Technological Change in Electric Power Supply Chain: Quantifying Economic Bene(cid:28)ts of General Electric’s GT11N2 M

This paper examines General Electric’s new combined-cycle gas turbine GT11N2 M upgrade. The new technology provides operational (cid:29)exibility and promises output and cost e(cid:30)ciencies. To investigate the bene(cid:28)ts of this technology, we propose a power supply chain model and construct cost functions for generation and service and maintenance using actual market and (cid:28)rm level data. The upstream (cid:28)rm is General Electric (GE) who invests in GT11N2 generators. The investment results in innovation of GT11N2 M upgrade facilitating di(cid:27)erent operational modes and e(cid:30)ciencies. The downstream (cid:28)rm is TransAlta’s Sarnia plant which utilizes this new technology to produce and sell electricity to residential, small business, industrial, and wholesale market customers in Ontario, Canada. We quantify equilibrium prices and outputs under various e(cid:30)ciency rates in costs of fuel, service, and maintenance. We (cid:28)nd a large variation in electricity generation depending on which operational mode ((cid:16)Maximum Continuous Load(cid:17) or (cid:16)Performance(cid:17) or (cid:16)Lifetime(cid:17)) of GT11N2 M is selected. Under a mixed usage of all modes, we expect 44% output expansion to the industrial customers and 0.2% sales increase in the Ontario wholesale electricity market. Under this mode, GE’s price should go down by 0.4% due to fuel cost e(cid:30)ciency. If GE’s cost was $2.8 per MWh, GE should have asked Trans-Alta an average price of $5.822 per MWh for service and maintenance prior to the new technology. With the new technology, GE should charge $5.502 per MWh to Trans-Alta. While GE’s sales to wholesale market are almost stable, the sales to industrial customers increase nonlinearly in downstream e(cid:30)ciency rates. This shows that the amount of greenhouse gas emissions will be largely impacted by the choice of operational mode and how long it is used.


Introduction
In the era of energy revolution, countries have been shifting away from dirty generation resources toward cleaner energy in their electricity markets. In this regard, Ontario, Canada became the rst North American government to eliminate coal-red electricity generation and pave the way for greener electricity system.
1 The closure of coal-red generation plants has lead to more natural gasred generators and renewables such as wind and solar. The shift from coal to green energy sources is an important structural change in the Ontario electricity generation portfolio. The province is ambitious to be a leading green energy provider and the entire country has committed to have 90% of electricity generation coming from non-emitting energy sources by 2030.
2 After decommissioning of coal-red plants, the share of natural gas-based electricity generation has been increased. This is due to mitigate intermittency issues of wind and solar electricity and ll in energy gap created by the absence of coal generators. Coincidentally, right after coal plant phaseout in the province, in 2014, General Electric (GE) purchased Alstom's power and grid businesses including 11N2 gas turbines, which are being produced by GE with the nameplate GT11N2 since then. The initiatives of upgrading 11N2 gas-red generators started in 2004 and became operational in 2008. The goals of the new technology GT11N2 M upgrade are to increase power output, reduce costs of operations and management, and allow exible operation modes. According to GE, these goals have been achieved as the new upgrade has been operational worldwide and provided competitive electricity costs.
3 In this research, we study this technology in a supply chain framework and quantify market outcomes with and without GT11N2 M.
The main research question is that what would be the economic benets of GT11N2 M to consumers and rms? GE claims possible eciency gains from the new technology which opens up the following question: Could we measure the net impact of product and cost eciencies of GT11N2 M? How would eciency rates aect prices, outputs, and emissions? 1 https://www.ontario.ca/page/end-coal 2 The source is cleanenergycanada.ca 3 https://www.ge.com/power/services/gas-turbines/upgrades/gt11n2-m To address these questions we propose a simple vertical relations (supply chain) framework between upstream rm GE and downstream rm TransAlta (TA). GE is the supplier of GT11N2 generators and provides total plant solutions to TA via gas turbine eld services, turbine repairs and parts, and rotor life extensions. 4 This implies that GE impacts TA's electricity generation cost function. We in detail construct cost functions for power production and service and maintenance using actual market and rm level data. The upstream rm GE invests in GT11N2 generators.
The investment results in invention of GT11N2 M upgrade which facilitates dierent operational modes and eciencies. The downstream rm TransAlta's Sarnia (TA-Sarnia) plant utilizes the new technology to produce and sell electricity to residential, small business, industrial, and wholesale market customers in Ontario, Canada. We specify demand for electricity by these dierent customer segments. The cost and demand functions change for each time period. We use daily data because input prices (such as natural gas spot prices) are daily. We specically focus on 2014 data because GE gained ownership and management of GT11N2 generators in 2014. Each rm is a prot maximizer: GT optimally chooses its service and maintenance price of GT11N2 M generators and TA optimally chooses its production quantities for three customer groups. We use Stackelberg equilibrium solution to characterize market outcomes.
The main novelty of this research is to examine GT11N2 generators and determine their impact on supply chain outcomes. To our knowledge, this research topic has not been studied before.
Furthermore, we construct a detailed variable cost function for electricity production taking into account of costs of fuel, service and maintenance, emissions, and of generator characteristics including heat and (CO2, NOx) emissions rates. In determining electricity customers of TA-Sarnia plant, we examine characteristics of residential, industrial and wholesale market customers. We then formulate their demand for electricity produced by TA-Sarnia.
After we construct cost functions and obtain model parameters by using real data, we run the model for each and every day of 2014 to gure out the impact of GT11N2 M upgrade on prices and outputs.
First we consider two types of cost eciencies of GT11N2 M: upstream service and maintenance cost eciency experienced by GE and downstream fuel cost eciency experienced by TransAlta. We perturb eciency rates and report equilibrium upstream prices and downstream outputs. We nd 4 www.ge.com/power/services/gas-turbines that GE's prices decrease in downstream eciency rates at decreasing rates, while prices decrease linearly in upstream eciency. Price volatility increases in eciency rates. TA-Sarnia's sales to the Ontario wholesale market increase in fuel cost eciency rates at increasing rates. Higher eciency brings about more volatility in outputs. In some days (and hours), Trans-Alta does not sell electricity to the wholesale market but its outputs are positive in residential and business customer markets. This stems from low supply conditions at Trans-Alta combined with low prices in the wholesale market.
Second we assess GE's expected eciency rates over three operating modes of GT11N2 M upgrade. Each operating mode is associated with a dierent performance rating. However, in reality, it is not known to us how long and how often these modes are used per hour/day. To quantify the benets of having switchable operating modes, we consider four scenarios. The rst scenario assumes that only MCL-mode (Maximum Continuous Load) is used at all times; the second scenario supposes that only P-mode (Performance) is utilized; the third scenario involves L-mode (Lifetime) only; the fourth scenario, which we coin Mixed-mode, assumes that each mode is used at equal proportions for each and every day of 2014. In addition, we consider a benchmark case which supposes what if the new technology was not used at all. We nd that TA-Sarnia's ouput to industrial and wholesale customers are the largest under MCL mode, which is the most ecient mode in short-term. This mode is also favorable to TA-Sarnia and consumer groups as GE's prices are lower. Under the mixed-mode, we expect 44% output expansion in the industrial customers market and 0.2% output increase in the wholesale market. GE's price should go down by 0.4% due to fuel cost eciency under the mixed mode. Prior to the new technology, if GE's cost was $2.8 per MWh, then GE should have asked Trans-Alta an average price of $5.822 per MWh for service and maintenance. With the new technology, GE should charge Trans-Alta $5.502 per MWh. While outputs in wholesale market are almost stable, output variations in industrial customer market are nonlinear and signicant. This shows that amount of greenhouse gas emissions will be largely impacted by operations mode and how long it is used.
The structure of the paper is as follows. Section 2 introduces a simple supply chain model and characterizes equilibrium outcomes. Section 3 explains how the theoretical model can be applied to an electric power supply chain along with the structures of the Ontario wholesale electricity market and energy rms GE and TransAlta in the jurisdiction. Section 4 provides details of data to be used for constructing cost functions and electricity demand by dierent customer groups. Section 5 quanties the benets of GT11N2 M upgrade under various cost and output eciency rates. Section 6 briey summarizes the paper with key ndings.

Model
We propose a generic model of vertical relations which will be adopted to a power supply chain in the following section. A rm (supplier S) in upstream market provides an intermediate product (or critical component or part) to another rm (manufacturer M) in downstream, which produces a homogeneous nal product and sells it to a variety of consumer groups.
There are three types of consumers. Type 1 (T1) consumers buy q 1 amount from the manufacturer at a contract price p 1 , which is xed for the duration of contract. Type 2 (T2) consumers are price responsive and their inverse demand is p 2 = a − bq 2 . Type 3 (T3) consumers has a broader access to market and can buy the product from multiple producers in the wholesale market, in which the manufacturer is a competitive fringe. Specically, the manufacturer can sell its production q 3 at the wholesale market price p 3 , which is stochastic and changes over time t.
The upstream rm engages in research and development (R&D), which leads to technological change or process innovation in a new product design or product improvement/upgrade which results in cost eciency. The cost of producing intermediate good before R&D is f 0 q s , where q s is its output.
After R&D it is f 1 q s , where f 1 < f 0 and f = f 0 − f 1 > 0 is the unit cost reduction as a result of R&D.
The intermediate product cost function C s (q s ) = f 0 q s could have several interpretations. It could correspond to cost of producing a part or a component. Alternatively, it could represent variable cost of service and maintenance, if the product is service and maintenance. For example, in the industry application section below, f 0 will refer to operations and maintenance cost of producing a megawatt of electricity per hour from GE's GT11N2 natural gas-red generator. GE provides this service at a price w to downstream electricity producer TransAlta-Sarnia.
R&D investment cost for the supplier is D(I) = dI 2 /2, where I is the level of investment carried out in order to achieve an innovation.
The supplier executing R&D and achieving ecient product improvement maximizes its prot function which is where w is a decision variable and represents price of intermediate product. Alternatively, w could refer to price of service and maintenance for intermediate product provided by the supplier.
The manufacturer buys the intermediate product/service from the supplier, produces a nal product, and sells it to three consumer groups. It maximizes its prot function, where production cost C(.) is convex and twice-continuously dierentiable in output: In the application section, the rst term will represent cost of service and maintenance to the manufacturer and the second term will involve costs, such as fuel and emission costs, associated with electricity generation. Notation-wise, c 1 represents cost coecient after R&D and c 0 refers to cost coecient before R&D such that c 1 < c 0 and c = c 0 −c 1 > 0 measures cost eciency in downstream.
Given the input-output relations and the sequential nature of decision making between rms (the supplier choosing its price rst and then the manufacturer choosing its quantities), we employ Stackelberg equilibrium approach. We solve the model and obtain the following.
Proposition 1: The Stackelberg equilibrium outcomes with R&D in the upstream are the following: We will apply the vertical relations model developed above to rms operating in electric power sector in Ontario. Specically, upstream rm General Electric (GE) invests in generator development, produces and sells GT11N2 type natural gas-red generators to downstream rm TransAlta which uses these generators to produce and sell electricity to a variety of customer groups in Ontario.
We analyze how outputs and prices in the supply chain change with respect to technological change, called GT11N2 M upgrade. Before we execute our theoretical model to electric power rms, we will rst explain the Ontario wholesale electricity market structure, expose the features of electricity and natural gas prices, and then oer details about the rms GE and TransAlta.

Ontario Electricity Market
Ontario is a manufacturing hub of Canada, and its power market is distinct from the neighboring jurisdictions (such as regulated power markets of Manitoba and Quebec, and restructured electricity markets of New York and Michigan) in many aspects such as its portfolio of production technologies, market clearing mechanism, price volatility (Genc and Aydemir, 2017). As such, the Ontario market price volatility is the highest in the North America (Genc et al. 2015). The Independent Electricity System Operator (IESO) is the clearing-house of wholesale electricity market and manages electricity ow in transmission network. The IESO runs a pool-type real-time auction for every 5 minutes and matches demand and supply to determine real-time prices. However, power transactions are based on hourly price called Ontario Hourly Energy Price (HOEP), which is the average of 5 minute-prices of auctions in an hour. Distribution companies and large industrial consumers are subjected to HOEP. There is no day-ahead forward market and the share of bilateral contracts is small due to the Ontario market design.
The IESO publishes actual hourly production and available capacity data for all generators, which are available at its website (www.ieso.ca). The size of power producers are asymmetric and there are a few strategic rms facing competitive fringe suppliers. The rms with large capacities include Ontario Power Generation Inc (OPG), Bruce Nuclear Inc (Bruce), and Brookeld Renewable Energy Inc (Brookeld). They are considered as dominant rms which can exercise market power.
The rest of the rms including TransAlta are considered fringe suppliers (Genc and Reynolds, 2019).
To give a glimpse of Ontario wholesale prices, we plot daily prices in 2014 in Figure 1. Interestingly, the Ontario wholesale electricity market prices in the rst quarter were highly volatile and expensive compared to prices in the nal quarters. The polar vortex trapped cold air throughout the northeast resulted in cold temperatures and caused homeowners and businesses to ramp up their electricity demand. Natural gas reserves in storage depleted due to strong withdrawals which considerably increased natural gas prices. Gas inventories in the northeast hit the lowest levels in the past 5 years, so gas prices soared record highs. Therefore, higher gas prices caused higher electricity prices. In the gure, we also observe some negative electricity prices which stem from excess wind power injections causing more supply than demand.
<< Figure 1>> As TransAlta-Sarnia runs gas-red generators, natural gas prices are part of inputs costs for electricity generation. We use Henry Hub natural gas spot prices which are the benchmark for natural gas transactions in the North America including Ontario. Henry Hub spot prices are published daily.
Figure 2 displays daily Henry Hub natural gas spot prices. Between January and March, residential and commercial demand for natural gas has increased due to low temperatures, as explained above.
High demand combined with pipeline constraints and low gas reserves contributed to record-high prices. In summer, the need for air conditioning has gone down because of mild temperatures. This led to reduced demand for natural gas by the electricity producers. Therefore, natural gas storage increased from April through November. Consequently, natural gas prices fell during the rest of 2014.
<< Figure 2>> 3.2 The Manufacturer: TransAlta Sarnia The electricity producer TransAlta (www.TransAlta.com) has the holdings of a variety of generators with dierent energy sources in the North America. In Ontario, TransAlta operates several wind farms and natural gas-red plants with installed production capacity less than 1000 MW. In our study, we will focus on its largest natural gas-red plant in Sarnia. Sarnia is the largest city on Lake Huron and in Lambton County. TransAlta's Sarnia Regional Cogeneration Plant has been producing electricity since 2003. The plant is located on a large land (268-acre) and this generation facility is registered as TA-Sarnia in the Independent Electricity System Operator's (IESO's) list of generators.  The web-link is http://www.ec.gc.ca/air/default.asp?lang=En&n=D6C16D01-1. production capacities looks more like standard normal distribution and the variability of available production capacity is low, as expected.

The Supplier: General Electric
The purchase of Alstom's power assets including GT11N2 generators in 2014 was GE's largest-ever industrial acquisition. 8 In addition to redesigning turbine blades, GT11N2 M upgrade has aimed to provide i) exibility which translates into three switchable operating modes for maximum extended lifetime, extra power output and eciency; ii) reduced maintenance costs through extended service intervals of up to 48,000 equivalent operating hours; iii) performance up to 14 MW more power output and up to 1.9% gas turbine eciency. GE reports that this new upgrade has been operational worldwide and provided competitive electricity costs. 9 In the following section, we will tabulate the specications of GT11N2 M upgrade.

Data and Implementation
We use hourly and daily market and plant level data for several years provided by the system operator IESO and others. The Ontario market and generator-level data have been been implemented by 7 https://www.ge.com/news/press-releases/ge-completes-acquisition-alstom-power-and-grid-businesses 8 https://www.powerengineeringint.com/world-regions/europe/how-a-continuous-improvement-cycle-benetsturbine-customers/ 9 https://www.ge.com/power/services/gas-turbines/upgrades/gt11n2-m previous research. For example, Genc (2016) measured wholesale price elasticity of demand using market power indices, Genc and Aydemir (2017)  10 Table 2 shows these rates (which correspond to p 1 in the model) and their evolution over years. They are applied through periods of a day (on-peak, o-peak, mid-peak) that T1 consumers are subjected to. The rates change two times a year in summer and winter. In summer (May 1-October 31), o-peak time covers 7pm-7am, on-peak corresponds to 11am-5pm, and the rest is for mid-peak. In winter (Nov 1-April 30), o-peak time covers 7pm-7am, mid-peak corresponds to 11am-5pm, and the rest is for on-peak. In any year and season, all weekends and statutory holiday hours are treated o-peak period. In 2014 residential and small business customers paid 10.75 cents/kWh on average, as can be seen from Table 2.
An Ontarion household uses about 9,500 kWh of electricity per year which implies 1.08 kWh 10 See https://www.oeb.ca/rates-and-your-bill/electricity-rates/historical-electricity-rates Their demand is price responsive as they can use alternative energy sources and their own backup generators when needed, and have exibility to shift production over periods. Their inverse demand is p 2 = a − bq 2 , where the coecients (a, b) have to be predicted. Sarnia is home to 62 industrial facilities and reneries. Their industrial customers are mainly petro-chemical companies and reneries including ArLanxeo, Styrolution, Shell Canada, Imperial Oil, Suncor Energy (Sunoco) and Nova, which are charged behind the fence (negotiated and condential) electricity prices. 15 Because of the nature of condentiality of industrial customer prices, we have too little information to estimate their demand coecients. However, we oer the following procedure.
Given p 2 = a − bq 2 , the demand function is q 2 = a/b − p 2 /b. The maximum output at the Sarnia plant is 436 MWh and the maximum available production capacity is 510 MW in 2014. Because T1 customers consume about 95 MWh and the average Sarnia output is 187 MWh, we assume that the maximum quantity for T2 consumers should be around 187-95=92 MWh, which corresponds to an estimate of intercept a/b in demand equation. That is, 92 MWh is the maximum quantity demanded at price zero. Zero price is not anomaly in electricity markets and it can even drop below zero when production exceeds demand and network is constrained. This frequently happens during night times in the Ontario market.
We do not have data regarding how much electricity is actually sold to the industrial customers for each hour by TA-Sarnia. In fact, the actual price paid and quantity consumed by each industrial customer are condential information. According to the U.S. Energy Information Administration Survey of 2010, the petroleum rening industry uses around one third of the electricity production.

16
Therefore, we assume that the average demand quantity q 2 is equal to 62 MWh which is one third of the average production (187 MWh) in TA-Sarnia plant in 2014.
We assume that the average wholesale market price (the hourly Ontario energy price, HOEP) represents a proxy to the behind the fence pricing applied to industrial customers. This average hourly price in 2014 is 32.4 dollars per MWh. Given this assumption, the average price paid by industrial customers is equal to 32.4, denoted by p 2 . 15 https://www.sarnialambton.on.ca/infrastructure/utilities 16 https://www.eia.gov/totalenergy/data/monthly/pdf/ow/css_2019_energy.pdf This leads to our estimates of b = 1.08 and a = 99.36. Consequently, the inverse demand estimate for T2 customers is p 2 = 99.36 − 1.08q 2 , with demand q 2 = 341.4 − 8.6p 2 . This implies that price elasticity of demand is equal to -0.16 at the average production and it is equal to -0.48 at the average consumption and price. The industrial consumers' demand is inelastic, but they are still responding to price increases at a low rate. Note that this elasticity gure is a point elasticity estimate for the yearly average. This estimate may refer to long-run elasticity and it is in line with the elasticity gures reported in the literature (see Genc, 2016). While short-run elasticities are estimated to be very close to zero, long-run elasticities can be close to -0.5 in general.

Type 3 consumers
When TransAlta's production in Sarnia exceeds total demands of T1 and T2 consumers, it can sell the remaining quantity to the Ontario wholesale electricity market (T3) through transmission lines. Because TransAlta is a small producer compared to others in the wholesale market, it is treated as a price-taker (see Genc and Aydemir, 2017).
Let q denote the total output of TA-Sarnia. Then, the output sold to wholesale customers (T3 type) is q 3 = q − q 1 − q 2 , where q 1 is the quantity sold to T1 type consumers and q 2 is the output sold to T2 type consumers. Based on the average demand gures of T1 and T2 customers, the average TA-Sarnia output to wholesale market should be 187-95-62=30 MWh: the average production in 2014 minus the average T1 type consumption minus the average T2 type consumption. Therefore, we expect that 30 MWh should be the average quantity demanded by wholesale market customers (q 3 ). Consequently, T3 customers' price, denoted by p 3 , will be equal to the hourly Ontario energy price (HOEP): p 3 = HOEP .
To see the relationship between HOEP, load (Ontario market demand), and TA-Sarnia output, we run the following OLS regression using the actual hourly data.
where p 3,t corresponds to HOEP, L t denotes load , T AS t is the TA-Sarnia output, t refers to hour in 2014, and t = 1, ..., 8760. The OLS estimation yields, p 3,t = −131.681 + 0.00718L t + 0.1839T AS t , where all coecients are signicant with p-value less than 0.01. The positive sign in front of TA-Sarnia output shows that TA-Sarnia has an incentive to sell into the wholesale market as HOEP prices keep rising. Alternatively, because TA-Sarnia is a high cost natural gas-red plant, it will ask a high price for its output in the auction. The market price increases as it keeps producing more and more.

Electricity Cost Function before GT11N2 M
The upgrade of GT11N2 M is considered as a process innovation achieved by the supplier GE. As explained in the model section, TA-Sarnia's electricity production cost function is quadratic.
C(q 1 , q 2 , q 3 ) = w(q 1 + q 2 + q 3 ) + c 0 (q 2 1 + q 2 2 + q 2 3 ) holds before the upgrade and C(q 1 , q 2 , q 3 ) = w(q 1 + q 2 + q 3 ) + c 1 (q 2 1 + q 2 2 + q 2 3 ) holds after the upgrade, where c 1 = c 0 − c > 0 and c 0 > 0 is the cost coecient before the GT11N2 M upgrade and c > 0 is the cost reduction stemming from the upgrade. In electricity context, w may correspond to unit variable cost of maintenance service and/or parts, provided by the upstream generator maker GE to the generation rm TA-Sarnia. This is a valid assumption because GE not only sells GT11N2 generators to TA-Sarnia, but also provides generator service, maintenance, and parts.
17 The cost coecient c 0 may reect the input (natural gas) cost plus emissions costs which we will specify next in detail.
The marginal cost of electricity production is M C(q) = w + 2c 0 q for each unit of output q. The actual average output of TA-Sarnia is 187 MWh in 2014. When taking into account of maintenance, service, parts, fuel, and emissions costs, the marginal cost M C(q = 187) at the average production will be a very large number. Therefore, to have a reasonable marginal cost gure representative of actual cost of generation, we need to rescale the above production cost function. The characteristics of the cost function assumed in the model section will be the same as the one reformulated below.
The coecients λ 0 and λ 1 are scalers and may be chosen based on market conditions of a given power market. For the Ontario market and rms GE and TA-Sarnia, we assume that λ 1 = 1/2K.
The number 2 in the denominator is to remove the eect of quadratic term when the derivative is taken. K corresponds to maximum available capacity at the Sarnia plant which can vary every hour depending on start-up, shut-down, ramp-up, ramp-down, maintenance schedules, etc. It is usually lower than the installed capacity of 510 MW and the average gure in 2014 was 436 MW, 17 www.ge.com/power/services/gas-turbines as reported in Table 1. As for λ 0 , it may be chosen depending on actual costs and outputs gures.
For λ 0 = 10, we run the model and obtain that the average equilibrium outputs are 65.05 and 27.6 MWh in T2 and T3 markets, respectively. For λ 0 = 5 we obtain that they are 62.18 and 30.95 MWh, respectively.
Observe that with λ 0 = 5 the equilibrium output in T3 market is in the ballpark of what we have estimated for average sales to be in T3 market (187-95-62=30 MWh: the average production in 2014 minus the average T1 type consumption minus the average T2 type consumption). Furthermore, a large change in this scaler does not lead to drastic changes in equilibrium outcomes. For other jurisdictions, an alternative way to nd out this parameter is that λ 0 be heuristically optimized via simulations until outcomes get closer to actual ones, if actual data is available for T2 and T3 markets.
Given this reformulation, we compute that the marginal cost of electricity production at Sarnia will be M C(q = 187) = $33.44/M W h, when the average output (q) is 187 MWh, the average available capacity (K ) is 436 MW, the average fuel and emissions cost (c 0 ) is $43/MWh, the maintenance service price (w) is $3/MWh, and λ 0 equals 5. This is a reasonable cost estimate for an ecient natural gas-red generator in Ontario (see Genc andAydemir, 2016, andGenc et al., 2007 for generation costs in Ontario).
On 10/1/2014, the TA-Sarnia output hit its lowest production of 100 MWh while its available costs are normal as GT11N2 generators can be run at dierent modes with dierent eciency rates which ultimately impact cost of generation signicantly. We will explain these issues in Section 5.
Next we will calculate actual input costs. Specically, we will compute c 0 from available data.
Note that w representing maintenance service and/or parts price is a strategy and will be optimally chosen by the upstream generator maker GE. The marginal cost coecient c 0 changes as time t changes and is formulated as follows.
c 0 (t) = c f uel (t) + c SO 2 + c N Ox + c CO 2 , The heat rate that varies over natural gas generators of TA-Sarnia is denoted by HR GT 11N 2 . 18 The emissions costs are  c SO 2 = HR N G11N 2 * p SO 2 * SO 2 rate.
Because SO 2 emission rate of TA-Sarnia generators are zero, reported by Environment Canada, the unit SO2 cost will be zero: c SO 2 = 0. Similarly, because p CO 2 = 0 in 2014 c CO 2 = 0 holds.
However, NOx emission cost is positive. Genc and Aydemir (2017) For our model calibrations the parameter c 0 will vary daily as c f uel changes daily.

Electricity Cost Function after GT11N2 M
The upgrade to new technology results in process innovation and cost reduction. Because c 1 is the cost coecient after the product upgrade and c 0 is the cost coecient before the upgrade, c 1 < c 0 holds and c = c 0 − c 1 > 0 is the generation cost eciency rate stemming from R&D. Specically, the total cost function with the new technology turns out to be C(q 1 , q 2 , q 3 ) = λ 0 w(q 1 + q 2 + q 3 ) + λ 1 c 1 (q 2 1 + q 2 2 + q 2 3 ).
In Section 5, we will examine how dierent cost eciency rates impact market outcomes.

Maintenance and Service Cost Function
The upstream generator maker GE provides service and maintenance of GT11N2 generators. As explained in the model section, the cost of maintenance and service is linear which is C s (q s ) = f 0 q s , where f 0 > 0 is the marginal cost per MWh before the GT11N2 upgrade.
The service and maintenance cost function after the upgrade will be C s (q s ) = f 1 q s ,

Eciency Rates of GT11N2 M
GE has redesigned turbine blades and come up with state-of-the-art turbine aerodynamics and cooling with GT11N2 M upgrade. This new technology provides switchable operating modes for maximum extended lifetime, extra power output, and eciency. It is also aimed to reduce variable service and maintenance costs, production costs, and emissions. GE states that this new upgrade has been contributing to competitive electricity costs. In the following table, we display the operating modes and eciency rates. 20 MCL (Maximum Continuous Load)-mode is optimized for peak demands, is associated with inspection (of hot gas path casing-the core) for intervals of 24,000 EOH (equivalent operations hours), and exhibits signicantly increased combined-cycle power and eciency. P (Performance)mode is optimized for performance and lifetime, is associated with inspection intervals of 36,000 EOH, and showcases increased combined-cycle power and eciency. L (Lifetime)-mode is optimized 20 https://www.ge.com/power/services/gas-turbines/upgrades/gt11n2-m for simple cycle applications which are suitable for low energy demand situations, corresponds to signicantly extended inspection intervals of 48,000 EOH, and provides GT (gas turbine) power and eciency. All these modes should lead to reduced CO2 emissions per MWh, and hence lower fuel costs, higher revenues, and reduced environmental impact.
Based on this table, it is clear that the new upgrade will reduce service and maintenance costs at TA-Sarnia plant, decrease cost of electricity generation, and improve air quality. However, neither GE nor Alstom does specically say how much cost savings will materialize from fuel (represented by c f uel in the model) and service and maintenance (represented by f in the model) per MWh electricity generation. In fact, the actual cost eciency rates should depend on factors such as age of GT11N2 generator, mode, time, ramp-up and -down rates, and actual output quantity. Therefore, we will arbitrarily assume several eciency rates in model calibrations to investigate how market outcomes will vary with respect to these rates. Specically, we will assume the eciency rates of f = 0%, 5%, 10%, 15%, 20%, 25% and c = 0%, 5%, 10%, 15%, 20%, 25%.
In Table 4 we display the model notation covering 19 parameters and 21 variables.

Objectives of TA-Sarnia and GE
In running the calibrations we have to consider production constraints and market conditions in Ontario in 2014. With the constraints, the objective functions are reformulated as follows. Before the upgrade, TA-Sarnia maximizes the following for each t = 1, 2, ..., 365 maxΠ T AS,t (.) = q 1,t p 1,t + q 2,t p 2,t (q 2,t ) + q 3,t p 3,t − λ 0 w t (q 1,t + q 2,t + q 3,t ) − λ 1,t c 0,t (q 2 1,t + q 2 2,t + q 2 3,t ) subject to q 1,t = 95, 0 ≤ q 2,t ≤ q 2,t , 0 ≤ q 3,t ≤ q 3,t , q 1,t + q 2,t + q 3,t = q T AS,t . Variables q 1 quantity sold to T 1 customers q 2 quantity sold to T 2 customers q 3 quantity sold to T 3 customers q total production in downstream q S production quantity in upstream w service/parts price chosen by GE I investment made by GE p 2 price charged to T 2 customers p 3 price charged to T 3 customers p t HOEP, hourly Ontario energy price Then GE maximizes its prot function for each day t of 2014, Π GE,t (.) = (q 1,t + q 2,t (w t ) + q 3,t (w t ))(w t − f 0 ) − D(I) Note that because T1 customer's price is xed and their demand is stable, it is assumed that TA-Sarnia plant delivers 95 MWh load to the residential consumers for each and every day of 2014.

Players Description
So q 1,t = 95 holds. In addition, we match the actual production of TA-Sarnia (q T AS,t ) to consumer demands in which T1 consumers are served rst, and then other consumer segments are served. In distributing the total output, we make sure that the outputs q 2,t and q 3,t are optimized and obey the non-negativity and maximum consumption constraints q 2,t and q 3,t in 2014.

Results
We calibrate the model to determine the impact of GT11N2 M upgrade on prices and outputs. Based on the ndings in Section 4, we use the following parameter values for all calibrations: a = 99.36, b = 1.08, λ 0 = 5, and f 0 = 2.8.
We run the model for each day of 2014 and report equilibrium price (w) for upstream rm GE with respect to cost eciency rates. In Table 6, w-f0 represents a benchmark case in which there is no cost saving from service and maintenance (f0) and GE's price is w; w-f5 corresponds to GE's price when 5% service and maintenance (S&M) cost saving occurs; w-f10 refers to GE's price in the case of 10% eciency in S&M; similarly others follow. Because f 0 = 2.8, 5% reduction corresponds to f5=2.66. Similarly,f10=2.52,f15=2.38,f20=2.24,and f25=2.1 hold at the assumed eciency rates.
The outcomes are reported in Table 6, where observe that the equilibrium S&M prices are highly volatile with minimum 1.184 and maximum 29.182 dollars per MWh. This price volatility stems from volatilities of downstream prices (in wholesale T3 market), costs of fuel (natural gas prices) and downstream available production capacities (of TA-Sarnia). In addition, S&M prices linearly Observe that equilibrium prices are non-linear in fuel cost eciency rates. Also, GE's price becomes more volatile as the eciency rate improves. The gap between minimum and maximum prices is the largest when eciency rate is 25%. Furthermore, for a given eciency rate, GE's charges higher prices under fuel and emission cost eciency than under service and maintenance cost eciency. Therefore, for a xed eciency rate, we claim that the upstream eciency (S&M cost savings), resulting in lower prices and higher outputs, provides more benets to the consumers, but the downstream eciency (fuel and emission cost savings), leading to higher prices and lower outputs, provides more benets rms and the environment. Table 7 presents TA-Sarnia's sales to the Ontario wholesale electricity market (T3) with respect to upstream and downstream eciency rates. In the rst part of Table 7, we observe how equilibrium outputs in T3 market change with respect to upstream cost eciency rates. In that q3-f0 represents the benchmark case in which there is no cost saving from service and maintenance (f0) and TA-Sarnia's output in T3 market is q3; q3-f5 corresponds to sales to T3 market in the case of 5% service and maintenance (S&M) cost saving; q3-f10 refers to output when 10% eciency in S&M happens; etc. The equilibrium downstream outputs are volatile due to supply conditions (represented by variability in capacity, cost, and wholesale price), with the minimum of 0 and the maximum of 41.854 per MWh, and the volatility increases in upstream cost eciency. TA-Sarnia increases its output to T3 market linearly as upstream cost eciency rate goes up linearly.
The second part of Table 7 exhibits distribution of T3 market outputs with respect to downstream cost eciency rates. The outputs increase in fuel cost eciency rates at increasing rates. However, compared to prices, the volatility is much higher and the minimum takes 0 and the maximum gets 41.96. The main reason for this wide output interval stems from the signicant changes in wholesale prices in the Ontario market.
In Table 8, we consider upstream and downstream cost eciencies simultaneously. The rst part of the table shows distribution of upstream prices as eciency rates vary. Specically, w-fc0% is the benchmark case when no cost eciencies are experienced; w-fc5% refers to GE's price when 5% upstream cost eciency (f=5%) and 5% downstream cost eciency (c=5%) take place. The most extreme case is w-fc25% which reects the lowest level of GE's prices when f=25% and c=25%. The prices decrease in eciency rates at decreasing rates, while the price volatility expands.
The second part of Table 8 shows distribution of TA-Sarnia's outputs in T3 market with respect to eciency rates. At the highest eciency gain (f=25% and c=25%) TA can sell 1.75 MWh more  Based on Table 4, we assume that there is no service and maintenance cost eciency in 2014

Expected benets of GT11N2 M
such that f = 0. One justication for this assumption is that the inspection intervals of these modes are 24,000 EOH (equivalent operations hours) for MCL-mode, 36,000 EOH for P-mode, and 48,000 EOH for L-mode. These operation hours for inspection together with the fact that there are 8760 For the mixed-mode, it should be 28.53 MWh, which is the average of these modes. These numbers represent output eciency gains over operating modes.
For downstream cost eciencies, we know from Table 4 that the fuel cost should go down 1.9%, 1.8%, 1.6%, and 1.77% for MCL, P, L, and Mixed modes, respectively.
Given these output and downstream cost eciency rates, we run the model for all days of 2014.
We report our ndings in Table 9, where q 2 and q 3 represent average outputs in T2 and T3 markets.
We also report output standard deviations and upstream GE's price and price standard deviations over the modes.
From TA-Sarnia's point of view, the most ecient generation mode in the short term is MCL. It can sell the highest output to both T2 and T3 markets. This mode is also preferred by the consumers as GE's average price is the lowest. Compared to the benchmark, which is the old technology, we expect that generation increase with the new technology in T2 market should be in the range of 19% (under L mode) to 66% (under MCL-mode). However, the more realistic gures should come from the Mixed-mode. Realistically, all modes should be used interchangeably during any given day because of electricity demand variability over the hours. Therefore, given the eciency gures in the Mixed-mode, we expect 44% generation expansion in T2 market and 0.2% output increase 21 On the other hand, it could be that the GT11N2 M generators were running for a long time, and they were scheduled for a service and maintenance in 2014. However, we would not know whether this happened or not. in T3 market. Under this mode, GE's price should go down by 0.4% due to downstream fuel cost eciency. Prior to the new technology, GE should ask Trans-Alta an average price of $5.822 per MWh for service and maintenance. With the new technology, under the mixed usage of all modes, GE should charge $5.502 per MWh to Trans-Alta. The outputs in T3 market are almost stable and GE's price changes over the modes are very small. However, the output variations in T2 market are nonlinear and signicant. This shows that the amount of greenhouse gas emissions will be largely impacted by the mode and how long it has been operational.

Conclusions
In this paper we have examined technological change in a power supply chain involving innovation of GT11N2 M generators. We have investigated economics benets of this new technology facilitating eciency, operational exibility, and durability. Specically, we study upstream eciency leading to cost reductions in service and maintenance experienced by General Electric and downstream eciency resulting in cost reductions in electricity generation and output expansion experienced by TransAlta-Sarnia plant. We have quantied the impact of possible and reported eciency rates on prices and consumptions over dierent customer segments.
To be able to measure eciency gains in service, maintenance, and generation, we have constructed cost functions in detail using market and rm level data. We have identied power consumer groups and formulated their demands for electricity. We have examined GT11N2 M's three switchable operation modes for exibility in power production, and compared it to old technology without having eciency, performance, and exibility features. Given these ingredients we have modeled vertical relations between General Electric and TransAlta-Sarnia, solved their strategic objective functions, and characterized equilibrium prices and outputs.
Qualitatively, we nd that equilibrium prices and outputs are non-linear in downstream (fuel cost) eciency rates, but linear in upstream (service and maintenance) cost eciencies. The outputs increase in fuel cost eciency rates at increasing rates, but higher eciency brings about more volatility in outputs. GE's prices decrease, but become more volatile as the eciency rates increase.
For a given eciency rate, GE's charges higher prices under fuel and emission cost eciency rates than under service and maintenance cost eciency rates. Consequently, for a xed eciency rate, we claim that the upstream eciency provides more benets to consumers, but the downstream eciency provides more benets rms and the environment.
Quantitatively, we have determined how eciency types and rates aect prices and outputs.
However, the actual impact of GT11N2 M's operational modes will depend on real-time demand conditions, supply and network constraints, as well as how long they will be used over time.

APPENDIX
Proof of Proposition 1: We solve the game backwards, starting with the manufacturer who maximizes its prot function to choose outputs for dierent consumers.
Given these strategies, the supplier maximizes the following prot function to choose its price. Π S = (q 1 +q 2 +q 3 )(w −f 1 )−dI 2 /2 subject to I min < I < I max . The constraint on the investment quantity is not critical, does not impact output choices, and implicitly implies a budget constraint on investment expenditures. ∂Π S ∂w = − 2(b + c 1 ) + c 1 2c 1 (b + c 1 ) (w − f 1 ) + (b + c 1 )(p 1 + p 3 − 2w) + c 1 (a − w) 2c 1 (b + c 1 ) = 0 which implies w = (p 1 + p 3 )(b + c 1 ) + f 1 (2b + 3c 1 ) + ac 1 4b + 6c 1 . This can be inserted into the manufacturer's strategies to obtain outputs shown in the proposition. Furthermore, the signs of second order conditions are all negative, implying that the price and output strategies maximize rms' prots. Ontario Wholesale Electricity Prices