In The Monopoly of Credit (1931), C.H. Douglas presents his second proof for the A+B theorem, arguing that the two core accountancy cycles of an industrial economy: the creation and destruction of money (Cycle 1) and the creation and liquidation of costs (Cycle 2) are misaligned, resulting in a systemic deficiency in purchasing power. The money cycle (Cycle 1) operates at a faster pace than the cost creation and liquidation cycle (Cycle 2), creating a gap between prices and purchasing power that widens with greater dyssynchrony and narrows with greater synchrony. Indeed, if the cycles were perfectly aligned, money creation/spending and cost creation/liquidation would occur simultaneously, eliminating the gap entirely.
This misalignment stems from the nature of B-Costs (e.g., depreciation, loan repayments, maintenance charges, etc.), which are included in prices but contribute minimally to consumer income. These B costs are also recovered over a much longer period than the period of the money cycle (Cycle 1). A payments (e.g., wages), by contrast, align perfectly with the money cycle’s quicker pace and are fully distributed as income. Consequently, for any volume of producer credit completing a cycle — from bank to businesses, to consumers or other businesses, and back again to the bank via loan repayment — total costs and prices accumulate faster than incomes are distributed, precisely because credit diverted into the B channel is destroyed (e.g., loan repayments), saved, or reinvested, rather than being distributed as concurrent consumer income.
This particular proof has been, for many people, one of the most difficult passages in Douglas’ writings to understand, so it seemed fitting to take this time now to first present the passage in question, then to analyze it, and finally to provide some actual numbers to show how the algebra would work in concrete examples.
The text in question reads as follows:
It is also clear that the longer the average period over which money is collected in respect of the creation and destruction of a capital asset (which corresponds to the "life" of an asset), and the shorter the average period over which money is collected for day-to-day living on the part of the community (which corresponds to the "life" of consumable goods), the greater will be the discrepancy between purchasing power and prices.
The former period is the average time in years (N2) taken to make and wear out a capital asset; it is the time covered by the production and destruction of a cost. Obviously, such a period will vary greatly according to the nature of the asset, but a fair and usual average is twenty years.
The latter period is the average time in years (N1) during which the money at the disposal of the community (total income) circulates from industry to the consumer and back again.
"In Great Britain, for instance, the deposits in the Joint Stock Banks are roughly £2,000,000,000. In rough figures, the annual clearings of the clearing banks amount to £40,000,000,000. It seems obvious that the £2,000,000,000 of deposits must circulate twenty times in a year to produce these clearing-house figures, and that therefore the average rate of circulation is a little over two and a half weeks. . . . The clearing-house figures just quoted contain a large number of 'butcher- baker' (second-hand) transactions, and these must be deducted in estimating circulation rates."* *C.H. Douglas in The New and the Old Economics.
After making the necessary correction for the volume of second-hand transactions and for payments that do not go through the clearing-house, we may conclude that the average period of circulation of the money spent upon consumable goods is about two months, or one-sixth of one year.
The effect of the very great disparity between these two rates is as follows:
Let n1 = 1 / N1 = number of circulations per year, say 6.
Let n2 = 1 / N2 = number of circulations per year, say 1/20.
Let A = all disbursements by a manufacturer which create costs = wages and salaries
Let B = all disbursements by a manufacturer which transfer costs = payments to other organisations
The manufacturer pays £A per annum into the N1 system, and £B per annum into the N2 system.
Disregarding profit, the price of production is £ (A + B) per annum. But to purchase (i.e.to cancel the allocated cost of £(A + B)) there is present in the hands of the consumer :-
£(An1 + B n2 )/ n1 =£ (A + B n2/n1 )
Consequently, the rate of production of price values exceeds the rate at which they can be cancelled by the purchasing power in the hands of the consumer by an amount proportional to
B (1 – n2/n1) = approximately B
This deficit may be made up by the export of goods on credit, by the writing down of goods on credit, by the writing down of goods below cost, by bankruptcies, and by money distributed for public works and charged to debt. But in the main it is represented by mounting debt.
It will readily be seen how this situation in which, not production, but money, is chronically insufficient, must transfer control to the institutions which have acquired the monopoly of money-making. In order that the industrial system may not grind to a standstill, an increasing issue of money, chiefly for capital production, is necessary to bridge the gap between purchasing power and prices – a gap which is the only possible explanation of the anomaly between a half-idle production system and a half-starving population. But as this fresh money is claimed by the banking system, and has to be repaid, the situation is cumulatively worsened.[1]
Section 1: Disparity in Cost Recovery Periods
Original Text: “It is also clear that the longer the average period over which money is collected in respect of the creation and destruction of a capital asset (which corresponds to the ‘life’ of an asset), and the shorter the average period over which money is collected for day-to-day living on the part of the community (which corresponds to the ‘life’ of consumable goods), the greater will be the discrepancy between purchasing power and prices.”
Comment: Douglas highlights that the differing periods for recovering capital costs (B-Costs) versus circulating wages (A-Costs) create a systemic gap between prices and consumer income, which grows larger as the capital recovery period lengthens and the wage circulation period shortens, due to their combined effect on the cumulative purchasing power deficit over time.
Explanation: Capital assets (e.g., machinery) have a long economic life (e.g., 20 years, N2 = 1/20 annually), meaning their costs (B-Costs, e.g., depreciation, loan repayments) are recovered slowly through prices, while contributing minimally to consumer income in the short term (e.g., 1/120 in a 2-month cycle). In contrast, consumable goods (e.g., food) are produced and consumed quickly (e.g., 2 months, N1 = 6 cycles/year), with their A-Costs, e.g., wages, fully distributed as income in each cycle.
This timing mismatch creates a per-cycle deficit: prices include all costs (A + B), but purchasing power is limited to A payments plus a small fraction of B-Costs, as B payments (e.g., to suppliers, banks) are mostly saved (e.g., depreciation reserves), destroyed (e.g., loan repayments), or reinvested (e.g., into other firms’ B-Costs), triggering only limited anticipatory A payments (e.g., supplier wages).
The shorter the money cycle (larger N1), the more cycles occur annually, amplifying the annual deficit. For example, at N1 = 6, annual costs are 6 times the per-cycle costs, but income lags due to B-Costs’ limited contribution. Simultaneously, the longer the capital recovery period (smaller N2), the more money cycles occur over that period, accumulating a larger total deficit. For example, over 1 year (N2 = 1), 6 cycles occur, but over 20 years (N2 = 1/20), 120 cycles occur, each adding to the gap. A shorter money cycle (e.g., 1 month, N1 = 12) doubles the annual cycles, and a longer recovery period (e.g., 40 years, N2 = 1/40) doubles the total cycles, together maximizing the cumulative discrepancy.
Section 2: Defining Recovery and Circulation Periods
Original Text: “The former period is the average time in years (N2) taken to make and wear out a capital asset; it is the time covered by the production and destruction of a cost. Obviously, such a period will vary greatly according to the nature of the asset, but a fair and usual average is twenty years. The latter period is the average time in years (N1) during which the money at the disposal of the community (total income) circulates from industry to the consumer and back again.”
Comment: The recovery period for B-Costs and the circulation period for A-payments set the rates at which money is created/destroyed (Cycle 1) and costs are created/liquidated (Cycle 2), driving the misalignment.
Explanation: Douglas defines the capital recovery period as the average life of a capital asset, assumed to be 20 years (N2 = 1/20 annually). This reflects a typical depreciation schedule (e.g., a £100,000 machine depreciated at £5,000/year) that is based on 1930s industrial norms, where assets like machinery or factories often lasted 10–50 years, with 20 years as a reasonable average. The circulation period for consumable goods, tied to wages, is the time money circulates through the economy (e.g., 2 months, N1 = 6 cycles/year) as it moves from banks to businesses to consumers and back. B-Costs (e.g., depreciation, loan repayments) are recovered over 20 years, contributing only a fraction to income per cycle (e.g., 1/120 in 2 months). While B payments trigger limited A payments (e.g., a supplier’s wages), A payments (wages) are fully distributable as income in each 2-month cycle, aligning with the money cycle’s pace. This disparity in rates — rapid for A-Payments, slow for B-Payments — means many money cycles occur within the capital recovery period, each adding to the purchasing power deficit.
Section 3: Estimating N1 Using Banking Data
Original Text: “In Great Britain, for instance, the deposits in the Joint Stock Banks are roughly £2,000,000,000. In rough figures, the annual clearings of the clearing banks amount to £40,000,000,000. It seems obvious that the £2,000,000,000 of deposits must circulate twenty times in a year to produce these clearing-house figures, and that therefore the average rate of circulation is a little over two and a half weeks. . . . The clearing-house figures just quoted contain a large number of ‘butcher-baker’ (second-hand) transactions, and these must be deducted in estimating circulation rates.”
Comment: The money cycle’s frequency is derived from economic data on money circulation, providing a practical basis for the A-payment distribution rate.
Explanation: Douglas uses 1930s UK banking data to estimate the circulation period of money, initially calculating a 2.5-week cycle (20 cycles/year) based on bank deposits (£2 billion) and annual clearings (£40 billion). However, he adjusts for “butcher-baker” transactions (second-hand exchanges, e.g., consumer-to-consumer payments) and other non-clearing-house payments, concluding in the next section that the adjusted circulation period for consumable goods is about 2 months (N1 = 6). This reflects the average time for money to move from banks (via loans) to businesses (as production costs), to consumers (as wages), and back to banks (via repayments), aligning with the rapid distribution of A payments (e.g., wages paid out during a two month period). This contrasts with the slow recovery of B-Costs over 20 years. As more money cycles occur concomitantly within the capital recovery period, this adds cumulatively to the deficit. A shorter money cycle (e.g., 1 month, N1 = 12) would increase the annual cycles to 12, further amplifying the annual and cumulative gap, since each cycle generates costs faster than income.
Section 4: Formalizing the Disparity
Original Text: “After making the necessary correction for the volume of second-hand transactions and for payments that do not go through the clearing-house, we may conclude that the average period of circulation of the money spent upon consumable goods is about two months, or one-sixth of one year.
The effect of the very great disparity between these two rates is as follows:
Let n1 = 1 / N1 = number of circulations per year, say 6.
Let n2 = 1 / N2 = number of circulations per year, say 1
Let A = all disbursements by a manufacturer which create costs = wages and salaries
Let B = all disbursements by a manufacturer which transfer costs = payments to other organisations
The manufacturer pays £A per annum into the N1 system, and £B per annum into the N2 system.
Comment: The disparity is quantified by calculating purchasing power as a function of A payments, B payments, and their respective rates (N1, N2), showing that B payments contribute minimally to income.
Explanation: Douglas concludes that the circulation period for consumable goods is 2 months (N1 = 6), and formalizes the disparity with a N2 = 1/20 capital recovery rate (20-year capital recovery), A-Costs (wages, salaries), and B-Costs (payments to other organizations, e.g., for raw materials, bank charges). Purchasing power per cycle is £A + £B × (N2 / N1), where £A is fully distributed, but £B contributes only 1/120 in a 2-month cycle (0.833% of £B), as B payments are mostly saved (e.g., depreciation reserves), destroyed (e.g., loan repayments), or reinvested (e.g., into other firms’ B-Costs), with a small fraction becoming consumer income via secondary effects (e.g., a supplier paying wages).
The 1/20 annual rate (5%) is a simplifying assumption by Douglas, based on a 20-year average asset life, implying that 1/20 of B payments annually become A payments through economic activity (e.g., a firm paying a supplier who then pays wages), though the actual rate may be lower due to B payments often flowing into further B-Costs (e.g., the supplier’s depreciation). In a given cycle, prices are £A + B, but purchasing power is limited, creating a deficit that accumulates over more cycles as N1 increases or N2 decreases, i.e., as more frequent cycles (shorter money cycle) and more total cycles (longer recovery period) exacerbate the gap.
Section 5: Price vs. Purchasing Power
Original Text: Disregarding profit, the price of production is £ (A + B) per annum. But to purchase (i.e. to cancel the allocated cost of £(A + B)) there is present in the hands of the consumer :-
£(An1 + B n2 )/ n1 =£ (A + B n2/n1 )
Consequently, the rate of production of price values exceeds the rate at which they can be cancelled by the purchasing power in the hands of the consumer by an amount proportional to
B (1 – n2/n1) = approximately B
Comment: The mismatch between prices and purchasing power in each cycle drives the systemic deficit, which grows over time as the number of cycles increases.
Explanation: In a 2-month cycle, prices are £A + B, reflecting all production costs, but purchasing power is £A + £B × (N2 / N1), as B-Costs contribute minimally to income due to their slow conversion rate (e.g., 1/120 in 2 months, or 0.833%). This per-cycle deficit accumulates over the capital recovery period—for example, over 20 years (N2 = 1/20), 120 cycles occur at N1 = 6, each adding to the gap. A shorter money cycle (e.g., N1 = 12) doubles the annual cycles to 12, increasing the annual deficit, while a longer recovery period (e.g., N2 = 1/40, 40 years) doubles the total cycles to 240, amplifying the cumulative deficit. B-Costs remain in prices but are not fully liquidatable by the income that is released during the same productive process, forcing reliance on debt to bridge the gap, which compounds over time as more cycles occur.
Section 6: Consequences of the Deficit
Original Text: “This deficit may be made up by the export of goods on credit, by the writing down of goods on credit, by the writing down of goods below cost, by bankruptcies, and by money distributed for public works and charged to debt. But in the main it is represented by mounting debt.”
Comment: The deficit forces reliance on debt, credit sales, or bankruptcies, often resulting in mounting debt as the primary mechanism to clear goods.
Explanation: The per-cycle deficit requires new money (e.g., loans) to sell goods, as consumers lack sufficient income to purchase all production due to B payments’ limited income contribution (e.g., 0.833% per cycle). Over 20 years, with 120 cycles at N1 = 6, this debt accumulates significantly (e.g., £4.76 million as per example #1 below), exacerbating economic distortions. Firms may resort to credit sales (increasing future repayment burdens), write down goods below cost (incurring losses), or face bankruptcies if goods remain unsold, while public works funded by debt (e.g., infrastructure projects) add to the debt burden. In the main, however, the deficit results in mounting debt, as banks create new money to bridge the gap, increasing future B-Costs (e.g., loan repayments) and compounding the cycles’ misalignment over the capital recovery period.
Section 7: Systemic Implications and Banking Control
Original Text: “It will readily be seen how this situation in which, not production, but money, is chronically insufficient, must transfer control to the institutions which have acquired the monopoly of money-making. In order that the industrial system may not grind to a standstill, an increasing issue of money, chiefly for capital production, is necessary to bridge the gap between purchasing power and prices – a gap which is the only possible explanation of the anomaly between a half-idle production system and a half-starving population. But as this fresh money is claimed by the banking system, and has to be repaid, the situation is cumulatively worsened.”
Comment: The systemic deficit creates a dependency on bank credit, centralizing economic control and perpetuating the gap.
Explanation: The cumulative deficit (e.g., £4.76 million over 20 years at N1 = 6, N2 = 1/20) forces continuous borrowing, as each cycle’s gap requires new debt to clear goods. A shorter money cycle (e.g., N1 = 12) or longer recovery period (e.g., N2 = 1/40) would increase the total cycles (e.g., 240), raising the cumulative deficit to £9.56 million, further increasing debt. This empowers banks, which create money as loans, increasing their control over the economy. Over time, the debt burden grows and grows, as do future B-Costs (including interest payments), further widening the purchasing power gap and entrenching banking dominance. This is a key systemic flaw which Douglas critiques in industrial economies, where the half-idle production system (e.g., factories at partial capacity) can coexist with a half-starving population due to insufficient purchasing power.
Key Points
- The two cycles are out of sync: money creation/destruction (Cycle 1) operates at N1 = 6, while cost creation/liquidation (Cycle 2) is slowed by B-Costs’ 20-year recovery (N2 = 1/20).
- A shorter money cycle (higher N1) and longer capital recovery period (smaller N2) would increase the cumulative deficit by generating more cycles, each adding to the gap.
- B-Costs contribute little to income (e.g., 0.833% per cycle) because B payments are generally saved, destroyed, or reinvested, not distributed as, or rather triggering, much by way of wages.
- The systemic deficit forces the contracting of more and more debt-money, empowering banks and perpetuating economic imbalance.
- Douglas proposes debt-free credit (e.g., Social Credit dividends and discounts) to, in a sense, synchronize the cycles, by providing consumers with purchasing power independently of the process of production and its associated costs.
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Appendix: Concrete Examples of the Equations in Action
Below are six concrete scenarios exploring the impact of varying N1 (money cycle frequency) and N2 (capital recovery period) on the purchasing power deficit. All models assume the revolving volume of money that is issued for production per money cycle (Cycle 1) to be £100,000.
Once again, the price of production is £ (A + B) per annum. But to purchase (i.e.to cancel the allocated cost of £(A + B)) there is present in the hands of the consumer :
£(An1 + B n2 )/ n1 = £ (A + B n2/n1 )
- Basic Model (2-Month Money Cycle, 20-Year Capital Recovery)
Per-Cycle (2-Month Cycle, N1 = 6, N2 = 1/20):
- Purchasing Power: £A + £B × (N2 / N1) = £60,000 + £40,000 × (1/20 ÷ 6) = £60,000 + £333.33 = £60,333.33.
- Per-Cycle Deficit: £100,000 - £60,333.33 = £39,666.67.
Annualized (N1 = 6):
- Total Costs: £100,000 × 6 = £600,000.
- Total Income: £60,333.33 × 6 = £362,000.
- Annual Deficit: £600,000 - £362,000 = £238,000.
- Faster Money Cycle (1-Month Money Cycle, 20-Year Capital Recovery)
Per-Cycle (1-Month Cycle, N1 = 12, N2 = 1/20):
Purchasing Power: £60,000 + £40,000 × (1/20 ÷ 12) = £60,000 + £166.67 = £60,166.67.
Per-Cycle Deficit: £100,000 - £60,166.67 = £39,833.33.
Annualized (N1 = 12)
Total Costs: £100,000 × 12 = £1,200,000.
Total Income: £60,166.67 × 12 = £722,000.
Annual Deficit: £1,200,000 - £722,000 = £478,000.
- Slower Money Cycle (6-Month Money Cycle, 20-Year Capital Recovery)
Per-Cycle (6-Month Cycle, N1 = 2, N2 = 1/20):
Purchasing Power: £60,000 + £40,000 × (1/20 ÷ 2) = £60,000 + £1,000 = £61,000
Per-Cycle Deficit: £100,000 - £61,000 = £39,000.
Annualized (N1 = 2):
Total Costs: £100,000 × 2 = £200,000.
Total Income: £61,000 × 2 = £122,000.
Annual Deficit: £200,000 - £122,000 = £78,000.
- Faster Capital Recovery (2-Month Money Cycle, 10-Year Capital Recovery)
Per-Cycle (2-Month Cycle, N1 = 6, N2 = 1/10):
Purchasing Power: £60,000 + £40,000 × (1/10 ÷ 6) = £60,000 + £666.67 = £60,666.67.
Per-Cycle Deficit: £100,000 - £60,666.67 = £39,333.33.
Cumulative Deficit Over Capital Recovery Period (10 Years, N2 = 1/10):
Total Cycles: 10 years × 6 cycles/year = 60 cycles.
Cumulative Deficit: £39,333.33 × 60 = £2,360,000.
- Slower Capital Recovery (2-Month Money Cycle, 40-Year Capital Recovery)
Per-Cycle (2-Month Cycle, N1 = 6, N2 = 1/40):
Purchasing Power: £60,000 + £40,000 × (1/40 ÷ 6) = £60,000 + £166.67 = £60,166.67.
Per-Cycle Deficit: £100,000 - £60,166.67 = £39,833.33.
Cumulative Deficit Over Capital Recovery Period (40 Years, N2 = 1/40):
Total Cycles: 40 years × 6 cycles/year = 240 cycles.
Cumulative Deficit: £39,833.33 × 240 = £9,560,000.
- Combined Faster Money Cycle and Slower Capital Recovery (1-Month Money Cycle, 40-Year Capital Recovery)
Per-Cycle (1-Month Cycle, N1 = 12, N2 = 1/40):
Purchasing Power: £60,000 + £40,000 × (1/40 ÷ 12) = £60,000 + £83.33 = £60,083.33.
Per-Cycle Deficit: £100,000 - £60,083.33 = £39,916.67.
Annualized (N1 = 12):
Total Costs: £100,000 × 12 = £1,200,000.
Total Income: £60,083.33 × 12 = £721,000.
Annual Deficit: £1,200,000 - £721,000 = £479,000.
Cumulative Deficit Over Capital Recovery Period (40 Years, N1 = 12, N2 = 1/40):
Total Cycles: 40 years × 12 cycles/year = 480 cycles.
Per-Cycle Deficit (from prior calculation): £39,916.67.
Cumulative Deficit: £39,916.67 × 480 = £19,160,001.60 (approximately £19.16 million).
[1] C.H. Douglas, The Monopoly of Credit 4th edition (Sudbury, England: Bloomfield Books, 1979), 46-50.
