Tuesday, 7 October 2025

Notes on the UK Steel Industry

 1. the ever-brilliant House of Commons Library published British Steel and government special measures, June 23rd. Some notes.

On 12 April 2025, Parliament passed the Steel Industry (Special Measures) Act 2025, giving the Secretary of State powers to issue directions or take control of steel undertakings in England at risk of closure. This allowed the government to take control of British Steel’s operations, including securing raw materials, and maintaining blast furnace activity.

What is it costing

2.  On 20 June 2025, the Minister for Industry, Sarah Jones stated that the amount of working capital provided for British Steel since passing the emergency legislation on 12 April stood at £100 million.

On 27 March 2025, announcing its plans to consult on closing the two blast furnaces at Scunthorpe, British Steel said that despite Jingye’s investment of £1.2 billion since 2020, the operation of the blast furnaces caused losses of £700,000 a day. British Steel’s costs of building an electric arc furnace have previously been estimated to exceed £1 billion.

Comment. 0.7m per day is £255m per year.


Employment.

3. The company had opened a formal consultation on “the closure of the blast furnaces, steelmaking operations and a reduction of steel rolling mill capacity in Scunthorpe”, which means a consultation with its workforce on redundancies.14 The closure of blast furnaces at Scunthorpe would put 2,700 jobs at risk out of a workforce of 3,500, according to BBC News

in UK Steel Industry: Statistics and policy we learn 

"According to the latest (May 2024) UK Steel estimates, the industry employs 33,700 people and a further 42,000 in the wider supply chain." 

Comment.  2,700 jobs is 8% of the whole workforce.  A payment of £255m per year is £94,000 per job.  There is more or less full employment in the UK at the moment. It's not clear those individuals wouldn't get another job.


Green.

4. From  in UK Steel Industry: Statistics and policy we learn:

"The steel industry is a significant contributor to greenhouse gas emissions. It is responsible for 13.4% of greenhouse gas emissions from manufacturing, and 2.2% of total UK greenhouse gas emissions, while it contributes 0.1% of the UK economy and 1.0% of UK’s manufacturing output." 

"Two main methods dominate steelmaking in the UK: the blast furnace and electric arc furnace method" 

Tata Steel has closed its blast furnaces at Port Talbot and is investing in EAFs, as set out in more detail in section 6. Also British Steel had plans to decarbonise steelmaking at Scunthorpe by closing its blast furnaces. This together was estimated to reduce the UK’s territorial greenhouse gas emissions by 2%

However, the extent to which an EAF is green will depend on the electricity that powers it. For example, if the electricity is produced from fossil fuels, the EAF will have limited emissions savings, whereas if the electricity is produced from a mixture of technologies including some that are low carbon (as the electricity grid in the UK is) then the EAF does provide emissions reductions to the steel making process.

Comment.  So if we are to decarbonise then we will have to spend on an EAF. This is estimated to be £1bn. 


Energy costs

5. UK electricity prices for very large industrial consumers in the second half of 2023 were higher than for any EU member state. They were 23.04 pence per kWh which was 71% above the median price in the EU.




The main support measure for energy intensive industries’ electricity costs is a series of exemptions and compensation. The government provides compensation or exemptions to energy intensive industrial users for the indirect costs (higher electricity prices) associated with funding certain decarbonisation policies. The policies include the climate change levy, contracts for difference mechanism, renewables obligation and feed-in tariffs. The government said in November 2023 it had provided the steel sector with more than £730 million of relief since 2013 to make energy costs more competitive

Comment.  So additional support comes from these exemptions. 

Security

6. "With the closure of the blast furnaces at Port Talbot, and the possible closure of British Steel’s blast furnaces in Scunthorpe, and the transition to solely electric arc steelmaking, the UK would lose its primary steelmaking capacity. 150 Should that happen, the UK would be the only G20 country that does not produce its own virgin steel. This has led to some questions around national security and whether virgin steel production should be retained as a sovereign capabiliy". 

"According to the Royal United Services Institute for defence and security studies, prime contractors supplying the MoD have a mixed record on the use of UK steel. The Financial Times reported the facilities at Port Talbot were not used to produce steel used in defence" 

"In the Opposition Day Debate on 23 January 2024, the Secretary of State for Wales acknowledged that historically there was an issue with the quality of the steel produced in an arc furnace. Experts had reassured him, however, that it was steadily improving. He said: Tata expects an electric arc furnace to be able to supply about 90% of the products that it currently supplies through the blast furnace"

the Business and Trade committee take the view " The committee refers to evidence that blast furnaces still play a critical role in strategic and high-grade steel production, including for infrastructure construction. Keeping the Scunthorpe blast furnace open would maintain supply chains" 

Comment.  It's a bit obscure to me whether this steel is security necessary.  And if it needs blast furnaces then it won't be very green. 


Updates.

1. the New York Times reports, August 22nd 2025, "for the second time this year, the British government is set to take control of a large, ailing steel business.

The move comes after a court approved on Thursday the liquidation of the unit, called Speciality Steel UK, which is part of Liberty Steel, a metals business started by the industrials entrepreneur Sanjeev Gupta. The government is expected to guarantee pay for the nearly 1,500 employees there" 

2. speaking in Parliament, we have the minister: it's not clear, but I think she is supporting the workforce on furlough. 

But she then advances a new argument regarding Scunthorpe:

"It is worth noting that Liberty Speciality Steels uses electric arc furnace technology that can be powered up or down as needed" 

"The circumstances in Scunthorpe were fundamentally different. British Steel operates the UK’s last remaining blast furnaces—assets that, once shut down, cannot simply be restarted. Allowing those blast furnaces to be closed pre-emptively would have removed our ability to make strategic choices about the future of steelmaking in Scunthorpe, and that was not a position this Government were prepared to accept. Scunthorpe was therefore a truly exceptional situation and that is why we took the unprecedented step of implementing the Steel Industry (Special Measures) Act 2025 to maintain the safe operation of the blast furnaces."


As for Liberty, the support seems to be for the workforce:

"The situation with Liberty Speciality Steels is not comparable. The company was issued with a winding-up order by the High Court due to longstanding financial issues. Spending taxpayers’ money on a company operating in such a way would have exposed taxpayers to hundreds of millions—potentially billions—of pounds in hidden costs." 

R&D and productivity: some notes

I'm kindly invited to the British Academy to discuss a report https://www.thebritishacademy.ac.uk/publications/mapping-the-economic-returns-of-r-and-d-in-the-uk/  Mapping the Economic Returns to R&D.

Here are some notes.

1. A puzzle. “changes to the Office for National Statistics (ONS) Business Enterprise R&D (BERD) survey methodology suggests that business investment in R&D is higher than previously thought. However, the UK is still seeing stagnating productivity and economic growth.” 


How can this be?  There is a confusion here on levels and growth.  Remember that the level of productivity depends on the level of the capital/labour ratio.  The level of capital this year depends on the net of deprecation last year capital plus investment.  If we have discovered more investment then 

a. The level of GDP rises since there is less intermediate and more investment 

b. The level of capital rises with more investment.  

c. What about growth? proportional capital growth is I/K – deprecation.  So discovering more I only raises capital growth if there is no more K, but the more I means more K.  So in the steady state, capital growth is the same. 


2. Is the “UK good at research but bad at commercialisiation”.  Commercialisation costs money.  So if we were bad at it, then the returns to UK investment would be very low.   Below is a picture of the return on UK market sector capital. 


 



The UK is the thick black line. No sign that it’s particularly low. 


3. The report rightly points out that there are many pathways to innovation.   Using the latest ONS data on intangible investment, https://www.ons.gov.uk/economy/economicoutputandproductivity/productivitymeasures/bulletins/investmentinintangibleassetsintheuk/latest#investment-by-industry-section-in-2022, we have the following

a. R&D GFCF as a proportion of GVA is largest in manufacturing





 


b. But viewed besides other intangibles, it’s relatively small: notice the investment in software.  

 



c. There’s an important point here: in the national accounts, ESA10, software made in the process of conducting R&D is counted as GFCF in software and not R&D.  


4. The report has an interesting take on government innovation around it’s discussion of “moats”.  I think the idea is this

a. There is a wedge between the private value of spending on innovation and social value if spenders cannot appropriate returns from spending e.g. rivals copy their ideas.  

b. The usual economics answer is that if returns can be appropriated = a “wide moat” e.g. watertight IP, then firms need no support and vice versa for a “narrow moat”. 

c. They then distinguish between “tradeable” and “non-tradeable” technologies and processes.  They say “For non-tradeable technologies and processes, or those that primarily operate in a domestic market, research, commercialisation, and adoption tend to occur in domestic pathways, with commercialisation and adoption more tightly bound, often with a single actor or firm. There is a high proportion of process-led innovation and direct implementation within firms.”  I think the terms are unfortunate since tradeable and non-tradeable mean something specific in economics, but I think what is implied is whether commercialisation occurs, for reasons of technology, secrecy etc., either largely within firms or could also occur outside.  

d. Their examples are in their Table 1: 

 




Where for example mRNA is tradable, by which I think they mean potentially developed anywhere, but has patent protection.  Innovative galleries, are, non-tradable ie. Found in a particular country, but have a wide moat, which means they are hard to duplicate.  

e. This leads to policy proposals

 




5. Some thoughts on this

a. The point that knowledge is non-rival is often used to justify that innovation will not earn returns.  But this depends if the knowledge is also excludable, which is the moat point.  This is valuable.  The UK Patent box costs £2bn with 145 companies accounting for 92% of relief. They probably have IP protection, so this feels like money that can be reassigned (https://haskelecon.blogspot.com/2025/10/how-much-is-uk-r-tax-credit-scheme.html). 

b. The R&D tax credit costs not £7.6bn, with around 40% going to large firms.  Perhaps we have to live with this since we have a relatively high corporate tax rate (https://obr.uk/box/corporation-tax-in-historical-and-international-context/) , 2020 data from OBR below.



 


c. What is the problem we want to solve here?  In my work with Hans Neilson we have some of the following: a.       

                                                              i.      The UK post GFC slowdown is mostly a slowdown in TFP in non-ICT service industries. 

                                                            ii.      The UK productivity growth story since the pandemic is this. Excluding sector L, GVA per hour grew 0.34pppa 2011-18 and 0.24pppa 2019-24.  (Notice how important sector L is, Whole econ data are 0.50 and 0.35).

                                                          iii.      The Marimekko diagram is this 



Where notice that health and education have growth and shares of -3.5%pa and 1.8%pa and 10% and 7% (pre-pandemic, 2011-18 growth rates were 0.4%pa and -0.3%pa).  Thus the 2019-24 contributions to labour productivity growth were -0.31%pa and 0.12%pa. 

So to a first approximation, the answer to the question " we are doing all this R&D and what is happening to labour productivity growth" is, since 2019, the drag from the health service. 



Friday, 3 October 2025

How much are the UK R&D tax credit and Patent Box schemes costing? (Around 7.6 and 2.0 bn in 2023/4)

 1. There are some new figures just out, 30th Sept 2025 (next ones due in a year):  "

Research and Development Tax Credits Statistics: September 2025


here

2. "The total support claimed through both R&D schemes for the tax year 2023 to 2024 is estimated to be £7.6 billion (figure 2 and table RD2). This is a decrease of 2% from last year’s total of £7.7 billion."





3. Broadly, the green and purple are SMEs .  The lighter orange/red is large firms. 
4. There is some explaination of these schemes here. Broadly, the RDEC is aimed at large companies, but some small ones claim.  
5. One interesting point is that cloud computing and data expenses are now eligable, since April 2023. As usual ForrestBrown are on top of this.  This is an evolving area, but their broad view is, I think, that cloud computing and data licenceing costs, if they are used in R&D, qualify for relief.
6. it is interesting how. much R&D tax credits have grown, they were around 4bn in 2016.  
7. There is also the Patent Box This costs about £2bn, with 145 companies accounting for 92% of relief. It is very concentrated in manufacturing.  Some excerpts: 

"In financial year 2023 to 2024, it is estimated that the top 145 companies (by the value of the relief they receive each year) accounted for 92% of the relief." 

"
  • in the financial year 2023 to 2024, it is provisionally estimated that 1,650 companies elected into the Patent Box regime. 

  • the value of relief provided under the Patent Box is estimated to have increased to £1,977 million in the financial year 2023 to 2024 from £1,449 million in the financial year 2022 to 2023. This was driven by the change in the main rate of Corporation Tax from 19% to 25% on 1 April 2023

  • of the companies that elected into Patent Box in financial year 2023 to 2024, it is estimated that 28% were classified as ‘Large’ and accounted for most of the relief provided (95%)"





Friday, 26 September 2025

How important are intangibles in accounting for productivity growth?

1. I was asked today: if intangible capital deepening slows, is that a big effect on productivity growth?  This is part of a broader question; what's the relative importance of intangible assets in accounting for productivity growth (value added per hour growth)?

2. Growth accounting allows a decompositition of labour productivity growth into the contributions of:  

a. reallocation = workers moving between industries of different productivity levels 

b. labour composition = increased skills, age and experience

c.  ICT capital deepening = increased ICT capital (computers, comms equip) per hour 

d.  NonICT capital deepening = increased NonICT capital (buildings, vehicles, non-ICT plant) per hour 

e.  Intangible capital deepening = increased intangible capital (R&D, software, artistic originals, design, marketing, business process, training) per hour 

f. TFP = increased total factor productivity (what's left over, which increased efficiency plus mismeasurement etc.)

Here are some results from our EUKLEMS-INTANProd database, in hopefully obvious notation.  Countries are US, UK, EU (France, Germany, Spain, Italy, Denmark, Holland, Austria, Sweden, Finland). Industries are all ommiting A (agriculture), OPQ (defence, education, health), B (mining), D-E (gas, electricity, water), F (construction).  All these are not well measured, and/or mostly public sector. 

As the results show, intangible capital deepening is much the most important contributor to labour productivity growth in the 2011-19 period (tangible capital deepening contributions is the sum of ICT and NonICT, which is still lower than the intangible contribution).

Table:  of contributions

 


And a picture


As we saw in a recent blog the employment rights bill will very likely lower intangible investment. That will lower intangible capital deepening, other things equal.  This then is a policy measure lowering the major source of UK productivity growth.  Not a good policy if you want growth to increase. 

What has happened to R* recently?

 The 2025 Brookings Papers conference had a sesssion on this.  

The slides from Lukasz Rachel and the discussants are available. 

The discussant Adrien Auclert makes some very nice points. I picked up on some.


First, the framework.  R* is the price that balances demand for capital for use in production by firms with the supply of savings by consumers.  But terminology is hard here: the savings by consumers causes them to build up wealth, which is in part demand for durable assets (e.g. a house).  So wealth accumulation is asset demand which is capital supply.   And the demand for the use of capital is by firms and governments to produce goods/svcs, and they issue claims on the owernship of such assets e.g. shares (and for government, government debt).  So the value of assets issued by firms and government is asset supply or capital demand.  This is nicely illustrated by his graph which highlights the demand/supply nomenclature 


Thus he talks nicely about forces that raise asset supply which raise r*



And forces that raise asset demand, which lower r* 


He summarises the main finding of the paper as being that asset demand has won



with the main drivers falling productivity, rising aging and rising risk


Here is the prediction for the future


most of these are putting upward pressure on r*, but intangibles are lowering. why? this is because in his model more intangibles offset competition and innovation and so lower productivity.  

Thus we have

1. business as usual, small and gentle fall in r*

2. more productivity growth, r* rises. 





Thursday, 18 September 2025

Will the Employment Rights Bill help or hurt growth?

 

  

1.      The Employment Rights Bill is making its way through the UK Parliament at the moment. There are a lot of details, set out in, for example, the Impact Assessment,  here.  Among the provisions quoted there are unfair dismissal, paternity and sick pay rights from the first day of employment, repealing laws that require minimum service levels in some industries during strikes, strengthening union rights etc.

2.      What will the effects be on growth? Since the government says its entire policy is about growth this is an important question.

3.      To understand the effect on growth it will be helpful to understand the effect on investment. The graph below makes dismal reading. Using the OECD index of employment regulation, there's a negative relationship which is that more employment regulation means less intangible investment. To the extent that intangible investment is important for growth, this is bad news for the policy.

 

 

Source: own calculations

 

4.      This graph might seem obvious. But a moment's reflection raises a few puzzles. First, if the cost of employing workers goes up firms would presumably substitute towards capital. That should tell you that more employment regulation would give you more investment, not less.  Second, the proponents of this bill argue that it will make workers happier and productivity will go up for that reason.

5.      So what's going on?

6.      Let's start by thinking about investment. There are two important effects of costs on investment.

a.      The first is the cost of capital effect. Once the firm has decided to invest, other things equal, a fall in the cost of capital, say from a tax break, will make the firm invest more. By this logic, a rise in the price of labour, due to this bill, lowers the relative cost of capital relative to labour, thereby potentially raising investment. This logic gives rise to the first part of the puzzle above.

b.     But there is an important second effect on investment. The outcome of investment is uncertain. Further, much investment is sunk, which is to say that it is often difficult to get that investment back once you have made it.  Think for example about Nokia's investment in software which became Windows Mobile. When the market for Nokia's mobile phones collapsed, around $5 billion worth of software investment had to be just written off. This is important because the cost of capital effect applies once the firm is actually decided to invest. But the uncertainty effect means that a rise in uncertainty makes the firm postpone its decision to invest. With uncertainty and sunk capital, there is an additional cost of investment, which is that investing today costs the firm the value of waiting.  That waiting has value (formally an option value), since underlying uncertainty might be resolved in the future.

7.      So the Bill has potentially two effects. The cost of capital effect is good for investment, because it raises the relative price of labour. The uncertainty effect is bad for investment, because firms will postpone investment until the uncertain costs are clearer.

8.      What then will we expect? My best prediction is that the employment rights bill is a rise in uncertainty for firms. The reason is that these employment rights are set out in broad outline in the bill, but then end up being interpreted by the courts.. The backlog of court cases is now over a year. It will in practise take a long time for the full implications of these employment rights to become clear to firms.  Look for example at the avalanche of cases around equal pay, the Next case for example ((https://assets.publishing.service.gov.uk/media/66d190b2bdecebe01a183399/Miss_M_Thandi___Others_V__Next_Retail_Limited_-1302019-2018-Resreved_Judgment.pdf). .  These cases have taken years, and in the case of retailers precede retailer by retailer.

9.      In case this might seem a matter of theoretical curiosity it is worth remembering the effects of Brexit are precisely this uncertainty effect. As Josh Martin and I showed, after the Brexit referendum investment literally stopped in its tracks for many years. A significant slowdown in growth thereby followed.

10. This uncertainty effect explains why the bill would likely particularly affect intangible investment. Intangible investment is likely to be more sunk, more company and market specific than tangible investment: British Airways can always sell its planes, but much harder to sell its brand name. This in turn is why the cross country evidence sometimes finds employment market regulation is negatively correlated with investment and sometimes positively correlated: It depends upon whether the underlying investment considered is both sunk and if the regulation is uncertain.

11. Finally, moving outside investment, some remarks. 

12. First, my baseline model of the labour market is a simple one: there are wage and non-wage attributes of every job.  The non-wage attributes are, for example, paid tea-breaks, effort on the job and contractual form (employees v freelancers for example).

13. Second, the CMA has done an extensive study of the presence of “monoposony” power in labour markets (Competition and market power in UK labour markets, CMA Microeconomics Unit 25 January 2024 Report no. 1).  This is hard to do, since we don’t really know what the labour market is, especially in the era of working from home.  Taking the “labour” market as the Travel to Work Area, they find

a.      87% of workers work in “low-concentration” labour markets (in 2019, that fell to 80% in the unusual conditions of the pandemic), see p.104

 

b.     The effect of moving between concentrations is not large.  (para 5.14, see also the notes to figure 21),  “…an increase in concentration …by 10% …would be associated with just a 0.1% fall in wages.”.  This means that going from medium concentration, 2,500 to low, 1,500 which is a 51 log point change would change wages by ½ a percent.

14. Further work by the CMA, on my reading at least, has not found widespread product market monopoly power either (except in some cases).  It seems unlikely to me then that monopoly and monoposony power is widespread.  Thus the first-order effect of a rise in costs on firms will be adjustment of wage and non-wage margins, or, if this is not possible (due to wage floors for example), adjustment of quantities.  Thus the assumption that workers will be “happier” and so more productive after the  passing of the bill seems questionable; we don’t know what other margins will adjust.  For example, the Next case found that following the minimum wage, Next abolished paid rest breaks (unpaid rest breaks were the industry norm so this was reverting to the industry standard).

Wednesday, 17 September 2025

A portrait of UK R&D

 Getting a handle on innovation support is hard with many schemes, funding etc.  Just looking at R&D, here is some data from Cambridge UK Innovation Report, 2025, using the latest 2022 data.


1.  Spending on R&D, excluding tax credits looks like this: where the Sankey diagram nicely shows the potential difference between an intangible asset that can be financed in one area and have the performed investment be in another place: 



(btw, within UKRI are a number of other institutions; research councils (competitive grants allocation, about 50% of the money: innovateUK(working with companies to derisk innovation, catapult centres etc. about 20% of the money).  HEFCE/Research England give out REF-based money to universities.  See here,). 

.  

2.  What does business spend the R&D money on (notice these are products and not industries)?  Notice the massive figure on software development; and notice too the seperate line for computer programming and info services.  The days of R&D being mostly pharma and transport are over. 




3. Finally, notice too that government support for R&D can also be tax credits.  They are much more than direct funding as the below shows:


4. and the figures for tax credits are very large; £7.5bn in 2022-3 "For the 2022–23 tax year, UK businesses claimed a total of £7.5 billion in R&D tax relief support. This figure is more than twice the £2.6 billion of direct support to business R&D provided by the government and UKRI in 2022" 




By size "In terms of R&D tax credit claims by firm size in the UK, in the 2022–23 tax year:[2] • 67% (US$5 billion) were claimed by small and medium enterprises • 33% (£2.5 billion) were claimed by large firms." 

 

Did persisently low interest rates post GFC lower productivity growth?

Many allege that the long run of low interest rates post global financial crisis lowered productivity growth via zombie firms.  These low productivity firms survived more than they should have done and hence productivity growth stalled.  

An alternative view is that low productivity growth, for other reasons, lowered r* and hence interest rates.  

A paper "Aggregate productivity decompositions using structural business surveys: Evidence from the UK by Russell Black, Rebecca Riley and Garry Young", available here sheds a bit of light on this for the UK.

It uses UK company data to decompose productivity growth into that 

a. within surviving companies

b. reallocation of market share between surviving companies

c. the net effect of exit and entry.

One might think that the zombie firms view would say that the net entry/exit effect would be less as fewer low productivity firms exit.  

Their chart shows this isn't the case.


1. Using various different methods the change in the net entry effect, see middle panel is very small, a slight fall.

2. instead, the fall in productivity growth is due more or less equally to falling within firm growth and falling between firm reallocation.  The latter might be a zombie phenominon, but it isn't clearly so.

Tuesday, 16 September 2025

Thinking on the margin, or economic thinking as a system, again

 As we often say in class, economics is about thinking on the margin.  Statement "tobacco taxes rose, but my friend carried on smoking, so economics is rubbish". No.  Your friend might be inframarginal.  It's very likely that for a person on the margin, they will stop smoking.

Another way to say this is that economic thinking is systems thinking. Don't just think about the consequences for your friend, but for the system as a whole.  And the system as a whole will be influenced by marginal smokers. 

Here's an application of that.  

1. The Earned Income Tax Credit subsides workers on a low wage and is much more generous for workers with children.  See the discussion in Leigh, https://docs.iza.org/dp4960.pdf. 

2. What happens when it is introduced? One non-marginal model is to say: well, if more workers with children work, that raises supply and lowers the wage of low paid workers with children.

3. The marginal argument is different.  If the supply of labour rises, then wages will fall for all marginal workers, those with and without children.  

4. what does the paper find? 

"Although the EITC has a much larger effect on the labor force participation of workers with children than those without, the wage effect appears to be similar for workers with and without children. This suggests that what matters is the average EITC rate in a labor market, not an employee’s own EITC rate."

So when someone tells you how beneficial tax credits are, think of the system.  Subsidising firms to pay low wages has systemmatic effects.

Monday, 1 September 2025

Rates of return, net present values and cost-benefit ratios

 1. suppose the government spends £x on some investment, say a road or R&D.  What is the rate of eturn/ 

2. Following some excellent notes from the OBR, we have that the IRR of that spend is the discount rates that solves the equation

 Title: N P V equals sum from n equals 0 to infinity of B over open parentheses 1 plus r times close parentheses to the power of n minus x equals 0

 - Description: {"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>N</mi><mi>P</mi><mi>V</mi><mo>=</mo><munderover><mo>&#x2211;</mo><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow><mo>&#x221E;</mo></munderover><mfrac><mi>B</mi><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mi>r</mi><mo>&#xB7;</mo></mrow></mfenced><mi>n</mi></msup></mfrac><mo>-</mo><mi>x</mi><mo>=</mo><mn>0</mn><mspace linebreak=\"newline\"/><mspace linebreak=\"newline\"/></math>","origin":"MathType Legacy","version":"v3.19.0"}

 that, is the rate of return that sets this number to zero.

3. the Benefit from spending on some investment is more GDP.   That increase in GDP is dY/dK.=alphaY/K where alpha is the elasticity of output with respect to capital.  If Y/K is constant and we imagine spending £1 investment we have 


which says that the IRR is the marginal product of the project less the depreciation rate.  Or, the marginal product of the product is the gross rate of return.