Tariff-Rate Quotas : Difficult to model or plain simple?

The difficulty of reliably and accurately incorporating tariffrate quotas (TRQs) into trade models has received a lot of attention in recent years. As a result of the Uruguay Round of GATT negotiations, TRQs replaced an assortment of tariff and nontariff instruments in an effort to standardise trade barriers, and facilitate their future liberalisation. Understanding the nuances of TRQs is now particularly crucial for New Zealand because of the preferential access arrangements that New Zealand has for a number of products in highly protected markets such as the European Union, Japan, and the United States. It has been argued that TRQs are complex instruments and are difficult to model because for any trade flow between two countries, one of three regimes may be applicable : 1. The import quota may not be binding and the within-quota tariff applies; 2. The quota may be binding, the within-quota tariff applies, and a quota rent is created; or 3. Trade occurs over and above the quota, in which case an over-quota tariff applies (although, even in this regime, someone is still able to collect the quota rent on within-quota trade). But even this characterisation, which many claim is too complex to model, is a major simplification of reality. Bilateral preferences are ubiquitous, and such preferences are usually included in the determination of multilateral market access quotas. It is usual, therefore, that the TRQ instrument has several tiers to the quota schedule, plus a number of within and over-quota tariff rates applicable on either a bilateral or a multilateral basis. Further trade liberalisation creates something of a dilemma for New Zealand. Any decrease in over-quota tariffs and/or increase in quota levels potentially reduces the value of quota rents, many of which accrue to New Zealand due to the bilateral preferences. It is important, therefore, that New Zealand trade negotiators understand how much additional trade is required to offset the loss of New Zealands quota rents. Modelling trade in the presence of TRQs is the only way to ascertain this knowledge. The purpose of this paper is to show that complex TRQs can be modelled very easily and precisely. The only catch is that the model must be formulated as a complementarity problem rather than the more conventional linear or nonlinear optimisation problem. The concept will be demonstrated using a simple 3-region, single commodity spatial price equilibrium model of trade.Tariff-rate quota, trade modelling, mathematical programming, complementarity

Tolling, Capacity Selection and Equilibrium Problems with Equilibrium Constraints

An Equilibrium problem with an equilibrium constraint is a mathematical construct that can be applied to private competition in highway networks. In this paper we consider the problem of finding a Nash Equilibrium regarding competition in toll pricing on a network utilising 2 alternative algorithms. In the first algorithm, we utilise a Gauss Siedel fixed point approach based on the cutting constraint algorithm for toll pricing. In the second algorithm, we extend an existing sequential linear complementarity approach for finding Nash equilibrium subject to Wardrop Equilibrium constraints. Finally we consider how the equilibrium may change between the Nash competitive equilibrium and a collusive equilibrium where the two players co-operate to form the equivalent of a monopoly operation

An exact solution method for binary equilibrium problems with compensation and the power market uplift problem

We propose a novel method to find Nash equilibria in games with binary decision variables by including compensation payments and incentive-compatibility constraints from non-cooperative game theory directly into an optimization framework in lieu of using first order conditions of a linearization, or relaxation of integrality conditions. The reformulation offers a new approach to obtain and interpret dual variables to binary constraints using the benefit or loss from deviation rather than marginal relaxations. The method endogenizes the trade-off between overall (societal) efficiency and compensation payments necessary to align incentives of individual players. We provide existence results and conditions under which this problem can be solved as a mixed-binary linear program. We apply the solution approach to a stylized nodal power-market equilibrium problem with binary on-off decisions. This illustrative example shows that our approach yields an exact solution to the binary Nash game with compensation. We compare different implementations of actual market rules within our model, in particular constraints ensuring non-negative profits (no-loss rule) and restrictions on the compensation payments to non-dispatched generators. We discuss the resulting equilibria in terms of overall welfare, efficiency, and allocational equity

Using EPECs to model bilevel games in restructured electricity markets with locational prices

CWPE0619 (EPRG0602) Xinmin Hu and Daniel Ralph (Feb 2006) Using EPECs to model bilevel games in restructured electricity markets with locational prices We study a bilevel noncooperative game-theoretic model of electricity markets with locational marginal prices. Each player faces a bilevel optimization problem that we remodel as a mathematical program with equilibrium constraints, MPEC. This gives an EPEC, equilibrium problem with equilibrium constraints. We establish sufficient conditions for existence of pure strategy Nash equilibria for this class of bilevel games and give some applications. We show by examples the effect of network transmission limits, i.e. congestion, on existence of equilibria. Then we study, for more general EPECs, the weaker pure strategy concepts of local Nash and Nash stationary equilibria. We model the latter via complementarity problems, CPs. Finally, we present numerical examples of methods that attempt to find local Nash or Nash stationary equilibria of randomly generated electricity market games. The CP solver PATH is found to be rather effective in this context