Sep 19, 2017

(FIRE SALE EXTERNALITIES AND TOTAL SURPLUS-ENHANCING CARTELIZATIONS). THIS EXERCISE ENDOGENIZES…

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(fire sale externalities and total surplus-enhancing cartelizations). This exercise endogenizes the resale price P in the redeployability model of Section 4.3.1 (but with variable investment). The timing is recapped in Figure 4.11. The model is the variable-investment model, with a mass 1 of identical entrepreneurs. The representative entrepreneur and her project of endogenous size I are as in Section 4.3.1. In particular, with probability x the project is viable, and with probability 1−x the project is unproductive. The assets are then resold to “third parties” at price P. The shocks faced by individual firms (whether productive or not) are independent, and so in equilibrium a fraction x of firms remain productive, while a volume of assets J = (1 − x)I (where I is the representative entrepreneur’s investment) has become unproductive under their current ownership. The third parties (the buyers) have demand function J = D(P ), inverse demand function P = P (J), gross surplus function S(J) with S (J) = P, net surplus function Sn(P ) = S(J(P )) − PD(P ) with (Sn) = −J. Assume P (∞) = 0 and 1 > xρ0. (i) Compute the representative entrepreneur’s borrowing capacity and NPV. (ii) Suppose next that the entrepreneurs ex ante form a cartel and jointly agree that they will not sell more than a fraction z Check that this condition is not inconsistent with the stability of the equilibrium (the competitive equilibrium is stable if the mapping from aggregate investment I to individual investment i has slope greater than −1). (iii) Show that total (buyers’ and firms’) surplus can increase when z is set below 1.

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