értekezés - Budapesti Corvinus Egyetem

10. függelék - Az Adam-Dasgupta-Titman [2004] modell
Adam et al. [2004] consider a two-stage Cournot game, in which N identical firms receive
identical but uncertain cash flows at date 1, which they fully invest in productive capital
(k). 184 Cash flows are exposed to a common shock across the firms, therefore at date 0
each firm decides whether to completely hedge or to remain completely unhedged given
the hedging strategies of all other firms. That is, hedging is determined within a Nash
equilibrium. Each firm observes then the investment decisions of all other firms, followed
by the second stage of the game, where firms choose their outputs in the context of a
Cournot equilibrium. 185 The size of investment and the choice of output quantity are
interrelated, but unalike decisions. The level of investment (k) impacts the production cost
– an increase in k (a more capital intensive production) reduces both variable and marginal
production costs, hence increasing the productivity. The choice of output level in turn is
determined in an attempt to maximize expected profit. This necessitates, however, the
taking into account of the resulting cost function of production.
The equilibrium outputs and product price in the second stage game will depend on the
number of firms that chose not to hedge (m u ) in stage 1 and the realization of the random
variable w, which represents the cost shock to an unhedged firm. Hence, firms need to
optimize in this setting by trying to foresee in stage 1 the impact of their hedging decision
on their production costs, the hedging strategies of their competitors, and, consequently,
the optimal level of output quantity and price in the equilibrium.
An unhedged firm – in a rather hedged industry – faces relatively constant industry prices
but has random costs. This gives the firm the flexibility to cut output when its costs are
high and increase output when costs are low. A firm like this benefits from uncertainty in
[P(w) – w]. A hedged firm – in a less hedged industry –, on the other hand, faces constant
costs but random prices (assuming that prices here co-vary with costs as the majority of
firms in such industry pass through their cost shocks onto product prices). This provides
the hedged firm with an opportunity to produce more (less) when prices are high (low). A
firm that hedges, hence, benefits from uncertainty in output prices P(w).
184 Firms are assumed to be financially constrained, hence they invest all their cash flows.
180