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# Incremental costs methodology

The web tool calculates the incremental cost of one pathway relative to another (as shown in the “costs in context” and “costs sensitivities” windows). This note outlines the methodology used to do this when:

• Based on point estimates for costs
• Based on cost ranges.

## Point estimates

The web tool presents cost results using the default costs (point estimates) unless the user adjusts the cost assumptions. In this instance, the incremental cost of one pathway over another is calculated very simply as the difference between the two pathways. For example, if “baseline” pathway costs £1,000 and the “abatement pathway” costs £1,200, then the incremental cost of the abatement pathway over and above the baseline is £200.

## Cost ranges

When there are cost ranges, the method for calculating incremental cost is more complex. To explain the approach we have used, we set out below a worked example.

For example, imagine there are only two technologies available – fossil fuels and renewables. The user decides the levels of these two technologies for 2050. Imagine our user creates two different pathways: “baseline” and “abatement pathway”. Both pathways have different quantities of fossil fuels and renewables. These example pathways are shown in table 1.

The price of fossil fuels and renewables in 2050 is uncertain. Assume these inputs have a price range as set out in table 2.

#### Figure 1: Diagram of incremental cost example inputs ### Total cost of pathways

Therefore it is possible the total cost of the baseline and abatement pathways in 2050 are uncertain. The total costs of both pathways are shown in table 3 and illustrated in figure 1.

### Incremental cost of pathways

There are three possible ways to work out the incremental cost of the “abatement pathway” over and above the “baseline”:

• Option 1: compare high, high and low, low costs
• Option 2: compare high, low costs
• Option 3: compare best, worst
 Option 1: compare high, high and low, low costs Incremental cost of “abatement pathway” over “baseline” = (X – A) to (Y – B) This is £160 to £640.
 Option 2: compare high, low costs Incremental cost of “abatement pathway” over “baseline” = (X – B) to (Y – A) This is - £880 to £1680.
 Option 3: compare best, worst Lower end of incremental cost = (W + P) – (D + E) £760 - £920 = - £160 Upper end of incremental cost = (V + Q) – (C + F) £1640 - £680 = £960 Final answer: - £160 to £960.

#### Further explanation of option 3

Option 3 (compare best, worst case) is quite complicated so needs more explanation. Using this approach, the incremental cost of the abatement pathway over the baseline is worked out by comparing the incremental costs when:

• prices are favourable to the abatement pathway
• prices are favourable to the baseline.

Table 4 shows the workings behind this calculation.

The abatement pathway has the most favourable outcome (lowest total cost) relative to the baseline when:

• Fossil fuel prices are high (because £400 (W) Vs £800 (D) is cheaper than £80 (V) Vs £160 (C))
• Renewable prices are low (because £360 (P) Vs £120 (E) is relatively better than £1560 (Q) Vs £520 (F)).

The baseline has the most favourable outcome (lowest total cost) relative to the abatement scenario when:

• Fossil fuel prices are low (because £160 ( C) Vs £80 (V) is relatively better than £800 (D) Vs £400 (W))
• Renewable prices are high (because £520 (F) Vs £1560 (Q) is cheaper than £120 (E) Vs £360 (P)).

Key distinguishing feature of option 3:

• Unique price combinations: the combination of prices used to compare any two pathways will be unique. Whereas options 1 and 2 work out incremental costs by assuming that all prices are high or all are low, option 3 varies the prices of every technology in order to work out the best and worse case for the abatement pathway. So using option 3, the baseline is not a “fixed comparator” because, even though quantities are fixed, prices are variable.

### Pros and cons of the 3 approaches

All three approaches are mathematically valid. The question is which one is most suitable for the purposes of the Costs Calculator?

Key advantage of options 1 and 2 are that they are simple and easy to understand.

However, when used in the Costs Calculator options 1 and 2 give some perverse results. To explain this, the results we obtained from our worked examples above are summarised again in table 5.

#### Figure 2: Diagram illustrating options for calculating incremental cost • Option 1 generates a narrow range, option 2 a very broad range, and option 3 is somewhere in between*. This result holds no matter what worked example you use.

The Costs Calculator web tool contains an incremental cost bar (see highlighted in screen shot). When experimenting with these approaches in the Costs Calculator web tool, we found that using option 1, incremental costs could “jump outside” this range depending on the technology input assumptions selected.

We also found that when using option 2, we found that the incremental cost contained some “impossible tails”. In other words, it was impossible to generate any combination of technology prices to reach the upper and lower ends of this range.

• However using option 3 we do not have these problems*. Using an appropriate combination of technology prices, it is possible to reach both ends of the incremental costs range. Also costs never jump outside it.

### Conclusion

One of the key functions of the Costs Calculator is experimenting with the impact of different technology prices on the total costs of pathways. Therefore it is crucial that our methodology for calculating incremental costs allows us to do this. Of the three methodologies, the only one which gives intuitive results when using it is option 3: compare best, worst. Therefore this is the one we have used.