Budget Constraints

What is a Budget Constraint?

In our case, a budget constraint is a graph, or a table, which shows how the amount of income a family would have available to spend or save varies as their hours of work increase. An example should make this clear.

This is the default budget constraint for our single parent example family. In the graph gross earnings (at an assumed net wage of £4.95 per hour) is measured along the x-axis and net income - the amount the family would actually have to spend - is measured along the y-axis. Everything is measured in £s per week. With no taxes and benefits, and no other income, the line describing the relation would be a simple 45° line through the origin - an extra £1 earned would mean an extra £1 available for consumption.

Clearly, life ain't like that! The graph shows that, in fact, this family would have just under £120 per week net income if they earned nothing, just under £125 if they earned £5 and the same income if they earned £70 per week. Thereafter the graph:

• jumps down sharply (indicating a point where the family would actually lose is they earned slightly more);
• jumps up even more sharply (indicating a point where they stand to make a lump-sum gain for a small extra amount of work);
• smooths out a bit, then jumps up again;

These graphs may seem startling. They sometimes startle us! But they have been comprehensively checked and we believe them to be accurate, given our assumptions. If anything, real life is even more complicated than this.

Often, economists use the term "budget constraint" more generally than we do here, to mean a graph showing the maximum amount of one good that is affordable to a consumer, or a family, given the quantity of other goods being purchased. In our case, the two "goods" are consumption (i.e net income, measured along the y-axis), and leisure (measured negatively along the x-axis i.e. an extra hours work means one hour less leisure). The slope of the budget constraint then gives the trade-off between consumption and leisure. With no taxes and benefits, the slope would equal the gross wage rate (so if you "consume" an extra hour of leisure you lose one hour's wage worth of consumption). Plainly, the tax system makes the actual slope at times very different from this. For example, flat parts of the graph, with a 100% marginal tax rate, are areas where an extra hour of leisure is effectively a free good.

How Do You Interpret The Tables That Come With The Graph?

The tables attempt to explain exactly what's happening at each kink point in the graph. The model produces one table for each system. Again, these are best understood by example (this is the table corresponding to the graph above):

Original System

There is one table row for each point at which the graph changes it's slope. Each row hase five columns. From left to right, they are:

Gross Income

The x-axis quantity from the graph;

Net Income

The graph y-axis variable;

Hours of work (per week)

This is simply gross earnings divided by an assumed hourly wage rate (£4.94 per hour in this case).

The persons effective marginal tax rate.

The marginal tax rate answers the question: "if this person earned another £1, how much in total would the Government take away?". A marginal tax rate of 0% means they would want none of it, whilst 100% means they want all of it. Looking at rows 2 and 3 above, you can see that this family faces a marginal tax rate of 100% on gross earnings of between £5 and £70.13. This is because they would be eligible for Income Support (IS) at earnings below this £70.13, and IS is withdrawn £ for £ as income rises. Looking at row 3, you can see that income falls discretely by £4 at this point (this is because she would no longer be entitled to free school meals for her children). Marginal tax rate is hard to measure at such a point: it is in a sense minus infinity, since even a tiny increase in earnings at £70.13 would cause you to lose £4. So, instead, the table shows the pre- and post- change net income.

An explanation of what is changing at that point.

By and large, these should be self-explanatory. One point to note, however, concerns the withdrawal rates cited for means tested benefits. For Family Credit and Housing Benefits (Rent and Council Tax Rebates) these will usually be less than the actual withdrawal tapers for these benefits. This is because these entitlement to these benefits is calculated using post-tax income. So, for instance, someone receiving Family Credit (FC) whilst paying income tax at 24% and national insurance at 10% would, if she earned another £1, pay 24p income tax, 10p national insurance, but would (in the long run) lose 53.2p Family Credit, that is (£1 - 24p - 10p) x 70% , where the 70% is the FC taper. The FC withdrawal rate would be quoted as 53.2% in this case. Likewise for Housing Benefits where the income used is also net of Family Credit.

What Assumptions Do You Make In Drawing These Graphs?

A number of assumptions are implicitly made here, amongst which are:

Hourly Earnings are constant

On the one hand, this implies that there is no overtime and no bonus payments. On the other, it implies that people's earnings would indeed rise if they worked another hour. For many salaried people, including the present author, this is not the case.

All benefits are taken up, and all taxes are paid.

Generally, entitlement to means-tested benefits will fall as income rises. However, there is good evidence that families are less likely to claim small amounts of benefit than large ones. Consequently, net income of the family might be different from that shown in the model, because benefits might not be claimed. Likewise, small amounts of earnings are assumed always to be declared, and not to disappear into the "black economy".

All other Income is constant

Most importantly, the earnings of the other family member in a married couple is held constant. For two-earner couples, or the non-working spouse in a single earner couple, this generally means that they have enough income to be disqualified from means-tested benefits even at the zero hours point on the graph. So these graphs tend to be less kinky.

There is an additional problem with Family Credit. FC is paid unchanged for six months at a time, regardless of any changes in income. So effectively we are plotting a long-run position for those families who qualify for FC. (And probably also Housing Benefits, although the legal and practical position is less clear for these, and probably varies from place to place).

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