5 Benefit take-up
All the above discussion has made the implicit assumption that there is 100 per cent take-up of benefits by eligible individuals. However, suppose that there is a non-recoverable fixed cost of claiming benefits, and consider the simple case of a means-tested benefit with a single taper rate, combined with an income tax, also imposed at a fixed rate above the tax-free threshold corresponding to the earnings level where the benefit is exhausted. The basic budget constraint is shown as ABC in Figure 25. The line from the origin to point B indicates net wage income, excluding any benefit, although the individual is entitled to claim the benefit: hence the slope of B′B is equal to the gross wage rate.
The net income obtained by the individual after claiming the benefit is reduced by the fixed cost of claiming, so that the section AB drops down by a vertical distance equal to the cost of claiming. The new effective budget constraint is the line A′B′BC. For hours of work beyond the point B′ the individual is better off by not claiming the benefit because the reduced amount of benefit, as a result of means testing, is less than the fixed cost of claiming. Hence along the new range B′B, the individual neither claims the benefit nor earns enough to pay income taxation. The effect is to introduce a further kink in the effective budget constraint, in this case arising from the increase in the effective marginal tax rate (from zero along B′B to the income tax rate as the individual starts to pay income tax at B).
One possible resulting relationship between gross earnings and the wage rate is shown in Figure 26. In this case the individual jumps from working and receiving benefits along A′B′ to working and not claiming benefits, or paying income tax, along B′B. This is shown as the jump from J to K in Figure 26. Beyond this point the individual works, until reaching the kink where there is an associated horizontal section. There are other possibilities. For example, an indifference curve may simultaneously touch points A′ and B in Figure 26. This means that there is no range where the individual works and receives the means-tested benefit; take up is complete at the non-participation corner at A′. Or an indifference curve may be tangential to the constraint along A′B′ and touch the corner at B. In this case there is also no range where take-up is incomplete, though there is a range where the individual works and receives the benefit.
