A Model of Optimal Corporate Bailouts - Faculty of Business and ...

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A.8 Proof of Theorem 3Proof: The optimal bailout policy replaces the incumbent manager if and only if V n ≥ V o , or:∗2co·en 1e1·(R + S) −2+ (1 − e n 1 )·svn 2 − I1 ≥ e1·(R o + S) − co·eo 21 + (1 − e o 12)·svo 2 − I 1 .The left-hand side of the inequality is decreasing in c n (since T n 1 is increasing in cn ) and the right-handside is independent of c n , hence, there is a threshold ¯c such that V n ≥ V o for all c n ≤ ¯c. Furthermore,we have e n 1 > eo 1 and V n1 > V o when c n = c o , thus ¯c > c o .A.9 Proof of Theorem 4Proof: Lemma 1 continues to hold in the presence of general tax revenues, so T ∗ 2condition is satisfied, the government’s problem is given by:= 0. If the firm’s (IR)max V ∗ ∗= eT 11·(R + S) − 0.5·c·e∗21 + (1 − e∗ 1 )·sv 2 − I 1 − a·z,Imposing the (IC) conditions for managerial effort and, by Lemma 1, imposing the new budget-balancecondition (BB ′ ) with equality (i.e., z = g − R−T 12·c ·(g + T1 )), the government’s problem can be restatedas: R − T1R − 2 T1R − T1 R(3R + 4S)max V ∗ =(R + S) − 0.5c+ 1 −− I 2 − I 1T 1 2·c2·c2·c8c R − T1− a· g − ·(g + T 1 ) .2·cTaking the derivative of V ∗ with respect to T 1 yields:δV ∗ (R + S)/δT 1 = −2·c+ aR2·c − a2·c ·Setting this equal to zero and collecting terms yields:T ∗∗1+ (R − T 1)+4cI 2 − R24c(3+2a)R2−S + (a − 0.5)R +8c=0.5 + 2aR(3R + 4S)16c 2 − I 22·c− aT 1c .+ RS2·c − (1 + a)I 2.The second-order condition is δ 2 V ∗ /δT 2 ∗∗1< 0 so T1 maximizes V ∗ .Recall that T ∗ 1in Proposition 1 is the firm-level tax that fully funds the bailout when the government doesnot have access to general tax revenues (z = 0). It is straightforward to show that (i) T ∗∗1is increasingin a, (ii) T ∗∗∗∗1> 0 if a > a, (iii) T1 < T ∗ 1if a < a, and (iv) a < a. The comparative statics results followimmediately from the expression for T ∗∗1 . 36
BFiguresFigure 1: The Social Value Function (SV)1.00.8SV0.60.40.2First−BestGovernment Would Prefer Continuation(given unremediable internal agency issues)No GovermentG+FireFirm Will Continue By Itself0.00.0 0.2 0.4 0.6 0.8 1.0Parameters: S = 1, c = 2, I 1 = 0, I 2 = 0.1. Dashed lines apply in the absence of government. Solidlines apply in the presence of government. (Their dotted continuation lines are the inferior Laffersolution.) Blue lines apply in cases in which the manager is retained, red lines to cases in which themanager is fired.R37
Page 1 and 2: A Model of Optimal Corporate Bailou
Page 3 and 4: The U.S. sold almost half of its st
Page 5 and 6: As a practical matter for policy ma
Page 7 and 8: firms. 4 However, if government rea
Page 9 and 10: • A “restarted” project proce
Page 11 and 12: constraints, and budgetary constrai
Page 13 and 14: As long as the firm reinvests, sv
Page 15 and 16: In sum, when restarts are unprofita
Page 17 and 18: managers forced the firm into distr
Page 19 and 20: Consequently, when the optimal bail
Page 21 and 22: government bails out the firm optim
Page 23 and 24: expropriated in case of a bailout.
Page 25 and 26: 4.2 Government Funding Constraints
Page 27 and 28: incentives to invest ex ante. When
Page 29 and 30: immediately raises moral-hazard con
Page 31 and 32: In other words, if it is too cheap
Page 33 and 34: A.4 Proof of Lemma 2If the replacem
Page 35: Under this tax regime, however, it
Page 39: Figure 3: Change in Critical Level

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