Understanding Keynes on Income, Saving, and Investment.

Keynes covers these topics in chapter 6 of his General Theory. The chapter is very wordy and contains few examples – Keynes was not a good communicator of his ideas. This piece seeks to present his key ideas from chapter 6 in a more user friendly way so as to make them more accessible to a wider audience. A brief case study will be used.

Keynes’s model excludes the foreign sector and thus assumes UK firms operate within a closed economy. Apart from the business and possibly the household sector, Keynes’s model makes no explicit reference to other sectors of the UK economy, eg the government or financial sector.

However, Keynes is correct to make this apparent omission because the trading section of a firm’s traditional income statement is alone relevant to the determination of how much wealth has been created in a period. The remaining sections of a traditional income statement report the revenues associated with the other sectors of the economy, and merely show how the created wealth has been distributed among the factors of production. Keynes calls these remaining costs “factor costs”. These factor costs, eg wages, rent, taxes, interest, and dividends can be associated with suitably chosen sectors, eg households, government, financiers, and/or rentiers. Keynes concentrates on wealth creation, not on how the wealth is distributed between the other sectors. For this reason, this exposition starts with a traditional, widely used and understood trading account before developing it into a value added statement.

Consider the following consolidated trading accounts of the B2B and B2C sectors of the domestic economy. The trading accounts are prepared in traditional format which any accountant would instantly recognise.

Trading Accounts (£k)Consolidated
Purchases 01,000
Closing inventories+100+200
Cost of goods sold– 1001,200
Gross profit + 900+ 800

The purchases figures in trading accounts consist entirely of revenue expenditure, eg raw materials, goods for resale, etc. The purchases figure for the consolidated B2B sector is zero because the aggregate purchases of B2B firms will cancel against B2B sales revenue on consolidation. In other words, B2B firms will be selling and buying from each other and, in aggregate, the sector’s purchases and sales will cancel out to zero (unless they import). For this reason, only sales made to B2C firms will be recorded in the B2B sector’s consolidated account. This is why the sales revenue of the consolidated B2B sector is identical to the purchases of the B2C sector. These like items will cancel when the B2B sector is consolidated with the B2C sector. The following table shows the consolidation of the two sectors and the cancellation of the like items:

Trading Accounts (£k)Consolidated
AdjustmentB2B consolidated
with B2C
Revenue+ 1,000+ 2,000 – 1,000+ 2,000
200400– 600
Purchases 01,000+ 1,000 0
Closing inventories+ 100+ 200+ 300
Cost of goods sold1001,200+ 1,000– 300
Gross profit + 900+ 800+ 1,700

The above trading accounts can be rearranged so that value added is yielded by the bottom line in place of gross profit. Value Added is what Keynes deemed, in the context of national income accounting, to be income (Y). He rejects using the bottom line (the net profit or net income) of traditional income statements as a relevant measure of income in the context of national income accounting. This is because net profit is calculated after deducting factor costs from gross profit. The factor costs are the revenue of the other sectors of the economy and so will cancel out on consolidation.

The value added statements of the two business sectors are shown below.

Code DescriptionConsolidated
B2B (£k)
B2C (£k)
ARevenue+ 1,000+ 2,000
A1Purchases 0– 1,000
IInventory adjustment100 200
Y Value Added+ 900+ 800

The letters appearing under the code heading are those used by Keynes in his General Theory to denote either a) the category into which an item falls or b) as a specific identifier. For example, closing and opening inventories both fall into the “Investment” category and hence have an I against them. A and A1 are specific identifiers and denote Revenue and Purchases respectively. The inventory adjustment ensures that it is materials used, or goods sold, that is set against revenue, not the purchases figure. So for the B2C sector, raw materials used, or goods sold, £1,200k has been set against revenue.

Value Added Statements can be consolidated using the same rules as with the trading account, i.e., cancel linked items and then aggregate the remaining items, as shown below.

Code DescriptionConsolidated
B2B (£k)
B2C (£k)
Adjustment (£k)Consolidated Value
Added Statement (£k)
ARevenue+ 1,000+ 2,000– 1,000+ 2,000
A1Purchases 0– 1,000+ 1,0000
IInventory adjustment100 200 300
YValue Added+ 900+ 800+ 1,700

Purchases (A1)

In a traditional trading account, the purchases figure (A1) will consist entirely of revenue items. An inventory adjustment is usually required to ensure that unused materials, or unsold goods, from the previous period are set against the current period’s revenue. The inventory adjustment also ensures that unused materials or unsold goods in the current period are carried over to the immediately following period.

Keynes, however, in his General Theory, includes both capital and revenue items within A1. So for Keynes, if a firm makes a one-off purchase of capital equipment from another firm then Keynes would designate the transaction as (A) by the seller and as (A1) by the purchaser. When capital items are included in A1, the purchasing firm’s value added will be understated because A1 will be overstated. An adjustment is necessary to correct for this and this is done via a capital adjustment which will show the part of A1 which is capital expenditure as investment (I).

Capital Adjustments

In his General Theory, Keynes brings up the need to recognise the deterioration of the entrepreneur’s capital equipment in the calculation of value added. He proposes what, in practice, might be an over elaborate calculation for capital consumption. However, his formula is elegant because it also yields how much capital formation has taken place. This calculation is hopefully explained correctly below.

Keynes’s calculation seeks to compare the theoretical value of capital equipment which has been hypothetically mothballed, to the actual value of the same equipment after it has been used in production. His premise is that capital equipment used in production loses value due to use and should have a lower value than identical, well maintained capital equipment that has hypothetically lain idle in the period. His method for determining the capital adjustment, using his notation, is to apply the following formula:

(G – B) – G

where G represents the theoretical end value of capital equipment that has been idle for the period after B has been spent improving it or keeping it in good working condition, and

where G is the actual end value of capital equipment after it has been used in production in the period.

G – B enables the opening valuation of the capital equipment to be determined.

Three possible cases may arise and Keynes’s formula is used below to illustrate.

Case 1: Capital consumption occurs

This occurs when (G – B) > G.

Put simply, this means the closing valuation of the capital equipment is less then the opening valuation. This indicates depreciation through use has occurred.


The theoretical end value (G) of idle equipment was £300,000 after spending £100,000 on idle equipment maintenance (B) during the period. The actual value (G) at the period end was £175,000.

The first step is to insert the relevant figures on the left hand section of the table. The theoretical opening balance can thereby be obtained and transferred to the right side section. The actual closing valuation (given) is then inserted. The capital adjustment (shown in red) is the difference between the actual closing valuation and the theoretical opening valuation.

Equipment idle£kEquipment used£k
Opening valuation (G – B)200Opening valuation200
Maintenance expenditure (B)100Capital consumption(25)
closing valuation (G)
closing valuation (G)

So in case 1 capital consumption is £25,000 and this amount should be charged to the entrepreneur’s value added statement. It represents disinvestment and should be coded with an I. The accountant’s production unit basis for depreciation may suffice as a reasonable proxy measure consistent with Keynes’s conception of capital consumption.

Case 2: No capital consumption or formation occurs

This occurs when (G – B) = G

The theoretical end value (G) of idle equipment was £300,000 after spending £100,000 on idle equipment maintenance (B) during the period. The actual value at the period end was £200,000.

Equipment idle£kEquipment used£k
Opening valuation (G – B)200Opening valuation200
Maintenance expenditure (B)100Capital consumption0
closing valuation (G)
closing valuation (G)

In this case, no capital consumption occurred so no charge to the value added statement is required in respect of capital consumption.

Case 3: Capital formation occurs.

This occurs when (G’ – B) < G.

Put simply, this means the closing valuation is higher than the opening valuation. This indicates that capital equipment has been acquired during the period


The theoretical end value (G) of idle equipment was £300,000 after spending £100,000 on idle equipment maintenance (B) during the period. The actual value at the period end was £450,000.

Equipment idle£kEquipment used£k
Opening valuation (G – B)200Opening valuation200
Maintenance expenditure (B)100Capital formation250
closing valuation (G)
closing valuation (G)

In this case, the firm may have been increasing its capital equipment by its own labour or by purchasing it from another firm. When capital equipment is produced in-house, the wages and salaries of that part of the labour force assigned to the production of the capital equipment will have been capitalised (i.e., included in the actual valuation). Capital equipment produced by an individual firm for its own use should be recognised in the individual’s firm’s value added statement as investment expenditure and should be coded as I.

In the value added statements that follow the capital adjustment from case 1 above has been incorporated into B2B’s results. The capital adjustment from case 3 has been incorporated in B2C’s results.

IInventory adjustment(100)(200)(300)
ICapital adjustment(25)250225
Value Added8751,0501,925

Apart from items on the edges, eg Suplementary Costs, income determination under Keynes’s scheme is concluded.

Consumption Expenditure (C)

The revenue figure of £2,000 in the consolidated column represents the total sales made by B2C firms to consumers. This is because all B2B sales figures have been eliminated by the consolidation process. The revenue figure in the consolidated value added statement thus represents consumption expenditure (C). Using Keynes’s notation consumption expenditure can be otained from the total of A minus the total of A1. The consolidated revenue, as shown above, is the result of the sum of A minus the sum of A1 .

Saving (S)

Saving is by (strict) definiton equal to income minus consumption. The consolidated value added figure of £1,925 represents aggregate income. Subtracting the aggregate consumption expenditure figure of £2,000, a negative figure for aggregate saving (S) of – £75 is obtained. It is no accident that the aggregate saving figure is equal to the aggregate investment figure shown in the consolidated value added statement.

User cost (U)

Keynes appears to set much store by this figure. The user cost repesents the costs that have been consumed (as distinct from being incurred). It is the sum of materials used/goods sold (A1 – inventory adjustments) and capital adjustments (capital consumption – capital formation). The user cost (U) can (theoretically) be negative in which case it is added to revenue. The user cost (U) can be calculated from A1 – I. It is most meaningful at individual firm level since A1 becomes zero on consolidation. The user cost for the B2C sector can be seen to be equal to £950 (£1,000 + £200 – £250). Value Added, which is now the accepted definition of income for national income determination, can be obtained from subtracting an individual firm’s user cost from the firm’s revenue (A) (eg, £2,000 – £950 = £1,050).

Investment Expenditure (I)

This is equal to the inventory adjustment plus the capital adjustment. If the closing inventories are higher than the opening inventories then investment will have occured. If the closing inventories are lower then disinvestment will have occurred.

Capital consumption decreases the period’s investment. Capital formation will increase investment.

Positive investment increases value added.


The above exposition is a condensed summary of chapter 6 of Keynes’s General Theory. The exposition is intended to make accessible the important material in that difficult-to-read chapter to a wider, less specialised readership, eg accountancy and business studies students. The more marginal topics in that chapter have not been given much weight in this exposition.

Chapter 6 shows that income for national income accounting is most closely aligned to the gross profit figure which is found in traditional commercial income statements. Gross profit figures are augmented with capital adjustments to arrive at value added. Keynes’s proposed formula for capital adjustments has been unpacked so as to make it more understandable. The resulting income is known as value added.

Keynes’s analysis has its focus on the creation of wealth. The distribution of wealth to the other sectors of the economy does not figure in his analysis. However, the government does prepare analyses to show “who got what” via the income approach to GDP determination.

Keynes shows how investment is equal to saving by adhering strictly to the defintion of saving as being equal to Income minus Consumption. In the consolidated value added statement value added (income) has been determined as £1,925k and consumption expenditure as £2,000k. Hence saving is – £75k.

Keynes’s analysis assumes a closed economy. The introduction of a foreign sector would appear to render some of his analysis inadequate.

Self-built assets and value added

Dealing with capitalised costs

Instead of purchasing non-current assets from third party suppliers, a firm may choose to itself construct or erect an asset for use in its own business. In these cases, costs and expenses which would otherwise be revenue in nature should be capitalised. Capitalised costs will not appear in a firm’s statement of profit or loss and hence materials and labour costs will be understated in this account, notwithstanding disclosure by way of a note.


ca[italised costs profit or loss

During the period, a new warehouse was constructed by the firm’s workforce for the firm’s own use at a cost of £4m. The materials cost of the construction was £1m and the labour cost assigned to the construction came to £3m. These costs were capitalised and hence do not appear in the above statement of profit or loss. A value added statement brings these costs in to view because the construction is part of the value created by the firm during the period.

Capitalisation of costs value added statement

Workings and notes

Bought in materials, goods, and services

Purchases of all materials, goods, and services whether or not capital or revenue but excluding depreciation.

To pay employees

All wages and employment on-costs including labour costs assigned to the construction of the new warehouse.

Investment adjustment

The capitalised cost of materials (£1m) and labour (£3m)

Inventory adjustment

Closing inventory minus opening inventory. This represents additional investment in inventory if positive or disinvestment in inventory if negative.

Depreciation adjustment

The total of the depreciation charges shown in the profit or loss statement. This is a measure of capital consumption during the period. In the national accounts, the government may substitute its own figure for a firm’s measure of capital consumption.

Link to the national income accounts

The total of the adjustments will be shown as an investment activity in the national income accounts where it will be denoted as I


I is for investment

How is the investment component, denoted by I, of national income determined? An explanation is proffered here by converting the following simple statement of profit or loss into a value added statement.

Investment and VAS

Additional information

During the period, the firm replaced some plant and machinery at a cost of £10m.

Points to note

A statement of profit or loss does not record purchases of a capital nature. Hence the purchase of plant and machinery for £10m is not reported in the statement of profit or loss.

A value added statement does report purchases of a capital nature.


Investment and VAS 2


Working for investment and VAS

National Income Accounts

If every firm prepared a value added statement the total of the net investment adjustments would represent the nation’s periodic investment activity shown in the national accounts prepared by the government. This figure for the periodic investment activity is shown as I in the national accounts.  

NB. The government may substitute its own standard calculation of the depreciation adjustment so as to achieve consistency.


Value Added Statements for Dummies

This is a short presentation to demonstrate how value added statements are prepared and to explain how they differ from the accountant’s traditional profit or loss account. A single example will be used which will capture the essential differences.


Below is shown a firm’s statement of profit or loss and value added statement. The two statements are shown side-by-side for ease of comparison.

During the period, the firm purchased plant and machinery for use within the business at a cost of £30m. Because this is capital expenditure, there is no entry in the statement of profit or loss to record this purchase. In the value added statement, the £30m cost appears against “bought-in materials, goods, and services” to obtain the “net value of output” figure. The firm’s investment activity is then shown by the investment adjustment to arrive at “net value added.”

VAS for dummies

Derivation of value produced figures

Bought-in materials, goods and services is equal to the purchases figure taken from the profit or loss statement (£80m) plus the capital expenditure (£30m).

The inventory adjustment is equal to the closing inventory minus the opening inventory. If this figure is positive then it represents additional investment in inventory. If negative then it represents disinvestment in inventory.

The depreciation adjustment is the total depreciation charged to the profit or loss account. This will usually be shown as a negative figure in the value added statement and represents consumption of capital in the period.

The investment adjustment is equal to the capital expenditure during the period. If this adjustment is positive then investment in new productive capacity has occurred. If negative, then disinvestment in productive capacity has occurred. The new productive capacity may consist of either tangible or intangible assets or some mixture.

Derivation of value distributed figures

To pay employees is the wages figure taken from the profit or loss account. The figure should include employer’s on costs, including employer’s National Insurance Contributions, and other employment taxes where they exist

To pay government is the sum of business rates and corporation tax charged to the profit or loss account. The figure represents the contribution the firm makes to the upkeep of the nation’s infrastructure and public services that enable firms to flourish.

To pay rentiers is the sum of property rents, licence fees, patent and copyright charges and the like. Payments to parties who derive income from ownership rather than from provision of a service or goods are recorded under this heading.

To pay financiers is the sum of interest charges in the profit and loss account plus dividends paid in the year. Payments of interest and dividends paid should be offset by interest and dividends received. Interest and dividends received are distributions of  value added produced by other firms. 

Undistributed value is equal to the retained profits shown in the profit or loss statement.

Fallacies of Modern Monetary Theory (MMT)

Fallacies of Modern Monetary Theory (MMT)

Taxation does not fund government spending

It does! Governments can fund public spending in just three ways: 

  1. Through taxation;
  2. By borrowing from the private sector;
  3. By borrowing from its banker (the central bank).

The last option on this list is forbidden in most advanced economies. This leaves taxation and borrowing from the private sector as the only available funding sources.

Money is a liability of the government

No it’s not! Customer deposits held by retail banks are liabilities of those retail banks. These customer deposits are not liabilities of the government or of the central bank. As an aside, money deposited with these banks is an asset to the depositor (customer).

Government spending precedes taxation

This could be true if money was created and injected into the economy by the government. But this condition does not hold. Most money in circulation is created and injected into the economy by private banks. 

Taxation alone determines a currency’s value

It is true that governments require taxes to be paid in the national currency and this creates demand for the currency. However, a nation’s international trading performance and capital flows also affect demand for a nation’s currency and its value. So tax is not the sole determinant. 


The “magic money tree” does not exist!

Ricardian Equivalence is dead. Long live Keynes!


In this piece, I show how government spending on capital projects can be beneficial to the private sector. The demonstration shows the oft-cited objection to government spending, so called Ricardian Equivalence, is not correct. I use an example, which hints at the proposed HS2 rail project, to make my point. I also use accepted investment appraisal techniques.

An example

A government proposes to invest in a high speed rail line which will cost £30 billion to build. The government will commission a consortium of private sector firms to undertake the work. The consortium will be paid £30 billion and this will be treated as income in their financial accounts and for GDP measurement purposes.

The government proposes to fund the project by borrowing £30 billion from the City at a rate of 6% per annum. The bonds must be repaid at the end of 20 years. Once built, the line will be operated by a private rail company. The line is expected to last for 50 years after which time it must be replaced.


A prudent government should ensure the borrowed money will be repaid to the lenders when due and that interest payments are met. This can be done by calculating an “annual equivalent” of the interest payments and the loan repayment. The government can then levy the amount of the annual equivalent as an annual taxation charge on the private sector over the 20 years of the loan. This stream of annual tax receipts, which are additional to other tax receipts, will then be sufficient to pay the annual interest charges to the lenders and to repay the amount initially borrowed (the principal) when it falls due at the end of 20 years. In short, the government will be able to break even.

Annual Equivalent

The annual equivalent is obtained from a formula which converts an uneven stream of cash flows into an even stream of cash flows (an annuity). In this particular case, there are 20 payments of £1.8 billion for interest (6% p.a. x £30 billion) and a final payment of £30 billion by way of repayment of the principal to the lenders. The annual equivalent is £2.616 billion (3 d.p.).  So this amount should be the additional annual tax charge to fund this particular project. It will be enough to provide for the annual interest charge of £1.8 billion for 20 years plus £30 billion repayment of principal. See appendix.

Schedule of cash flows

To see how the annual equivalent calculation clarifies and makes tractable the analysis, here is a summary of the cash flows between the government and the private sector using the facts of this example.  Outflows are shown in brackets and inflows without brackets.

Cash Flows


At this point, a reader may observe that the government and private sectors are mirror images of each other; the flows in and out of the private sector being exactly matched by the flows out and in of the government.  This may induce  the same reader to consider that government spending does not benefit the private sector since the additional tax charges (20 x £2.62) exceed the £30 billion income received at the outset of the project.

Time value of money

However, this conclusion takes no account of the TIME VALUE of money. Very simply put, the time value of money is the preference to receive money sooner rather than later. Most people prefer to receive money sooner rather than later. There are several reasons why individuals, households and firms prefer to receive money sooner rather than later. The list of reasons includes inflation, risk, need and so on. For example, a starving pauper would prefer to receive £1 now, rather than in one week’s time, for otherwise he or she may not be able to eat for a week. The poorer an individual, the greater their time value of money; a millionaire does not really care if they receive  £1 now or in one week’s time since it will make virtually no difference to his or her life.

Discount rate

This is the time value of money expressed as an annual interest rate. The higher a time value is, the higher the discount (or interest) rate. The discount rate allows someone’s preference for immediate money to be linked to future money. For example, someone with a discount rate of 25% would see £125 receivable in one year’s time as having an immediate value of £100. Someone with a higher time value, say with a discount rate of 30%, would value the same £125 as having an immediate value £96.15. The immediate value is called the PRESENT VALUE. In general, the poorer an individual, a household, or a firm is, then the higher their time value of money and their discount rate. The higher the discount rate the stronger the preference to receive a given sum now rather than in the future.

Putting it all together

The above table of cash flows shows the cash flows of the government and private sector to be equal (but opposite). The PRESENT VALUE of the tax cash flows, which arise in the future, may differ between the government and the private sector. In short, the time value of money for the private sector may be different from the government’s time value. In reality, this is highly likely to be true. If the time values, and therefore the discount rates, are different then the PRESENT VALUE of the cash flows shown in the table will be different. We hence need to ascertain the PRESENT VALUE of these future tax payments if we are to conclude whether or not government spending increases private sector income.

We know the government’s discount rate in the example is 6% (its borrowing cost).  However, we do not know the private sector’s discount rate (or time value of money). But we do know the private sector is composed of many households as well as firms. Many households, perhaps the larger part, will struggle day to day to make ends meet. They will be at the poorer end of the income spectrum. Many individuals and households will be borrowing at annual rates in excess of 1000% via Pay Day loans. This fact alone signifies that many households have extremely high discount rates

Firms will often be under pressure from their shareholders to make short term profits. Moreover, firms race risk when investing funds and this risk increases their discount rate. These factors, among others, support a conclusion that the private sector will have a higher average discount rate than the government’s, although we may not be able to quantify it.

If the private sector’s average discount rate is assumed to be 18%, then the following summary table shows the private sector (and GDP) benefits from the government’s spending. This conclusion may run counter to some economists who argue that government spending does not promote growth or income. They believe the private sector’s response will be to immediately save the entire amount of the additional government spending and thereby withdraw the government injection totally and immediately. These economists believe the private sector’s response would be in anticipation of the government clawing back the additional spending via higher future taxation. This analysis shows the conclusion is wrong since it does not correctly adjust for the different time values of the parties to the transaction.

Investment decision summary

The net present value represents the surplus in present value terms. As planned, the net present value accruing to the government is zero (it has broken even). The NPV accruing to the private sector is positive. This means it has gained £16 billion as a consequence of the government’s capital spending of £30 billion. The size of the private sector’s surplus depends on the private sector’s discount rate. The higher the private sector’s discount rate then the higher will be the surplus. A surplus will arise so long as the private sector’s discount rate is higher than the government’s. As explained above, it is almost certain that the private sector’s discount rate is higher than the government’s.


Repayment schedule for 6% government bonds with a term of 20 years

Repayment schedule

The repayment schedule assumes that surplus funds can be invested at 6% – a realistic assumption because the government will be repaying maturing 6% bonds continuously, thus saving itself 6%.on each bond redemption.

Using the tax system to deliver a living wage

In a previous post, I proposed a formula for calculating income tax that would provide for a  negative income tax. I did so because I believe a negative income tax system would be simpler, fairer, more humane, technically more feasible , and cheaper to develop than the current Universal Credit project being rolled out by Her Majesty’s government. A negative income tax would be administered by HMRC and have at its core the following formula for calculating income tax:

T(n) = m∑Y(n) – c∑H(n) – ∑T(n-1)


m is the single marginal tax rate;

c is the hourly value of the tax shield

∑Y(n) is the cumulative market income received by the end of period n

∑H(n) is the cumulative hours worked by the end of period n

∑T(n-1) is the cumulative income tax paid by the start of period n.


The proposed tax system has a single marginal tax rate. The choice of this rate is a political as well as a technical decision (i.e., achieving the desired behavioural effects) An individual’s hourly tax-free pay is given by the grossed-up tax shield (c / m).

In this post, I want to show how a negative income tax system can deliver what many describe as a “living wage”. The figure of £10 / hour has been mooted as a living wage. I shall hence assume this figure for the living wage  in my illustration.


In this post, I will incorporate the UK’s national minimum wage (NMW), currently £6.50 per hour, into the model.

I will also use a marginal tax rate of 40%, a tax rate which is both comparable to and competitive with existing UK income tax rates (20%, 40%, and 45%). Hence m has been set to 40% or 0.4 in my illustrations.

I will assume a working week of 35 hours and an individual’s weekly hours will be capped at this level.

I will also show how the model can be used to generate a basic income. I will briefly set out my views on whether a basic income should be conditional or unconditional.

Calculating the tax shield

In this section, I will show how negative income tax can transform the minimum wage of £6.50 / hour into a living wage of £10.00 / hour.  To achieve this, the value of the tax shield (c) must be calculated with reference to the minimum wage and to the living wage of £10.00. The value of the tax shield (c) must be set so that the hourly negative tax payment makes up the difference of £3.50 

Ignoring the summations in the above f ormula (they are not necessary here), we have

T = m x (£6.50) – c = – £3.50

T= 0.4 x £6.50 – c = – £3.50

c = £6.10

The tax formula that transforms the hourly national minimum wage of £6.50 to an hourly living wage of £10 will thus be

T(n) = 0.4 x ∑Y(n) – £6.10 x ∑H(n) – ∑T(n-1)

or on a week 1 basis, the hourly tax charge will be:

T = 0.4 x £6.50 – £6.10

= – £3.50 (negative,  as required)


Lenny earns the adult minimum wage. He works 35 hours per week. His pay slip will show:

Market income (35 hours x £6.50/hour)                                       £227.50

Negative income tax  (35 hours x £3.50)                                     £122.50

Take home pay (35 hours x £10 hour)                                         £350.00


Lenny now receives £10 per hour.


The hourly post-tax income of someone whose market income is £10 would be transformed to £12.10.

T= 0.4 x (£10.00) – £6.10 = – £2.10 (negative)

Hence that individual would take home £10 – (- £2.10) = £12.10 for every hour worked at or below the 35 hour weekly cap on hours. So although the “differentials” between market incomes have narrowed the higher paid worker still receives more per hour than the minimum wage worker.

Tax free allowance

The break-even hourly income with an hourly tax shield of £6.10 and a marginal tax rate of 40% is £15.25. This means a worker with an hourly income of £15.25 will neither pay income tax nor receive a tax payment. This is equivalent to an annual tax free allowance of £27,755 (compared to the current allowance of £10,000 p.a.). Individuals with a a market income of above £15.25 per hour or £27,755 per annum would pay income tax of 40% on the excess.

Basic income

The parameters used in the formula produce an amount 0f £6.10 per hour for those who have no market income. This could be taken to be a basic income payable to anyone whose market income is zero.

T = 0.4 x £0.00 / hour – £6.10 / hour

= – £6.10 per hour (negative)

The issue is whether this fortunate by-product of negative income tax should be conditional or unconditional.

Unconditional basic income

An unconditional basic income would credit every citizen with 35 hours. The basic income would thus be received by every citizen of working age.  The basic income would amount to £213.50 (35 hours x £6.10 per hour).

Hourly income with unconditional basic income and living wage of £10/hour

Hourly income with unconditional basic income and living wage of £10/hour

Conditional basic income

A conditional basic income would credit some groups with 35 hours a week but not others. For example, the disabled, the infirm, and those with caring responsibilities could be credited.  This would automatically trigger a payment at HMRC of £213.50 to individuals falling in these groups. The unemployed would be credited with hours only to the extent of their hourly contributions to society via voluntary work and / or participation in counter hysteresis activities (such as internships, work placements, or work programmes).

Hourly income with a conditional basic income and a living wage of £10/hour

Hourly income with a conditional basic income and a living wage of £10/hour

Conditional or unconditional basic income?

My main concern is that every UK citizen should have access to honest and adequate income. For disadvantaged groups, income accessability, particularly with increased benefit conditionality, can often be an issue.

Provided plentiful opportunities for voluntary work and / or opportunities to engage in counter hysteresis activities are made available to physically and mentally capable individuals without a market income then basic income should be conditional along the lines described above. A reasonably generous income of £213.50 per week would accrue to such individuals if their engagement in these activities was for 35 hours a week. Lesser contributions would be rewarded proportionately.

Summary of the model

Basic income = £6.10 /hour. May be conditional or unconditional. Could replace unemployment benefit.

Minimum wage (statutory)  = £6.50 / hour.

Living wage (assumed) = £10.00 /hour.

Break-even wage = £15.25 /hour.

Marginal tax rate = 40%

Maximum hours of credit = 35

Some final points

The withdrawal rate for someone transiting from unemployment to minimum wage work is about 43% (0.4 x £6.50 / £6.10). This is substantially better than the proposed withdrawal rate of 65% planned for Universal Credit.

However, the withdrawal rate rises as the starting hourly wage rate rises. At a starting rate of £15.25 per hour the withdrawal rate is 100%. It is unlikely that such a high withdrawal rate would be a disincentive to accept work at this wage rate.

It seems likely that a negative income tax designed with the parameters outlined in this post would lead to a lower overall income tax take for the government. Some of this might  be due to a lower marginal tax rate of 40% for top earners compared to their current 45% and because the tax free allowance is more generous than the current £10,000 annual allowance. For this reason, it may be better to use income tax as a means of correcting the inequalities that arise from distortions in the labour market (eg directors effectively setting their own pay) rather than as a means of raising revenue.

Capping the corporation tax deductibility of market incomes to £27,779 per employee (the annual tax free allowance) may also help to mitigate reductions in the income tax take.

The redistribution of income arising from this variant of a negative income tax system is likely to have a stimulative effect on the economy. Poorer workers with a high propensity to consume relative to richer workers should increase demand and hence economic activity.

Should the poor be afraid of a “Flat-rate” tax?

I believe it depends on three things:

  1. How income is defined;
  2. The tax-free personal allowance; and
  3. The tax rate

Realised comprehensive income

In the UK there are three taxes that could be consolidated into a single income tax. These three taxes are Inheritance Tax, Capital Gains Tax, and the current income tax. All three levy tax on assets that flow from one party to another. Each of the three taxes has a separate and different  tax free allowance associated with it and are taxed at different rates.

A realised comprehensive income tax would make no distinction between these asset flows – all flows would be taxed as income. The annual inflows of assets received by an individual from the three sources would be aggregated and taxed as realised comprehensive income after deducting the individual’s annual tax-free personal allowance.

The advantages of a realised comprehensive income tax are:

  1. Simplification. Inheritance tax and capital gains tax would be brought under a single regime;
  2. Less incentive would exist to engage in tax avoidance;
  3. Legacies would be taxed according to the recipient’s circumstances, not the donor’s. This is more just as the recipient’s entitlement to the assets has not been derived through labour or through an identified contribution to society. Many donor’s feel resentment when it is their circumstances that determine the tax due on bequests, as is the case currently.

The annual tax-free personal allowance

Rolling up all three types of income into one obviates the need to have separate tax-free personal allowances for each of the three sources. Setting a single annual tax-free personal allowance of, say, £50,000 would provide generous relief to those whose comprehensive incomes are low or in the middle. It also supports simplification of the tax system.

The tax rate

In the presence of an annual tax-free personal allowance a flat-rate tax would by definition be a marginal rate (not an average rate).

Many ‘small-staters’ and their ilk hold that the state’s share of someone’s income should never exceed 50%. Setting the marginal rate of income tax to 50% respects this limit because of the annual tax-free personal allowance. In fact, many individuals with taxable income will have average tax rates that are far below the marginal tax rate of 50%.


Suppose the annual tax-free personal allowance has been set to £50,000 and the single rate of tax is 50%. An individual with a realised comprehensive income (earned + unearned + capital gains + bequests) of £100,000 would be liable for tax of

 0.5 x (£100,000 – £50,000) = £25,000

which is 25% of realised comprehensive income received in the year.

Here is a graph which shows average tax rates against realised comprehensive income in a flat-rate tax system with the parameters described above.


The average tax rate will get ever closer to the 50% marginal rate as comprehensive income gets larger and larger.

Conclusions and Summary

What I have shown is that flat-rate taxes, so often proposed by ‘small-staters’ et al, should not axiomatically be feared. This is because the fairness of such schemes can depend on their parameters and the definition of income. Flat-rate taxes need not mean low-taxes, as hoped for by their proponents. The battleground is really about the parameters of such a scheme, not about whether a flat-rate tax system is desirable in itself. A judicious selection of parameters can ensure equity, whilst simultaneously meeting the objections of ‘small staters’ to wealth taxes and high average tax rates on conventional income.

I suggest, in the wake of Piketty, that taxing flows of assets as income is a more feasible way of addressing runaway inequality than imposing taxes on stocks of assets (wealth taxes). The exception to this rule would be a land value tax, which can be perceived as a rental charge on privately sequestered natural assets. It is difficult to sustain a moral objection to taxing  a stock in the case of land.

I have not attempted to cost out this flat-rate tax proposal, either with the proposed or alternative parameters. It may be that a flat-rate tax system would raise less than the current sum of capital gains tax, inheritance tax and conventional income tax. If so, then perhaps a Land Value Tax would be needed to plug the gap. The challenge, as I see it, is to find ways of financing generous public services whilst simultaneously defeating the (sometimes spurious) moral objections that Libertarians et al advance.

Towards a truly progressive tax system

Is the UK’s tax system out of date and no longer fit for purpose?

Many people, including myself, would say it is.

Politicians, though, seem unable or unwilling to address the creaking tax and social security systems.

Here are some, perhaps radical, ideas that could transform the lives of ordinary people. The proposals are unlikely to meet with approval from the very wealthy, from those who receive very high incomes, or from those who otherwise have a stake in the status quo. Nevertheless, here goes:

1. Realised comprehensive income

By adding together an individual’s earned income, their dividend income, their savings income, their property income, their capital gains, and their receipts from legacies, one arrives at an individual’s realised comprehensive income.

Taxing comprehensive income simplifies the tax system and makes it harder to avoid tax because all types of income would be taxed at the same rate. The current system taxes the individual components of comprehensive income at different rates. The current system hence provides incentives for taxpayers to manipulate their affairs so as to take advantage of differential tax rates. For example, under the current system, it is usually advantageous for an individual to take the benefit of a transaction as a capital gain rather than as income. This is because capital gains are generally taxed at a lower rate for individual tax payers.

2.  Increase annual tax free allowance to £100,000

The first £100,000 worth of comprehensive income received in a year would be tax free. Such a move, were it to be implemented, would take most, perhaps as many as 98% of tax payers, out of income tax altogether. Only those with comprehensive incomes above £100,000 would be liable for income tax. Incomes above £100,000 are more likely to be unearned, they deriving from rent extraction activities, holding gains, and luck.  It is unlikely that extremely high incomes result from a commensurate contribution towards the common good. Genuinely earned income, that is income derived from an individual’s contribution to society, is likely to be lower than £100k per year and should therefore escape income tax altogether.

3.  Simplification of income tax

Every income tax payer would have the same marginal rate of tax. This would ensure the average income tax rate rises with comprehensive income.

A formula can be used to determine an individual’s tax rate taking account of their annual comprehensive income. The formula would only be applied to comprehensive incomes above £100,000 p.a.

An example of such a formula is a follows:

0.9 x (Y –  £100k)

where Y = annual comprehensive income, the £100k shown in brackets is the annual tax free allowance and the 0.9 (90%) is the marginal tax rate and the limiting tax rate (i.e., the tax rate will never exceed 90% however large an individual’s comprehensive income may be)

Here is a graph which plots comprehensive income against the applicable average tax rate using the formula shown in blue.

Top tax rates graph


The graph shows how an individual’s average tax rate is determined by their comprehensive income.  For example, an individual with an annual comprehensive income of £0.4 m would have an average tax rate of just under 70% of that income, (the exact percentage is 67.5%).

An individual with a comprehensive income of £0.1m or less would not pay tax on their comprehensive income at all.

As an individual’s comprehensive income increases the closer their average tax rate approaches the 90% limit. However, no individual, however high their comprehensive income, will have an average tax rate of 90%; but very high comprehensive incomes will come close to the 90% limit.

Taxing comprehensive income this way is consistent with free market principles. Company directors and others who can, and do, effectively set their own pay will continue to be free to do so. Using the proposed formula to assess tax on comprehensive income supports freedom but also enables society to benefit. A high marginal rate may also discourage “superstar” remuneration, and thus may help to address runaway inequality which is becoming increasingly prevalent.

4.   Universal Basic Income

The introduction of a universal basic income would guarantee every adult citizen of the UK an unconditional basic income. This would guarantee every citizen social security. This would obviously need to be funded and a Land Value Tax may provide such a fund. A quick estimate suggests that £208 bn per year would be need to be raised to pay a basic income of £100 per week to 40m adults. This is clearly a lot of money.

The universal basic income would have many benefits. For example, the minimum wage could be abolished. The bargaining power of workers would be be enhanced in wage negotiations with employers. Self-employment, because of the risk reduction impact of a basic income, should mean more workers eschewing employment in favour of self-employment. This would contribute to economic dynamism and creativity. A basic income may permit younger people to stay on at college to acquire skills from which they, employers and society benefit. The benefits of a universal basic income are manifold and, encouragingly, the concept is increasingly finding support from both the left and right ends of the political spectrum.

5.   Land Value Tax

A tax on the value of land is thought by many to be a rich potential stream of taxation income.  It has been suggested that, very approximately, one-third of the value of a house is due to the value of the land the house sits upon.

A land value tax would be an annual charge on land owners. It would be charged as a percentage of the value of land owned. Whether a Land Value Tax would provide sufficient funds to finance a meaningful Universal Basic Income is at the time of writing unknown to this author.

A powerful argument in favour of a Land Value Tax as a means of funding a Universal Basic Income is that it supports justice in distribution. Land is a God-given resource which should be available to everyone to profit from. But the land is owned by private individuals who capture the benefits of land ownership despite having acquired the land by means of dubious morality in the first instance. So it makes sense that landowners should fund a Universal Basic Income to compensate those who are forcibly displaced from the means of subsisting from the land.


Tax rates for comprehensive income of up to £8m p.a.

top tax table