EQUILIBRIUM MODELLING OF BENEFICIARY-PAYS TRANSMISSION CHARGES

PROF. ANDY PHILPOTT, DR. ANTHONY DOWNWARD

EPOC WINTER WORKSHOP 2013

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BACKGROUND / MOTIVATIONThe EA has proposed that, in order to fund current/future investments in the transmission grid, a beneficiary-pays scheme ought to be introduced.

The fundamental aim of this scheme is that those who benefit from the investment will be required to pay for the investment (in proportion to their benefit).

While the aim of this pricing mechanism may be fair, problems arise in actually being able to compute the benefits created by adding an asset to the grid.

The key proposal was that SPD would be run, with and without an asset (e.g. a transmission line), and the difference in an offers’ infra-marginal rent would be treated as the benefit.

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OVERVIEW• Beneficiary-pays Pricing• Computation of Rentals / Benefits• Incentives to Reduce Rentals / Benefits• Supply Function Modelling

• Uniform Pricing• Pay-as-bid Pricing

• Supply Function Equilibrium Examples• Single-node – tax on rentals• Two-node symmetric quadropoly – tax on

benefits• Conclusions

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BENEFICIARY-PAYS PRICING1. Run dispatch software with transmission asset

and record dispatch and price.2. Compute infra-marginal rental of agent , for

each .3. Re-run software with transmission asset

derated to represent previous (counterfactual) state, recording new dispatch and price.

4. Compute counterfactual rent of agent , for each .

5. Charge a proportion of benefits to agent . Suppose the cost of the asset is . Then the proportion of benefits paid by agent is:

Transmission Pricing Methodology Consultation Paper (2012)

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BENEFICIARY-PAYS PRICING

Solve 1 Solve 2 ChangeDemand A + B + C +D A B + C + D

Supply E + F + G B + E F + G – B

Transmission Pricing Methodology Consultation Paper (2012)

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INCENTIVES TO REDUCE CHARGESAfter the transmission pricing proposal was announced, there were concerns over the way the benefits would be computed.Particularly, the ‘profit’ of a firm would be assumed to infra-marginal rental.

Quantity (MW)

Price

P

D

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INCENTIVES TO REDUCE CHARGESThus, in a context where firms are charged based on infra-marginal rentals, there may be incentive to mark-up infra-marginal offers so as to reduce these rents.We will explore these incentives through a supply function equilibrium duopoly.

Quantity (MW)

Price

P

D Quantity (MW)

Price

P

D

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INCENTIVES TO REDUCE CHARGESEA TPM Consultation Presentation November 2012:

“Parties may be able to alter their offers to avoid the charge e.g. South Island generators could reduce their beneficiaries-pay charge for Pole 3 by offering as if only Pole 2 was available.

“To the extent parties can do this it would reveal the asset is not economically justified unless the SPD charge recovered costs from other beneficiaries e.g. costs of Pole 3 may be able to be recovered through the SPD charge from consumers.”

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SUPPLY FUNCTION AUCTIONAgents offer supply functions indicating how much they will supply at price . Let be the corresponding offer curve.There is a demand curve and a random demand shock .Demand realization occurs and all agents are paid:

a uniform price defined by the relation

for their respective dispatch quantity .

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SUPPLY FUNCTION AUCTION

Quantity (MW)

Price

∑S(p)D(p)

p

D(p)+h

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MARKET DISTRIBUTION FUNCTIONThe market distribution function defines the probability that a supplier is not fully dispatched if they offer the quantity at price .It can be interpreted as the measure of residual demand curves that pass below and to the left of the point .

Random residual demand curves faced by a supplier. Here is the probability of a curve being red.

Anderson and Philpott (2002), Wilson (1979)

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UNIFORM PRICE DISPATCH

The optimal offer curve for a supplier with profit facing a market distribution function maximizes:

Anderson and Philpott (2002)

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PAY-AS-BID DISPATCHWhen the market clears at quantity for a supplier under a particular demand realization, the supplier receives payoff:

The expected payout earned from a offer curve is then

Anderson, Holmberg and Philpott (2013)

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INFRAMARGINAL RENTALSWhen the market clears at quantity for a supplier at price then the regulator observes a rent of:

Given , the total expected rent earned by the curve is:

This is expected revenue from uniform pricing minus expected revenue from pay-as-bid pricing.

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MODELLING A TAX ON RENTALSSuppose that some fraction of these rentals is paid to the regulator as a tax. The after-tax total expected payoff will be:

is a convex combination of uniform price and pay-as-bid payoffs.

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SYMMETRIC DUOPOLYSuppose we examine a symmetric duopoly:• each firm has no costs, and capacity ;• there is no demand elasticity () and the demand

shock .

At the limit as , the equilibrium can be found to be:

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SYMMETRIC DUOPOLY

Symmetric equilibrium with no tax (black) and with 25% tax on observed profit (blue). Generators mark-up low priced offers.

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SYMMETRIC DUOPOLY

Welfare with 25% tax on observed rentals (times 4860).

Taking into account the tax on rentals, suppliers offer to improve their actual after-tax payoffs. A side-effect of this is a transfer of some wealth to consumers.

No Tax With Tax IncreaseSuppliers’ rentals 3,240 2,560 –680

Suppliers’ payoffs 6,480 6,344 –136

Tax 810 640 –170

Suppliers’ payoffs after tax 5,670 5,704 34

Consumer welfare 3,240 3,376 136

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TAX ON BENEFITSHowever, in the proposed transmission pricing methodology, the benefits would be computed based on the difference between the rentals in the current market, and those computed for a counterfactual without a transmission asset.In this context, the incentive to increase one’s offer curve is reduced.

Quantity (MW)

Price

P

DD’

P’

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INCENTIVES TO REDUCE CHARGESHowever, in the proposed transmission pricing methodology, the benefits would be computed based on the difference between the rentals in the current market, and those computed for a counterfactual without a transmission asset.In this context, the incentive to increase one’s offer curve is reduced.

Quantity (MW)

Price

P

DD’

P’

Quantity (MW)

Price

P

DD’

P’

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INCENTIVES TO REDUCE CHARGESHowever, in the proposed transmission pricing methodology, the benefits would be computed based on the difference between the rentals in the current market, and those computed for a counterfactual without a transmission asset.In this context, the incentive to increase one’s offer curve is reduced.

Quantity (MW)

Price

P

DD’

P’

Quantity (MW)

Price

P

DD’

P’

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INCENTIVES TO REDUCE CHARGESHowever, firms may be incentivised to mark-up supra-marginal offers.Consider the situation where a transmission investment has allowed additional supply into a node.• In the current market, a generator at that node is

unlikely to be dispatched for their final tranche;• whereas in the counter-factual they could be.

Quantity (MW)

Price

D(p)

p

pc

pc

counterfactual

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TRANSMISSION EXAMPLE

• Four (identical) suppliers.• Independent uniform demand shocks, and .• With a line capacity of the market distribution

function is .• A grid investment increases the capacity to ,

changing the market distribution function to .

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PREDICTED BEHAVIOUR?

The supplier benefit in a demand outcome giving , shown shaded for two candidate offer curves. The counterfactual (e.g. a lower capacity line) reduces dispatch to .

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TRANSMISSION EXAMPLEWe model line expansion as a change in market distribution function from to Recall that the benefits are the difference in rentals.

Thus, the expected benefit is:

So the expected payoff will be

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TRANSMISSION EQUILIBRIUMNow let us consider the symmetric equilibrium:• each firm has no costs, and capacity ;• there is no demand elasticity () and the demand

shock at each node is .

At the limit as , the equilibrium can be found to be:

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TRANSMISSION EQUILIBRIUMSupply function equilibrium when :

• with no benefits tax (black)• 25% benefits tax (blue)• 100% benefits tax (green)

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CONCLUSIONSOn the surface, if you consider a single dispatch point, clear incentives to avoid transmission charges exist.However, since the charge is based on benefits, the incentive to increase infra-marginal offers is limited.Ability of firms to mark-up in a supply function, with many demand realisations is restricted.Furthermore, competition restricts ability of firms to mark-up to reduce transmission charges.

Asymmetric playersDemand response

FUTURE EXTENSIONS