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# 5.5 Measuring the equity benefit

Table 2 reproduces Table 1, but with the addition of some further information. For example, looking at the lowest income households (Council Tax band A), it was estimated that 81,000 households would benefit from the financial subsidy. With an average subsidy per household of £490, the total cost of the subsidy for those households would be £39.7 million.

The next line of the table shows an ‘equity weight’ for each of the bands of households. This weight is based in the theory of the diminishing marginal utility of income that you considered in Section 3.2. The weight is higher for the lower income households, reflecting the greater utility they derive from extra income, than it is for higher income households.

The total cost of the subsidy for each band of households is multiplied by the equity weight to calculate what is called the ‘equity weighted subsidy’. For example, for the Band A households, £39.7 million is multiplied by 2.25 to give an answer of £89.3 million for the equity-weighted subsidy.

The final step is to subtract the unweighted subsidy from the equity-weighted subsidy. The answer is the ‘net equity benefit’. For the Band A households, this is £49.6 million (which is £89.3 million minus £39.7 million).

The next activity will help you understand how economists use this answer to take the distribution of benefits (in this case) and/or costs into account when doing a CBA.

## Table 2 Expected impact of Flood Re on home insurance premiums by Council Tax band for households at higher risk of flooding

| A | B | C | D | E | F | G
--- | --- | --- | --- | --- | --- | --- | ---
Baseline: fully risk-reflective premium for combined buildings and contents insurance | £1,140 | £1,165 | £1,185 | £1,290 | £1,430 | £1,560 | £1,850
Flood Re: cap on flood-risk part of the premium | £210 | £210 | £246 | £276 | £330 | £408 | £540
Cost of other cover in home insurance plus insurer overheads and profit | £440 | £440 | £474 | £524 | £590 | £692 | £1,010
Flood Re scheme: expected premium for combined buildings and contents insurance | £650 | £650 | £720 | £800 | £920 | £1,100 | £1,550
Reduction in premium (financial subsidy) | £490 | £515 | £465 | £490 | £510 | £640 | £300
Number of households receiving the subsidy | 81,000 | 93,600 | 121,300 | 92,000 | 60,600 | 28,000 | 23,000
Aggregate financial subsidy, £ million | 39.7 | 48.2 | 56.4 | 45.1 |  | 12.9 | 6.9
Equity weight | 2.25 | 1.45 | 1.05 | 0.75 | 0.45 | 0.45 | 0.45
Equity weighted subsidy | 89.3 | 69.9 | 59.2 | 33.8 |  | 5.8 | 3.1
Net equity benefit | 49.6 | 21.7 | 2.8 | -11.3 |  | -7.1 | -3.8

Authors’ table using data from DEFRA (2013a, 2013b) [1] Band H (the highest-value homes) were excluded from the scheme as originally designed, but later included (DEFRA, 2013a; 2014).

## Activity 11 Calculating and interpreting the equity benefit

Allow 15 minutes for this activity

1. Using the method described in this section, calculate the equity benefit for households in Band E.

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### Answer

The answer is -£17.0 million. This is calculated as follows:

- Multiply the average subsidy (£510) by the number of eligible households (60,600). The gives the total cost of the subsidy to all households in Band E of £30.9 million.
- Multiply £30.9 million by the equity weight (0.45). This gives the equity-weighted subsidy of £5.8 million.
- Subtract the unweighted subsidy (£30.9 million) from the weighted subsidy (£5.8 million). The answer is -£17.0 million

2. Can you explain why the equity benefit for higher-income households is negative?

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### Answer

The equity benefit is a measure of the value society is deemed to put on the fairness or unfairness of the cross-subsidy to flood-risk households. The negative values for higher-income households are telling you that giving subsidies to wealthier people is considered to be an economic cost to society – in other words, those resources could be better used elsewhere in the economy. By contrast, the equity benefit to poorer households is positive.

3. What is the total equity benefit when you add together the equity benefit for all seven bands?

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### Answer

The total is £35.0 million. (This is 49.6 + 21.7 + 2.8 – 11.3 – 17.0 – 7.1 – 3.8). Balancing out the economic costs and benefits of the subsidy, the equity benefit is £35 million a year. This figure of £35.0 million is included in the CBA.

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