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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 Free-Entry 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 Ｍａｔｓｕｍｕｒａ and Kanda and Kanda (2005) (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 LineTime 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 The equilibrium of the subgame given αgiven 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 The equilibrium of the subgame given θgiven θ

Comparative Statistics for these four variablesQuestion:(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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Free entry equilibrium Free entry equilibrium P

Y

private firm's AC

private firm's residual demand

0private firm's output

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a decrease in θa decrease in θP

Y

private firm's AC

private firm's residual demand

0private firm's output

long run ~ reduction of the number of private firmslong run ~ reduction of the number of private firms

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Optimal θOptimal θθ =0 is optimal. ←marginal cost pricing restrict wasteful entries (excess entry theorem).

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IntuitionIntuition 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 choiceFirst 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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Free entry equilibrium Free entry equilibrium P

Y

AC

private firm's residual demand

0private firm's output

MC

public firm's output

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SummarySummaryEffect of Privatization

CSCS PSPS TSTS

exogenous exogenous number of number of firmsfirms

decreasedecrease increaseincrease ambiguousambiguous

free entryfree entry unchangedunchanged ambiguousambiguousdecrease if decrease if the public the public firm’s profit is firm’s profit is positivepositive

ambiguousambiguousdecrease if decrease if the public the public firm’s profit is firm’s profit is positivepositive

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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 PNTSuppose 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 PNTSuppose that one firm is nationalized. Suppose thatall 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 PNTWhen 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 PNTPrivatization 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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ModelModel

The same demand and cost functions as in Matsumura and Kanda ~increasing marginal costIntroducing 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 subsidyResults ~ Unit subsidy

Lemma 1.(i)∂qM

1 /∂s>(=)0 if P’’ < (=) 0; (ii)qM

1 (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 TaxResults ~ Entry-License Tax

Lemma 2. (i) ∂qM0 /∂T>0;(ii) ∂qM

1 /∂T>0; (iii)dnM/dT<0. Lemma 3. The optimal entry-license tax TM is positive.Lemma 4. (i) ∂qP

1 /∂T>0;(ii) dnP/dT <0. Lemma 5. The optimal entry-license tax TP is positive.Lemma 6. For all T, (i)qM

1(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 Results ~ Two-Part Tax-Subsidy PolicyPolicy

Proposition 4. In both mixed and private oligopolies, the first-best outcome is attained by the same tax-subsidy combination and the government budget is balanced.

Neutrality-Results.