Relaxing Competition Through Speculation - Committing to a Negative Supply Slope

1. Relaxing Competition Through Speculation-Committing to a Negative Supply Slope Pär Holmberg (IFN, EPRG assoc) and Bert Willems (Tilburg) IAEE, 21 June 2011

2. Introduction • Trade of derivative/financial contracts is widespread • Firms manage risks • Market aggregate information • Derivatives is also a commitment device • Strategic contracting => firm influences outcome in spot market • Will it benefit competition? • Firms commit using a portfolio of call option contracts with a spectrum of strike prices. • Supply function competition in spot market as in wholesale electricity markets. (Klemperer & Meyer, 1989; Green & Newbery, 1992)

3. Summary of results • Firms commit to downward sloping (total)supply functions • Produce more when prices are low • => Competitors’ residual demand less elastic • => Competitors set higher prices • => Firm increases its profit • More demand uncertainty => less downward sloping supply • Contracts as commitment device • Sell forward contracts to commit to produce a lot at low prices • Buy portfolio of option contracts with spectrum of strike prices=> continuously reduces committed output as spot price increases.

4. Related results for other commitment devices • Delegation games: Shareholders decide whether managers use Bertrand or Cournot strategies • Playing Cournot is a dominant strategy (Singh and Vives, 1984) • Unless demand is very uncertain (Reisinger and Ressner, 2009) • Strategic investment • Zöttl (2010), firms invest in base-load, but not in peak capacity to commit to steep bid functions.

5. Introduction • Intuition • Model • Analysis • Conclusion

6. Why do firms commit to a negative slope? B. Downward sloping supply function A. Upward sloping supply function P P Total Demand Total Demand Competitor’s residual demand Competitor’s residual demand Firm’s supply Firm’s supply p Marginal Revenue Marginal Revenue p Q Q Competitor’s supply Competitor’s supply Firm sells same amount at higher price

7. Sell contracts => commitment • Sell forward contracts => firm commits to produce more (aggressive commitment) E.g. Wolak 2000, Bushnell et al. 2008, Newbery (1998), Green (1999). • Mechanism • Contract quantity is sunk • Firms maximize profit on the remainder of demand • => Lower price and higher production P Demand Contracted quantity Marginal Revenue p Q Q Total Production

8. How do firms commit to a downward sloping supply? P • Make contract position a function of the price • Large for low prices (aggressive commitment) • Small for high price (soft commitment) • Can be achieved by • sell forward contracts • buy portfolio of call options with spectrum of strike prices. Contracted quantity at p0 (contracts with strike price below p0) p0 ∆p ∆x Slope ∆x/∆p= density of options with strike price at p0 X

9. Introduction • Intuition • Model • Analysis • Conclusion

10. Set up Two stage oligopoly Firms simultaneously choose a portfolio of physical option contracts with a spectrum of strike prices, Xi(p). Firms simultaneously bid a supply function Qi(p) - Xi(p) in the spot market • Assumptions • Counterparty arbitrage perfectly between spot and contract market => Price of contracts • Uncertain demand is realized after firms bid in the spot market • Firms observe each other’s contract positions after stage 1 • Firms have no production costs • Extension of Allaz & Vila (1993), Newbery (1998), Green (1999), Chao & Wilson (2005)

11. Introduction • Intuition • Model • Analysis • Conclusion

12. Results 2nd Stage: Spot Market Equilibrium • SFE equilibria are ex-post optimal, as in Klemperer & Meyer (1989) • For each shock firm i chooses a point where its marginal revenue in the spot market is equal to marginal cost (=0). 2nd Stage Equilibrium Net sales in the spot market Slope of the residual demand function

13. 1st Stage: Contracting Equilibrium • Firm 1 maximizes expected profit • Subject to the 2nd stage Nash equilibrium • For each firm we have an optimal control problem with state variables Q1, Q2, and ε Klemperer Meyer Equations Market Equilibrium

14. Results 1st stage: Contracting equilibrium • The Nash equilibrium is symmetric and given by: 1st Stage equilibrium Optimality Condition Klemperer Meyer Equation Market Equilibrium

15. Example with Analytical solution • Linear demand • 2nd order Pareto distributed demand shocks Price Maximal Demand Total Contracted quantity Total Production Quantity

16. Introduction • Intuition • Model • Analysis • Conclusion

17. Conclusion • Anti-competitive effect of speculation in financial markets • Firms speculate in order to commit to a negative supply slope and to soften competition • Price might even be above the monopoly price! • More strategic contracting when the number of firms is large and demand uncertainty is small • Close to delivery, demand uncertainty is small and options are more likely to be abused • In practice we expect the bidding strategy to be less pronounced as this strategy is risky • Results for other commitment devices with the same flexibilityare likely to be similar.