),
Hashimzade (2007)
(2-b) Public Leadership, private leadership, mixed
Cournot, and private oligopoly yield the same welfare
under optimal subsidy policy above.
Poyago-Theotoky (2001), Tomaru and Saito (2010)
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Privatization Neutrality Theorem
Privatization Neutrality Theorem: Privatization does not
matter under optimal subsidy policy.
It implies that if the optimal subsidy policy is adopted,
discussing mixed oligopoly or privatization policy
does not make sense.
Most of the results in mixed oligopoly literature have
quite limited implications and importance if this
theorem is really robust.
Destructive Result, Disaster for researchers in this field.
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Intuition behind PNT
Suppose that all firms are symmetric. Consider the
private oligopoly.
The first best is achieved when P=ci' (price =marginal
cost) ~ all firms choose the same output level
It is achieved by the production subsidy s*.
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Intuition behind PNT
Suppose that one firm is nationalized. Suppose that
all of remaining firms do not change their outputs.
The nationalized firm, which is welfare-maximizer,
never changes its output .
All remaining private firms obviously have no incentive
to change their outputs.
→s* yields the first best outcome in the mixed
oligopoly.
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Condition for PNT
When I explain the intuition behind PNT, I do not use
any of the conditions
(1) profit-maximizing private firms
(2) homogeneous product market,
(3) single public firm
and so on.
All we use is the conditions that the first best is
achieved at the symmetric equilibrium, that the first
best is achieved by controlling outputs only, and that
the pubic firm is welfare maximizer.
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Robustness of PNT
Privatization Neutrality Theorem is far from robust:
(1) PNT obviously does not hold when there is cost
difference between public and private firms.
(2) PNT does not hold unless all firms are domestic.
~ Matsumura and Tomaru (forthcoming in JER)
(3) PNT does not hold at free entry markets~This paper
(4) If there is an excess burden of taxation, PNT does
not hold. ~Matsumura and Tomaru (forthcoming in
CJE)
(5) PNT does not hold if firms control two or more
independent variables.
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Model
The same demand and cost functions as in
Matsumura and Kanda ~increasing marginal cost
Introducing unit subsidy s(lump-sum subsidy T).
(1)The government chooses s or/and T to maximize
welfare.
(2) Each private firm chooses whether or not to enter
the market.
(3)Firms face Cournot competition.
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Results ~ Unit subsidy
Lemma 1.
(i) ∂qM1 /∂s>(=)0 if P’’ < (=) 0;
(ii) qM1 (s) = qP1(s) and QM(s) = QP(s) for all s;
(iii) nM(s) < nP(s) and dnM/ds > dnP/ds > 0 for all s.
Proposition 1. sM ≤ sP with the equality being satisfied
if and only if P’’=0.
Proposition 2. W P(sP)<WM(sM).
Non-neutrality results
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Results ~ Entry-License Tax
Lemma 2. (i) ∂qM0 /∂T>0;(ii) ∂qM1 /∂T>0; (iii)dnM/dT<0.
Lemma 3. The optimal entry-license tax TM is positive.
Lemma 4. (i) ∂qP1 /∂T>0;(ii) dnP/dT <0.
Lemma 5. The optimal entry-license tax TP is positive.
Lemma 6. For all T, (i)qM1(T)=qP1(T) and QM(T)=QP (T);
(ii) CSM(T) = CSP (T); (iii) nM(T) < nP(T) and
dnM/dT<dnP/dT;
(iv)WM(T)≥WP(T) if and only if Π0(T) +
{nM(T)+1}T≥nP(T)T.
Proposition 3. TM < TP .
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Results ~ Two-Part Tax-Subsidy
Policy
Proposition 4. In both mixed and private oligopolies,
the first-best outcome is attained by the same taxsubsidy combination and the government budget is
balanced.
Neutrality-Results.
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