Welfare effects of unbundling under different regulatory regimes in natural gas markets

Abstract

In this paper, we develop a theoretical model that enriches the literature on the pros and cons of ownership unbundling vis-à-vis lighter unbundling frameworks in the natural gas markets. For each regulatory framework, we compute equilibrium outcomes when an incumbent firm and a new entrant compete à la Cournot in the final gas market. We find that the entrant’s contracting conditions in the upstream market and the transmission tariff are key determinants of the market structure in the downstream gas market (both with ownership and with legal unbundling). We also study how the regulator must optimally set transmission tariffs in each of the two unbundling regimes. We conclude that welfare maximizing tariffs often require free access to the transmission network (in both regulatoy regimes). However, when the regulator aims at promoting the break-even of the regulated transmission system operator, the first-best tariff is unfeasible in both regimes. Hence, we study a more realistic set-up, in which the regulator’s action is constrained by the break-even of the regulated firm (the transmission system operator). In this set-up, we find that, for a given transmission tariff, final prices in the downstream market are always higher with ownership unbundling than with legal unbundling.

Appendix Proof of Proposition 3

The expression for total surplus, W(t) is given by

$$W(t)=\pi_{e}(t)+\pi_{i}(t)+CS(t)+\pi_{T}(t) $$

• 1. If 0≤p _e <p _g −μ + t:

  $$\begin{array}{@{}rcl@{}} W(t)&=&\frac{(p_{g}-p_{e}+\mu -t)^{2}}{4}+0+\frac{(p_{g}-p_{e}-t+\mu )^{2}}{8}+t\times \frac{p_{g}-p_{e}+\mu -t}{2}-F\\ &=&\frac{1}{8}(p_{g}-p_{e}+\mu -t)(3p_{g}-3p_{e}+3\mu +t)-F\\ \end{array} $$

  (20)

  Notice that, for p _e <p _g (which is holds in the domain we are considering), we have that total welfare is strictly decreasing in t, $\frac {dW}{dt}=\frac {p_{e}-p_{g}-t-\mu }{4}<0.$ Thus, for this domain of p _e , a regulator that does not care about the economic viability of the transmission operator, will optimally set t ^∗=0, and total surplus would be $W^{\ast }=\frac {3}{8}(p_{g}-p_{e}+\mu )^{2}-F$

• 2. If p _g −μ + t≤p _e <p _g :

  $$\begin{array}{@{}rcl@{}} W(t)&=& \frac{(2p_{g}-2p_{e}+\mu -t)^{2}}{9}+\frac{(p_{g}-p_{e}-\mu +t)^{2}}{9}+\frac{(p_{g}-p_{e}+2\mu -2t)^{2}}{18}\\ &&+t\times \frac{p_{g}-p_{e}+2\mu -2t}{3 }-F \\ &=& -\frac{2}{9}t^{2}-\frac{p_{g}-p_{e}+2\mu }{9}t+\frac{ 11(p_{g}-p_{e})^{2}+8\mu (p_{g}-p_{e}+\mu )}{18}-F \end{array} $$

  (21)

  with $\frac {dW}{dt}=-\frac {p_{g}-p_{e}+2(\mu +2t)}{9}<0.$ Thus, for this domain of p _e , the regulator will optimally choose the lowest possible tariff in this domain, i.e. t ^∗=0 and total surplus will be:

  $$W^{\ast }=\frac{11(p_{g}-p_{e})^{2}+8\mu (p_{g}-p_{e}+\mu )}{18}-F $$

• 3. If $p_{g}<p_{e}\leq p_{g}+\frac {\mu -t}{2}$:

  $$\begin{array}{@{}rcl@{}} W(t)&=& \frac{(2p_{g}-2p_{e}+\mu -t)^{2}}{9}+\frac{ -5{p_{e}^{2}}+5p_{e}(2p_{g}+\mu -t)-5p_{g}(p_{g}+\mu -t)+(\mu -t)^{2}}{9}\\ && +\frac{(p_{e}-p_{g}+2t-2\mu )^{2}}{18}+t\times \frac{p_{g}-p_{e}+2\mu -2t}{ 3}-F \\ &=& -\frac{2}{9}t^{2}-\frac{2(p_{e}-p_{g}+\mu )}{9}t+\frac{\mu (4\mu -p_{e}+p_{g})}{9}-\frac{(p_{e}-p_{g})^{2}}{18}-F \end{array} $$

  (22)

  Again, $\frac {dW}{dt}=-\frac {2(p_{e}-p_{g}+2t+\mu )}{9}<0.$ Thus, for this domain of p _e , the regulator chooses the lowest possible tariff, t ^∗=0 and total surplus is equal to:

  $$W^{\ast }=\frac{(2\mu -p_{e}+p_{g})(4\mu +p_{e}-p_{g})}{18}-F. $$

• 4. Finally, if $p_{e}>p_{g}+\frac {\mu -t}{2}$:

  $$W(t)=0+\frac{(\mu -t)^{2}}{4}+\frac{(\mu -t)^{2}}{8}+t\times \frac{\mu -t}{2} -F=\frac{(\mu -t)(3\mu +t)}{8}-F $$

As $\frac {dW}{dt}=-\frac {\mu +t}{4}<0$, we conclude that W is also decreasing in t for $p_{e}>p_{g}+\frac {\mu -t}{2}$. When t=0, the previous condition writes as $p_{e}>p_{g}+\frac {\mu }{2},$ implying 2p _g + μ−2p _e <0. Thus, also for this price domain, the regulator chooses the lowest possible value of t ^∗=0 and the (maximum) overall welfare is $W^{\ast }=\frac {3}{8}\mu ^{2}-F.$