Electricity market mergers with endogenous forward contracting

Abstract

We analyze the effects of electricity market mergers in an environment where firms endogenously choose their level of forward contracts prior to competing in the wholesale market. We apply our model to Alberta’s wholesale electricity market. Firms have an incentive to reduce their forward contract coverage in the more concentrated post-merger equilibrium. We demonstrate that endogenous forward contracting magnifies the price increasing impacts of mergers, resulting in larger reductions in consumer surplus. Current market screening procedures used to analyze electricity mergers consider firms’ pre-existing forward commitments. We illustrate that ignoring the endogenous nature of firms’ forward commitments can yield biased conclusions regarding the impacts of market structure changes such as mergers. In particular, we show that the price effects of mergers can be largely underestimated when forward contract quantities are held at pre-merger levels. Whether the profits of the merged firm are greater with fixed or endogenous forward quantities is ambiguous.

Appendices

Appendix 1: A proofs of formal conclusions

Proof of Lemma 1

(2) can be rewritten as:

$$\begin{aligned} a-bQ+bq_{i}^{f}=\frac{bq_{i}}{\beta _{i}}. \end{aligned}$$

(24)

Multiplying both sides of (24) by $\beta _{i}$ and summing across all firms yields:

$$\begin{aligned} B(a-bQ) + b\sum \beta _{i}q_{i}^{f} = bQ. \end{aligned}$$

(25)

(3) and (4) follows from (25) given $P(Q) = a - bQ$. (5) follows from (3) and (24).

Using (2), because b and $k_i$ are positive constants, each firm’s profit function is strictly concave in $q_i$:

$$\begin{aligned} \frac{\partial ^2 \pi _{i}(q_{i},q_{-i})}{\partial q_i^2} = -2b - \frac{1}{k_{i}} <0. \end{aligned}$$

$\square$

Proof of Lemma 2

Using (3)–(5) and that $\beta _i > 0\,\forall \,i = 1, 2, \ldots , N$, the following inequalities hold:

$$\begin{aligned}&\frac{\partial q_i}{\partial q_i^f} = \beta _i - \frac{\beta _i^2}{1+B} \mathop {=}\limits ^{s} 1 + B - \beta _i = 1 + \sum _{j\ne i} \beta _j>0; \\&\frac{\partial q_j}{\partial q_i^f} = \frac{-\beta _i \beta _j}{1+B}<0; \quad \frac{\partial Q}{\partial q_i^f} = \frac{\beta _i}{1+B} >0; \quad \text {and} \quad \frac{\partial P}{\partial q_i^f} = \frac{-b \beta _i}{1+B} <0. \end{aligned}$$

$\square$

Proof of Lemma 3

Using the marginal effects of forward contracting on spot market quantities identified in Lemma 2, (10) follows from (9).

Using (7) and from Lemma 2 $\frac{\partial q_i}{\partial q_i^f}$ and $\frac{\partial q_j}{\partial q_i^f}$ are independent of $q_i^f$ for all $i,j = 1, 2, \ldots , N$ with $i\ne j$ :

$$\begin{aligned} \frac{\partial ^2 \pi _{i}\left( q_{i}^{f}, q_{-i}^{f}\right) }{\partial {q_i^f}^2}= & {} P^\prime (Q)\frac{\partial q_{i}}{\partial q_{i}^{f}} + q_{i}P''(Q)\sum _{j=1}^{N}\frac{\partial q_{j}}{\partial q_{i}^{f}}\nonumber \\&+\,P'(Q)\, \frac{\partial q_{i}}{\partial q_{i}^{f}}\, \sum _{j=1}^{N}\frac{\partial q_{j}}{\partial q_{i}^{f}}-C_{i}''(\cdot )\left( \frac{\partial q_{i}}{\partial q_{i}^{f}}\right) ^2. \, \end{aligned}$$

(26)

Since $P'(Q) = - b<0$, $P''(Q) = 0$, $C_{i}''(\cdot ) = \frac{1}{k_i}>0$, and from Lemma 2 $\frac{\partial q_{i}}{\partial q_{i}^{f}}>0$ and $\sum _{j=1}^{N}\frac{\partial q_{j}}{\partial q_{i}^{f}} = \frac{\partial Q}{\partial q_{i}^{f}} >0$, (26) simplifies and satisfies the following inequality:

$$\begin{aligned} \frac{\partial q_{i}}{\partial q_{i}^{f}}\left[ P^\prime (Q) + P'(Q)\, \frac{\partial Q}{\partial q_{i}^{f}}-C_{i}''(\cdot )\, \frac{\partial q_{i}}{\partial q_{i}^{f}} \right] <0. \end{aligned}$$

(27)

$\square$

Proof of Proposition 1

It is without loss of generality to assume that firms 1 and 2 merge resulting in capital stock $k_M = k_1 + k_2$. Define $\beta _M = \frac{bk_M}{bk_M+1}$ and $\beta _j = \frac{b k _j}{b k_j +1}$ $\forall$ $j \ge 3$. Using (11), the difference between firm 1 and the merged firm’s proportion of forward contracted output satisfies:

$$\begin{aligned}&\frac{q_1^f}{q_1} - \frac{q_M^f}{q_M} = \frac{\sum _{j=2}^N \beta _j }{1+\sum _{j=2}^N \beta _j} - \frac{\sum _{j=3}^N \beta _j }{1+\sum _{j=3}^N \beta _j}> 0 \\&\quad \Rightarrow \left( \sum _{j=2}^N \beta _j \right) \left( 1+ \sum _{j=3}^N \beta _j \right) - \left( \sum _{j=3}^N \beta _j \right) \left( \sum _{j=2}^N \beta _j \right) = \left( \sum _{j=2}^N \beta _j \right) > 0. \end{aligned}$$

Similar reasoning applies for firm 2. Next, we illustrate that the non-merging firms reduce the proportion of output that is forward contracted. It is without loss of generality to focus on the non-merging firm 3. Denote ${q_3^f}^\prime$ and $q_3^\prime$ to be firm 3’s post-merger forward and spot market output, respectively. Using (11) and that $\beta _1+ \beta _2 - \beta _M >0$:

$$\begin{aligned} \frac{q_3^f}{q_3} - \frac{{q_3^f}^\prime }{q_3^\prime }= & {} \frac{\sum _{j\ne 3} \beta _j }{1+\sum _{j\ne 3} \beta _j} - \frac{\beta _M + \sum _{j=4}^N \beta _j }{1+\beta _M + \sum _{j=4}^N \beta _j }> 0\\\Rightarrow & {} \left( \sum _{j\ne 3} \beta _j \right) \left( 1+ \beta _M + \sum _{j = 4}^N \beta _j\right) - \left( \beta _M + \sum _{j=4}^N \beta _j \right) \left( 1+\sum _{j\ne 3} \beta _j \right)> 0\\\Rightarrow & {} \left( \sum _{j\ne 3} \beta _j \right) - \beta _M - \sum _{j=4}^N \beta _j = \beta _1 + \beta _2 - \beta _M > 0. \end{aligned}$$

$\square$

Proof of Lemma 4

Using (10) and that $\beta _i = \beta$ for all $i=1, 2, \ldots , N$ and $B = N \beta$:

$$\begin{aligned}&\left[ \frac{a}{b}\frac{\beta }{1+B}-\frac{\beta ^2 N\, q_{f}}{1+B}+\beta q^{f}\right] \, \left( \frac{-\beta ^2}{1+B}\right) + q^{f}\left( \beta - \frac{\beta ^{2}}{1+B}\right) =0 \nonumber \\&\quad \Rightarrow q^f \left( \frac{\beta }{1+B}\right) \left[ \frac{\beta ^3}{1+B}N(N-1)-\beta ^2(N-1)+1-B - \beta \right] \,= \beta ^3 \frac{a}{b} \left( \frac{N-1}{(1+B)^2}\right) .\nonumber \\&\quad \Rightarrow q^{f} = \frac{\frac{(N-1)}{1+B}\beta ^{2}\frac{a}{b}}{(1+B) - \beta + (N-1)\beta ^{2}(\frac{\beta N}{1+B} - 1)} = \frac{\frac{(N-1)}{1+NB}\beta ^{2}\frac{a}{b}}{1 +(N-1)\beta - \frac{(N-1)\beta ^{2}}{1+N\beta }} \nonumber \\&\quad \quad = \frac{(N-1) \frac{a}{b}}{(1+(N-1)\beta )(1+N\beta )-(N-1)} = \frac{(N-1) \frac{a}{b}}{ \frac{\left( \frac{1+Nbk}{1+bk}\right) \left( \frac{1+(N+1)bk}{1+bk}\right) }{\left( \frac{bk}{1+bk}\right) ^2} -(N-1)} \end{aligned}$$

(28)

$$\begin{aligned}&\quad \quad = \frac{(N-1) \frac{a}{b}}{ \left( N+ \frac{1}{bk}\right) \left( N+1+\frac{1}{bk} \right) -(N-1)} = \frac{(N-1) \frac{a}{b}}{ \left( N+ \frac{1}{bk}\right) ^2 + N + \frac{1}{bk} -(N-1)}. \end{aligned}$$

(29)

(14) follows from (29).

Using (14) and recognizing that $B = N \beta$ in this symmetric setting, (5) is simplified to:

$$\begin{aligned} q_{i}= & {} \frac{a}{b}\frac{\beta }{1+B}+q^f \beta \left[ 1 - \frac{\beta N}{1+B}\right] = \frac{a}{b}\frac{\beta }{1+B}+q^f \frac{\beta }{1+B}\nonumber \\= & {} \frac{a}{b}\frac{\beta }{1+B}+q^f \frac{\beta }{1+B} = \frac{a}{b} \frac{\beta }{1+N\beta }\left[ \frac{ \left( N+ \frac{1}{bk}\right) ^2 + N+\frac{1}{bk} }{\left( N+ \frac{1}{bk}\right) ^2 + (1+ \frac{1}{bk})}\right] \nonumber \\= & {} \frac{a}{b} \frac{1}{\frac{1}{\beta }+N}\left[ \frac{ \left( N+ \frac{1}{bk}\right) ^2 + N+\frac{1}{bk} }{\left( N+ \frac{1}{bk}\right) ^2 + (1+ \frac{1}{bk})}\right] \nonumber \\= & {} \frac{a}{b} \frac{1}{\frac{1+bk}{bk}+N}\left[ \frac{ \left( N+ \frac{1}{bk}\right) \left( N + \frac{1}{bk} +1 \right) }{\left( N+ \frac{1}{bk}\right) ^2 + (1+ \frac{1}{bk})}\right] . \end{aligned}$$

(30)

(12) follows from (30). Recognizing that $P(Q) = a - b N q$, (13) follows from (12). $\square$

Proof of Proposition 2

First, we illustrate that the spot market prices increase post-merger, holding forward contracting quantities at pre-merger levels. Define $q_{Pre}^f$ to be the symmetric pre-merger forward contracting level. Using (4) and that $B= N \beta _{NM}$ and $B_M = \beta _M + (N-2) \beta _{NM}$, the spot market prices pre- and post-merger, holding forward contracting quantities at pre-merger levels, equals:

$$\begin{aligned} P^{Pre}= & {} \left( \frac{1}{1+B} \right) \left( a - b q_{Pre}^f B\right) \quad \text {and}\nonumber \\ P^{Post}= & {} \left( \frac{1}{1+B_M} \right) \left( a - b q_{Pre}^f (\beta _M + B_M) \right) . \end{aligned}$$

(31)

Using (31) and that $B= N \beta _{NM}$, $B_M = \beta _M + (N-2) \beta _{NM}$, $\beta _{NM} = \frac{bk}{bk+1}$, and $\beta _M = \frac{2bk}{2bk+1}$:

$$\begin{aligned} P^{Post} - P^{Pre}= & {} \left( \frac{1}{1+B_M} \right) \left( a - b q_{Pre}^f (\beta _M + B_M) \right) - \left( \frac{1}{1+B} \right) \left( a - b q_{Pre}^f B\right)> 0\nonumber \\\Rightarrow & {} a(B-B_M) - b q_{Pre}^f \left[ (1+B) (\beta _M + B_M) - B(1+B_M) \right]> 0\nonumber \\\Rightarrow & {} a(2\beta _{NM} - \beta _M) - b q_{Pre}^f \left[ 2(\beta _M - \beta _{NM}) + N \beta _{NM} \beta _M \right]> 0\nonumber \\\Rightarrow & {} a \left( \frac{2(bk)^2}{(bk+1)(2bk+1)} \right) - b q_{Pre}^f \left[ \frac{2bk}{(2bk+1)(bk+1)} + \frac{2N (bk)^2}{(bk + 1) (2bk+1)}\right] > 0.\nonumber \\ \end{aligned}$$

(32)

Using (14), (32) simplifies:

$$\begin{aligned}&a\, bk - b \left( \frac{(N-1) \frac{a}{b}}{\left( N+ \frac{1}{bk}\right) ^2 + \left( 1 + \frac{1}{bk} \right) } \right) \left( 1+N bK \right)> 0\nonumber \\&\quad \Rightarrow N + 2 + N bk + \frac{1}{bk} + bk > 0. \end{aligned}$$

(33)

Because spot market prices are decreasing in total output Q, $P^{Post} - P^{Pre}>0$ implies that total output decreases post-merger, holding forward contracting quantities at pre-merger levels.

Second, we illustrate that total output post-merger is lower with endogenous forward contracts ($Q^{Post}_{Endog}$) compared to total output holding forward contracting quantities at pre-merger levels ($Q^{Post}_{Fixed}$). Using (3) and $B_M = \beta _M + (N-2) \beta _{NM}$, $Q^{Post}_{Endog} < Q^{Post}_{Fixed}$ if:

$$\begin{aligned}&\frac{a}{b} \frac{1}{1+B_M} + \frac{\beta _M q_M^f + (N-2) \beta _{NM} q_{NM}^f}{1+B_M}< \frac{a}{b} \frac{1}{1+B_M} + \frac{\left[ \beta _M + (N-2) \beta _{NM} \right] q_{Pre}^f}{1+B_M}\nonumber \\&\quad \Rightarrow \beta _M q_M^f + (N-2) \beta _{NM} q_{NM}^f < \left[ \beta _M + (N-2) \beta _{NM} \right] q_{Pre}^f. \text { } \end{aligned}$$

(34)

Using (10) and $B_M = \beta _M + (N-2) \beta _{NM}$, in the post-merger equilibrium the merged firms’ forward contract quantity satisfies:

$$\begin{aligned}&q_M^f \beta _M \left( 1 - \frac{\beta _M}{1+B_M} \right) = q_M \left( \frac{\beta _M \beta _{NM} (N-2) }{1+B_M} \right) \nonumber \\&\quad \Rightarrow \quad q_M^f (1+B_M - \beta _M) = q_M \beta _M (N-2). \end{aligned}$$

(35)

Using (5) and that $B_M = \beta _M + (N-2) \beta _{NM}$ and $\sum _{j \ne M} q_j^f = (N-2) q_{NM}^f$, the merged firms’ spot market quantity satisfies:

$$\begin{aligned} q_M= & {} \left( \frac{\beta _M}{1+B_M} \right) \left[ \frac{a}{b} - \beta _{NM} \sum _{j \ne M} q_j^f - \beta _M q_M^f + (1+B_M) q_M^f \right] \nonumber \\= & {} \left( \frac{\beta _M}{1+B_M} \right) \left[ \frac{a}{b} - \beta _{NM} (N-2) q_{NM}^f + q_{M}^f(1+(N-2)\beta _{NM}) \right] . \end{aligned}$$

(36)

Using (36), (35) simplifies:

$$\begin{aligned} q_M^f = \frac{ \beta _{NM} \beta _M (N-2) \left( \frac{a}{b} - \beta _{NM} (N-2) q_{NM}^f \right) }{\left( 1 +(N-2) \beta _{NM} \right) \left( 1+ \beta _M + (N-2) \beta _{NM} - (N-2) \beta _{NM} \beta _M \right) }. \end{aligned}$$

(37)

Using (10) and $B_M = \beta _M + (N-2) \beta _{NM}$, in the post-merger equilibrium a non-merging firm’s forward contract quantity satisfies:

$$\begin{aligned}&q_{NM}^f \left( 1 - \frac{\beta _{NM}}{1+B_M} \right) = q_{NM} \left( \frac{ \beta _{NM} (N-3) + \beta _M }{1+B_M} \right) \nonumber \\&\quad \Rightarrow q_{NM}^f (1+B_M - \beta _{NM}) = q_{NM} \left( \beta _{NM}(N-3) + \beta _M \right) . \end{aligned}$$

(38)

Using (5) and that $B_M = \beta _M + (N-2) \beta _{NM}$ and $q_j^f = q_{NM}^f$ for all $j \ne M$, a non-merging firm’s spot market quantity satisfies:

$$\begin{aligned} q_{NM}= & {} \left( \frac{\beta _{NM}}{1+B_M} \right) \left[ \frac{a}{b} - \beta _{NM} \sum _{j \ne M} q_j^f - \beta _M q_M^f + (1+B_M) q_{NM}^f \right] \nonumber \\= & {} \left( \frac{\beta _{NM}}{1+B_M} \right) \left[ \frac{a}{b} - \beta _M q_M^f + q_{NM}^f(1+\beta _M) \right] . \end{aligned}$$

(39)

Using (39), (38) simplifies:

$$\begin{aligned} q_{NM}^f = \frac{ \beta _{NM} \left( (N-3) \beta _{NM}+\beta _M \right) \left( \frac{a}{b} - \beta _{M} q_{M}^f \right) }{\left( 1 +(N-3) \beta _{NM} + \beta _M \right) \left( 1+ \beta _M + (N-2) \beta _{NM} \right) - \left( (N-3) \beta _{NM} + \beta _M \right) \beta _{NM} (1+\beta _M)}. \nonumber \\ \end{aligned}$$

(40)

Using (37) and (40), the post-merger forward contract quantities satisfy:

$$\begin{aligned} q_{NM}^f= & {} \frac{\frac{a}{b} D (H- \beta _M G)}{H E - (N-2)\beta _M \beta _{NM} G D} \quad \text {and} \quad q_{M}^f = \frac{\frac{a}{b} G(E - \beta _{NM}(N-2)D)}{HE - (N-2)\beta _M \beta _{NM} G D }, \quad \text {where} \\ D\equiv & {} \beta _{NM} \left( (N-3) \beta _{NM} + \beta _M \right) ; \text { }\nonumber \\ E\equiv & {} \left( 1+ (N-3) \beta _{NM} + \beta _M \right) \left( 1+(N-2) \beta _{NM} + \beta _M \right) - \left( (N-3) \beta _{NM} + \beta _M \right) \beta _{NM} (1+\beta _M);\nonumber \\ G\equiv & {} \beta _{NM} \beta _M (N-2); \quad \text {and}\nonumber \end{aligned}$$

(41)

$$\begin{aligned} H\equiv & {} \left( 1+ (N-2) \beta _{NM}\right) \left( 1+ \beta _M + (N-2) \beta _{NM} - (N-2) \beta _{NM} \beta _M \right) . \text { } \end{aligned}$$

(42)

Using (28) and (42), (34) can be rewritten as:

$$\begin{aligned}&\frac{(N-2)\beta _{NM} D H + \beta _M G E - 2(N-2) \beta _M \beta _{NM} D G }{HE - (N-2)\beta _M \beta _{NM} G D} \nonumber \\&\quad < \frac{(N-1)\left( \beta _M + (N-2) \beta _{NM}\right) }{\left( 1+ (N-1) \beta _{NM} \right) \left( 1 + N \beta _{NM}\right) - (N-1) }. \end{aligned}$$

(43)

Using (42), that $\beta _{NM} = \frac{bk}{1+bk}$ and $\beta _M = \frac{2bk}{1+2bk}$, and using Mathematica to simplify the algebraic expression, (43) can be rewritten as:

$$\begin{aligned}&\frac{2bk(1+bk(3+N +2Nbk))}{(1+3bk+2(bk)^2)^3} \bigg \{ 2+ bk \bigg [ 6 + 7N + bk \bigg ( 2 +19N + 7N^2 + 4(bk)^3 \left[ N^2 + N -2 \right] \nonumber \\&\quad + 2(bk)^2 \left[ 2N^3 + N^2 + 9N -8\right] + 2(bk) \left[ N^3 + 8N^2 + 4N -1\right] \bigg ) \bigg ] \bigg \} > 0. \end{aligned}$$

(44)

(44) holds for all $N\ge 3$. Hence, $Q^{Post}_{Endog} < Q^{Post}_{Fixed}$. This implies that the price increasing impact of mergers is magnified in the endogenous forward contracting environment.

Third, price increases strictly reduce consumer surplus. The price effects illustrated above imply that consumer surplus is lower post-merger and the reduction in consumer surplus is larger when forward quantities are endogenous. $\square$

Proof of Proposition 3

Using (4)–(6), the merged firm’s profit with endogenous forward contracts:

$$\begin{aligned} \pi _M(q_M^f, q_{NM}^f) = \left[ \frac{a - b \left( \beta _M q_M^f + (N-2) \beta _{NM} q_{NM}^f \right) }{1 + B_M} \right] q_M - \frac{(q_M)^2}{2 k_M} \end{aligned}$$

(45)

where $k_M = 2k$, $B_M = (N-2) \beta _{NM} + \beta _M$, and

$$\begin{aligned} q_M = \frac{a}{b} \left( \frac{\beta _M}{1 + B_M} \right) - \beta _M \left[ \frac{(N-2) \beta _{NM} q_{NM}^f + \beta _M q_M^f}{1 + B_M} \right] + \beta _M q_M^f. \end{aligned}$$

Using (4)–(6), the merged firm’s profit with fixed pre-merger forward contracts:

$$\begin{aligned} \pi _M(\overline{q}^f) = \left[ \frac{a - b \left( 2\beta _M \overline{q}^f + (N-2) \beta _{NM} \overline{q}^f \right) }{1 + B_M} \right] q_M - \frac{(q_M)^2}{2 k_M} \end{aligned}$$

(46)

where $q_M = \frac{a}{b} \left( \frac{\beta _M}{1 + B_M} \right) - \beta _M \left[ \frac{(N-2) \beta _{NM} \overline{q}^f + 2 \beta _M \overline{q}^f}{1 + B_M} \right] + 2 \beta _M \overline{q}^f$.

Using $\overline{q}^f$, $q_{NM}^f$, and $q_{M}^f$ defined in (14) and (41) and (45), (46), and Mathematica to simplify the following expression:

$$\begin{aligned}&\pi _M(\overline{q}^f) - \pi _M(q_M^f, q_{NM}^f)> 0 \nonumber \\&\quad \Leftrightarrow 1 - N + bk (17 - 9 N - 6 N^2) + (bk)^2 (112 + 4 N - 68 N^2 - 15 N^3)\nonumber \\&\quad \quad +\, (bk)^3 (398 + 268 N - 237 N^2- 170 N^3 - 20 N^4) - (bk)^4 (-870 - 1206 N\nonumber \\&\qquad + 171 N^2 + 674 N^3 + 214 N^4 + 15 N^5) \nonumber \\&\quad \quad +\, (bk)^5 (1244 + 2738 N + 928 N^2 - 1227 N^3 - 830 N^4 - 145 N^5 - 6 N^6)\nonumber \\&\quad \quad +\, (bk)^7 (1125 + 2923 N+4281 N^2 + 1088 N^3 - 2005 N^4 - 1011 N^5 {-} 133 N^6 {-} 4 N^7) \nonumber \\&\quad \quad +\, 16 (bk)^{12} (4 - 8 N + 13 N^2 - 5 N^3 - 5 N^4 + 10 N^5 - 6 N^6 + N^7)\nonumber \\&\,\,\quad - (bk)^6 (-1269 - 3621 N - 3125 N^2\nonumber \\&\quad \quad +\, 854 N^3 + 1668 N^4 + 512 N^5+ 48 N^6 + N^7) + (bk)^8 (932 + 1846 N \nonumber \\&\,\,\quad + 2741 N^2 + 2576 N^3 - 827 N^4\nonumber \\&\quad \quad -\, 1416 N^5 - 231 N^6 + 6 N^7 + N^8) + 4 (bk)^{11} (44 - 20 N + 151 N^2 - 166 N^3\nonumber \\&\,\,\quad + 182 N^4 - 66 N^5 - 2 N^6 - 10 N^7 + 3 N^8)\nonumber \\&\quad \quad +\, 4 (bk)^{10} (76 + 188 N - 48 N^2 + 250 N^3 + 25 N^4 - 89 N^6 - 2 N^7 + 4 N^8)\nonumber \\&\quad \quad +\, (bk)^9 (688 + 924 N + 1333 N^2 + 1296 N^3 + 709 N^4 - 976 N^5 \nonumber \\&\quad \quad -\, 405 N^6 + 28 N^7 + 7 N^8) > 0. \end{aligned}$$

(47)

For a given $bk>0$, inequality (47) holds for a sufficiently large value on N. $\square$

Appendix 2: Marginal cost estimation

Data on natural gas unit heat rates were obtained from Alberta’s Market Surveillance Administrator (MSA), the Alberta Utility Commission, and the AESO. Coal unit heat rates were obtained from CASA (2004). Data on technology-specific variable O&M costs were obtained from the Energy Information Administration (EIA 2016). Hourly natural gas prices were obtained from Alberta’s Natural Gas Exchange. We use weekly coal prices from Wyoming’s Powder River Basin (PRB) from the Energy Information Administration to estimate the marginal cost of coal units in Alberta.⁵³ PRB coal is sub-bituminuous coal which is the primary coal used for electricity generation in Alberta. Further, PRB coal and Alberta’s sub-bituminuous coal have similar heat-rate contents (Alberta Energy, 2014). We adjusted the PRB coal prices and USD based variable O&M costs from USD to CAD using Bank of Canada exchange rates. The environmental compliance costs are analogous to those detailed in Brown and Olmstead (2017, forthcoming). We obtained asset-level generation capacity from MSA. Derated forced outage statistics were obtained from the North American Electric Reliability Corporation’s Generation Availability Data System Reports.

Appendix 3: 100% increase in price-elasticity of residual demand

Tables 13, 14 and 15 demonstrate that the key qualitative conclusions of our analysis are robust to a 100% increase in the average price-elasticity of residual demand.

Table 13 Actual versus estimated market outcomes—100% increase

Table 14 Merger effects: changes in average market prices—100% increase

Table 15 Percentage changes in combined profit of merging firms—100% increase