The first chapter, Open-Loop Equilibria and Perfect Competition in Option Exercise Games , a joint work with Professor Kerry Back, is concerned with the optimal exercise and valuation of growth options within a partial equilibrium setting. A finite number of firms invest irreversibly into production capacities. It is well known (see e.g. Dixit and Pindyck (1994)) that irreversibility creates an option-like feature and it is usually not optimal for a monopolistic firm to exercise its investment option when its option is 'at the money'. But what if there is more than one firm competing for market shares? Competing firms invest earlier in equilibrium. With the number of firms going to infinity, the value of the option of waiting to invest approaches zero. In the limit, investment is undertaken as soon as its net present value reaches zero. Our contribution is to provide a rigorous proof for the statement that the strategies in Grenadier (2002) – properly reinterpreted - form an open-loop equilibrium. As open loop strategies lack subgame perfectness, we further show that perfect competition forms a subgame perfect equilibrium already for two firms.
In general equilibrium, the central planner's problem is analogous to the monopolistic problem in partial equilibrium. The planner maximizes utility over all admissible investment paths just as a firm maximizes profits. So it is natural to hypothesize that there also exists an 'option premium of waiting to invest' for a welfare maximizing central planner. But how would a delay reconcile with perfect competition and zero profits for firms? This question is addressed in the second chapter within a stylized general equilibrium model with irreversible investment. While it is true that with a single consumption good there are no relative prices within a particular instant of time, i.e. there are no intra-period prices, prices can still be related on their intertemporal dimension. It are precisely the dynamics of intertemporal prices, i.e. interest rates and future prices, that reconcile investment delays with zero profits in the context of the model. Longer term interest rates and futures on wages contain the expected growth-effect of optimally exercised growth options, rendering current investment opportunities unprofitable whenever a delay is efficient. In this sense, the term-structure of future prices reflects the option premium of waiting and leads to optimal delay in investment. Interestingly, this mechanism is similar to what Keynes termed the 'speculative motive' for money demand and liquidity preference.
Thinking about Keynes' theory and the speculative motive in particular, naturally leads to questions linked to liquidity preference, such as “What exactly is a liquidity trap? The third and last chapter attempts to make one first step towards this direction by approaching a more elementary question. It asks: Why do people exchange real goods against a piece of paper that neither provides intrinsic utility nor (unlike in Keynes times) constitutes a claim on a real good such as gold? Why is money a safe asset whose value people (can) rely upon? In the model presented in Chapter 3 money is 'safe': Fiat money has strictly positive value in the unique trembling hand equilibrium. This holds as each bank note is both: a witness for the existence of some agent in the economy with debt, backed by collateral, and the only matter that allows the debtor to settle her debt. Debtors fear to lose the collateral and compete with each other for not defaulting. Hence they compete for money. This creates money demand and thereby ensures positive money value. As not only a single but all debtors in the economy demand money, idiosyncratic shocks to solvency wash out. This makes fiat money a safe asset
