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

In other words, if it is too cheap to restart 2 to expend effort, it may not be socially optimal toexpend any effort in the first period (other than the requisite start up costs). I 2 ≥ 0 guaranteesthat c > R + S.2. Ex-ante, the project must obtain non-negative net social value, or SV ( e FB1 , eFB 2) ≥ 0. Using theexpression for SV ( e FB1 , eFB 2) above, under the first-best effort, it is optimal to invest initially in theproject iff(R + S)2I 1 + I 2 ≤ (R + S) 2 8·c 3 − R + S2·c 2 + 1 I2 (R + S)2+ I 2· −c 2·c 2·c 2 + R + S.cFor e FB1≤ 1, it must also be the case that(R + S)−c(R + S)22·c 2 + I 2c(R + S)2≤ 1 ⇔ I 2 ≤ c − (R + S) +2·c.However, this constraint is never binding, because the constraints on e FB2 posit that I 2 ≤ (R + S) 2 /(2·c)and c ≥ (R + S).In sum, an interior first-best solution obtains ifR + S ≤ c ,(R + S)20 ≤ I 2 ≤ ,2·c(R + S)2I 1 + I 2 ≤ (R + S) 2 ·8·c 3 − R + S2·c 2 + 1 + I 2·cI22·c(R + S)2−2·c 2 + R + S.cA.2 Proof of Theorem 1Note first that a bailout is never optimal when π 2 ( 0, 0 ) = R 2 /(4·c) − I 2 ≥ 0, because the firm wouldrefinance the project in the absence of a government bailout, and taxes are purely distortionary.Thus,there is no bailout, and g ∗ = T ∗ 1 = T ∗ 2 = 0. The government would consider a bailout only if π 2( 0, 0 ) < 0.In Section 2, we showed that for a given (g, T 2 ), the optimal managerial effort in the reinvestment stageis e ∗ 2 = (R − T 2)/(2·c) and the firm’s continuation value at the reinvestment stage is 2 R − T2π ∗ 2 ( g, T 2 ) = + g − I 2 .4·cThus, the government must choose g ≥ I 2 − (R − T 2 ) 2 /(4·c) ≡ g c > 0 to make it worthwhile for the firmto continue.The expected government revenue in the reinvestment stage is e 2·T 2 = (R − T 2 )·T 2 /(2·c). Thus, theminimum cost of the bailout, net of government revenue, in the reinvestment stage to encourage thefirm to continue is 2 R − T2 R − T2 ·T2g c − e 2·T 2 = I 2 − −4·c 2·c31= I 2 − 14·c ·(R2 − T 2 2 ) ,