Here's a fun one. (OK, I think it's fun, anyway.) Especially for those who teach macro.
A first year student emails me. Paraphrasing, he asks "For a closed economy, we know that national saving equals national investment, and investing in newly-produced goods counts towards GDP. And "saving" means anything we do with our income other than paying taxes and spending on newly-produced consumption goods. So if I take $100 from my pay and stick it under the mattress, does that count towards GDP?"
Your instinct is to answer "No!" of course. But you should be able to see his logic.
Let me restate his question in a different way, so "saving" refers to private saving, and for an open economy, so saving is not necessarily equal to investment.
It is a national income accounting identity (i.e. it is true by definition of the terms) that:
C + I + G + NX = Y = C + T + S
[Consumption+Investment+Government spending+Net eXports = GDP(income) = Consumption+Taxes+Saving]
The normal way to measure GDP is to add up all the terms on the left hand side of that identity (the "expenditure" method). So if you were adding up C+I+G+NX, and then found you had missed $100 in I, and re-did your calculation, your estimate for Y would be $100 bigger than your original calculation.
But suppose instead you decided to measure GDP by adding up all the terms on the right hand side of that identity (we don't have a name for that method, because nobody does it that way, AFAIK). So if you were adding up C+T+S, and found you had missed $100 in S, and then re-did your calculation, your estimate of Y would be $100 bigger than your original calculation.
[And the reason nobody measures GDP that way is precisely because "saving" means literally anything you do with your income except buying newly-produced consumption goods or paying taxes. It includes: buying a newly-produced investment good, buying land, buying a used car, buying financial assets, and sticking $100 under the mattress. So it would be much simpler just to ask people what their income was.]
The problem is this: If Y = X + Z, and we ask "does X count towards Y?", we are making an implicit assumption about whether or not Z stays the same. The number of my Kids equals the number of my Sons plus the number of my Daughters. K=S+D is an accounting identity. Does "if I have one more son" mean "if I have one more son and the same number of daughters" or "if I have one more son instead of having a daughter"?
We tend to read "If I put $100 under the mattress" as "If I put $100 under the mattress instead of spending $100 on newly-produced consumption goods." But we could equally well read it as "If I put $100 under the mattress instead of taking the day off work and earning $100 less".
But "if I buy $100 more newly-produced investment goods" has exactly the same ambiguity. Instead of doing what?
I think the lesson to be drawn is that we must always specify what the alternative is, and what else is assumed constant, so we answer the question: "instead of doing what?". It then becomes as trivial as playing with words should be.
Whenever anyone says "Y=C+I+G+NX, therefore if the government increases spending, GDP will rise" I will reply "Y=C+T+S, therefore if the government increases taxes, GDP will rise."
There must be a better way to teach national income accounting.
Worthwhile Canadian Initiative 
Thinking about this in some more detail, we might have a definitional issue: when does savings happen?
Imagine we have a haircut economy. Everyone wakes up to provide and receive haircuts; they pay the cash at the beginning of the day and empty out the till at the end (so the daily velocity of money is at most one, and there are no payment loops).
We can obviously measure GDP on a payment or income basis equally, as payments provided equals payments received. But if we measure GDP on a daily basis and I decide that despite receiving $10 today I’ll only spend $9 tomorrow and store $1 under the mattress, when – if ever – is savings equal to $1?
Measuring GDP from midnight to midnight, in day 1 I have a consumption of $10 and an income of $10; in day 2 I have a consumption of $9 and an income of $10, but someone else has a consumption of $10 and an income of $9. (In day 3, feedback kicks in and I might not have an income of $10). Yet all of this is “C=C”, not “C+I=C+S”.
To take a long-term and somewhat silly view of the question: does buried pirate treasure count towards GDP?
Professor Nick,
If Government increases G it will not necessarily crowd out “other demand components” (but it may), but if it increases Taxes those will have to come from C and/or S, isn’t that right?
So you can say that an increase in G may increase Y, but an increase in T won’t.
Am I wrong?
Thank you
Ricardo Martins (losinterest.wordpress.com)
(The punch line is in the final paragraph)
From the earlier JKH comment, we have
Y = C + I = C + S
where Y is simplified GDP, C is consumption, I is investment, and S is savings.
For simplified GDP we assume that private (not-Government) consumption income is equal to private consumption expense.
For this three equality equation, we have first GDP, then private income and third, private expense.
Notice that the C term does not account for all of the GDP recorded. Where did money for the excess GDP come from? It came from the I term (investment).
Of course, investment must come from a source. Some people saved their earnings from providing consumption services for others, filling the S term.
For many of us, this explanation is circular, and not a convincing answer. Inventory adjustments for production with life span greater than one year provides part of the answer. For example, housing is not expensed the year of building.
The complete GDP equation will include Government activity and exports/imports. We all know that government spends more than it receives in taxes. This excess spending is all borrowed and it counts towards GDP. In economics, we call this excess spending “investment”.
But there is even more to consider for a complete explanation!
Term Y, in the macro economic view , is the output for the whole economy. When output is defined as income, we count only the money exchanged for goods and think we have a reasonable measure of economic activity. In my view, this is an error. We have ignored the change in debt which is an additional payment that the macro economy has exchanged for output. In other words, speaking from a macro economic perspective, the output achieved in a one year time period should be measured in terms of both debt and cash money; the tallied consumed goods were exchanged for money and debt .
Here is an example to illustrate the preceding comment:
Remember the old western movies where a drink is exchanged for a tally on a tab? No money changes hands, only a drink and debt.
Should that exchange be included in GDP? If so, would you translate the value of the debt into cash money? How do you display both the income and expense methods of calculating GDP?
If you think about the economy in a more comprehensive way than simply “gdp” , you recognize that there are two monetary incentives that motivate us to work : consumption and wealth ( net worth ). Then you might ask : What is the monetary funding source for those two things ? It turns out that cumulated gross savings plus domestic nonfinancial debt matches up well with the sum of current consumption plus total net worth , i.e. ~ dollar for dollar if the mean of market fluctuations of net worth is used. FRED doesn’t have cumulated gross savings , but here’s a log plot of annual changes :
https://research.stlouisfed.org/fred2/graph/?g=3EUf
If you plot the long-term cumulated totals as a log-log scatter plot , you get a nice linear relationship , with slope = 1 , suggesting an intercept at zero , i.e. back to when two cavemen sitting by the fire negotiated the terms of the first-ever mortgage ( on a a nice little starter cave , in a good neighborhood , with highly-rated game trails ).
Roger,
To introduce debt, you need to introduce time into the equation.
Consumption(t1) + Investment(t1) + Government spending(t1) + Net eXports (t1) = GDP(t1) = Consumption(t0) + Taxes(to) + Saving(t0)
The first group of terms is the goods / services part – what is money spent on? This money is spent at time t1.
The second group of terms is the means by which money is obtained. Money can be income received from the sale of goods, it can be taxes, or it can be negative savings.
That is where debt comes into play. Negative savings at time period t0 becomes some type of expenditure at time t1.
Ricardo: “So you can say that an increase in G may increase Y, but an increase in T won’t.
Am I wrong?”
I think so. Government taxes everyone, so people work more to produce more income to pay the tax. The most obvious example is corvee labour, where the tax is paid in kind, but it makes little difference in principle if it’s paid in cash.
The thing about debt is that it is a two edged sword – there’s lender and there’s a borrower. In aggregate they neuter each other.
They are also stock items (balance sheet items) and not income flow items (income statement items).
Interest on debt is an income flow item. Presumably the lender is making a profit on the loan so his profit will appear in the income flow.
Majromax,
“To take a long-term and somewhat silly view of the question: does buried pirate treasure count towards GDP?”
I would say if left buried, no.
If retrieved, yes. Think of the expenditure incurred. This ends up in the income flow. As for the treasure itself, I would say it’s like the production of a new capital good – i.e. a good that keeps giving.
Professor Nick,
I would kindly disagree with you. I guess nowadays people work the amount they are offered to work, so it doesn’t make a difference.
But maybe it’s just my naivety.
Thank you for your response
If you have time, please read my (still enfant economics blog)
Ricardo
Frank R:
You write “To introduce debt, you need to introduce time into the equation.
Consumption(t1) + Investment(t1) + Government spending(t1) + Net eXports (t1) = GDP(t1) = Consumption(t0) + Taxes(to) + Saving(t0)”
I think time is already in the equation. Consumption(t1) is the consumption measured as a sum-of-transactions between measurement t0 and t1 (with a time period between the two measurements).
If this is correct, then your equation should read
Consumption(t1) + Investment(t1) + Government spending(t1) + Net eXports (t1) = GDP(t1) = Consumption(t1) + Taxes(t1) + Saving(t1)
with any t0’s changed to t1’s.
Any exchange that is added to GDP is an “exchange”. This requires two parties for every exchange. One party receives income but the other party has an expense. GDP can be counted by either adding incomes or adding expenses.
Roger,
“Remember the old western movies where a drink is exchanged for a tally on a tab? No money changes hands, only a drink and debt.”
No-one seems to want to have a go at this one, so I will give it try.
Presumably the bottle of whiskey was added to inventory and income in a prior period.
In the current period (when drink was provided):
Income = Bar owner’s Profit = Sale of drink – value of one shot reduction in whiskey inventory
Forget the debt – it’s a stock item – if there is no interest being paid, there is no income impact.
Henry,
I am thinking this through as I write.
As you say, when the bottle was purchased by the barkeeper, it should have been counted as GDP. The barkeeper spent money, the bottle producer received money.
We are discussing a single bottle so I doubt that GDP is aware that the bottle is inventory. Of course it is inventory in the eyes of the barkeeper.
Now an economist walks into the bar to count GDP. I think an economist walking into the bar to take GDP would begin as he walked in. This would be measurement tO. He would count a bottle on the shelf (full) as inventory but as inventory received in the prior period (before t0).
Nothing happens for a while, and then, just before the economist decides to end the GDP measurement period, recording no sales, in comes Joe and orders a drink, “Put it on the tab.”. How does the economist record this transaction?
I think he would record the cash money value of the exchange as GDP. Joe has expense (which Joe calls an investment – it makes him feel better) and the barkeeper has income (a mark on the tally – which is hopefully cash-income someday).
The economist leaves, with a t1 GDP measurement of one drink exchanged for debt. He also notices that the bottle is partially full, down from full at first observation.
The challenge for the economist is to decide what to record. Should he record the fair cash value of the drink, the change in level of the bottle, the tally in the tally book, or Joe’s better disposition?
Up to this point, the economist had no drinks so hopefully he put all this on the correct sides of the income/expense sides of the GDP equation. We have just enough difficulty keeping track of these concepts to make we wonder (about who is drinking what). (I hope you all smile!)
In the real economy, debt may be masked by bank lending. Joe would have plenty of money so the GDP increment would be the value of the cash transaction. The tally mark and debt acquisition would be hidden behind a bank deposit and loan document.
“Nick,.
You say saving includes…”buying a newly-produced investment good, buying land, buying a used car, buying financial assets, and sticking $100 under the mattress.”
I would say:
saving = buying a newly produced investment good
dishoarding = buying land, buying a used car, buying financial assets
hoarding = sticking $100 under mattress.”
Just need to clean something up from this post.
I would like to add to “dishoarding = buying land, buying a used car, buying financial assets”, “as long as there is no profit/loss on the transactions, which if there was, would appear in the income flow”.
Roger,
“In the real economy, debt may be masked by bank lending. Joe would have plenty of money so the GDP increment would be the value of the cash transaction. The tally mark and debt acquisition would be hidden behind a bank deposit and loan document. ”
Isn’t it all in the timing?
The transaction did occur. It must have an immediate income effect (and I will still argue that the income effect is reduced by the change in inventory). When the cash is received is immaterial. When cash is actually handed over, it in effect becomes a change to a stock (i.e. balance sheet) item, there is no income effect. When a business sells a good on credit, it has notionally recorded a profit and a profit is recorded in its income statement. When the cash is received to repay the credit another profit is not booked – that would be double counting. There is merely a shift between assets (credit to cash) in the business’s balance sheet.
This one seems rather obvious. Look at the transactions. He got the $100. That transaction counts as part of the GDP. If he spent the $100, then that transaction would have been part of the GDP as well.
I think some of the confusion is that people try to follow the money, but a $100 bill can be used in any number of transactions over a year. You get this problem with physics. Accounting transaction statements are like free body diagrams. If nothing changes velocity, then there is no force. If there is no transaction, there is no economic impact.
Henry,
You raise a valid point about the inventory change; the bottle did go from full to partly full.
The BEA (Bureau of Economic Analysis) produces a guide to national income and product accounts (NIPAs) which includes the GDP measure. This guide can be found at
Click to access nipaguid.pdf
in PDF format.
A change in inventory that is consumed is counted in GDP. To prevent double counting, the sale of the full bottle to a re-seller would NOT be counted towards GDP. Instead, the retail value of the drink (which Joe purchased) would be counted. I think the economist recording GDP would report Joe’s drink as income to the barkeeper but – because there was no money exchanged – the income would be classified as “savings (S)”. Joe would clearly be a consumer who reduced the barkeep’s inventory but did not pay money. Joe’s consumption would be recorded as an investment. Measured in this fashion, GDP, I, and S would increase but term C would remain unchanged.
The only alternative to this GDP distribution would require that term C be unequal on each side of the simple GDP/income/expense equation.
Roger,
” the income would be classified as “savings (S)”
Was the drink consumed or not? Are you saying it was not consumed?
“Joe’s consumption would be recorded as an investment.”
You have consumption and investment in the same sentence. It can’t be both. Can Joe consume this drink again, and again, and again, etc.? I don’t think so. (Unless of course he spits it out into a flask, then you might have point. 🙂 )
If a bar owner tallied an added debt-increment this has a value as an account payable (it is a financial asset from this perspective).
The scenario is unlikely to unfold unless the drinker and the bar owner have personal relationships where the bar-owner assumes the financial risk but for no real gain – no GDP, from that perspective.
I think Roger Sparks is pointing out that the more likely scenario is the drinker who has a bank give them a loan, and then they buy a drink with some of the money. The bank’s lending account is Investment. The buying of a drink is consumption by the drinker, decrementing the Savings they own in the lending account at the bank (at some time before or afterwards if they pay with a check) with the exchange being counted toward positive GDP on the bar-owner side. But the point again, is that the money came from whole cloth at the bank – it did not come from aggregate Savings as this term is viewed in a lay sense – but NIPA has defined rules allowing you to call it a decrement from Savings by the drinker, even though the savings came from nothing, and were in NIPA accounted for as an Investment (identity shows up, I decrement some bucket and in one context I call it Savigns, but in the context of why the bank established the account, it is counted as Investment – but it is the same bucket. And it is filled up with what?? Whole cloth.
Need to teach this NIPA system as it is, but make sure it is not used in a tail-chasing way to explain the present tense or the future (except as a type of depiction of the end state of the prior period).
henry, I haven’t changed my tune
investment is the addition of the preexisting wealth to the economy that goes into income which is Y
Y = I (investment) + C (consumption)
at then end of the given time period the investment, as Keynes showed, is preserved as savings “in someones pocket” if you will
so since this part of the savings is actually just the investment preserved, it then is part of income, since it is actually just the investment with we have already determined “by definition” is part of the income
there is another part of savings, if we consider savings as that which we are left with, after the giving time period
and that is net production
it does not matter where the production occurred, capital goods or durable consumption goods or public goods like infrastructure
that which we are left with should considered as savings
so wealth is in that way increased, by net production, which becomes part of total savings, or total wealth, or total capital, whatever you prefer to call it
“so wealth is in that way increased, by net production, which becomes part of total savings, or total wealth, or total capital, whatever you prefer to call it,” but this wealth increase is not part of gdp, and it should be considered as savings
djb,
” but this wealth increase is not part of gdp, and it should be considered as savings”
Then you are not defining “saving” as a macroeconomic accountant would. This is your own definition. Saving is not capital, it is not a stock item. In macro accounting terms it is defined as what is not consumption in the income flow.
Wiki: Saving differs from savings. The former refers to the act of increasing one’s assets, whereas the latter refers to one part of one’s assets, usually deposits in savings accounts, or to all of one’s assets. Saving refers to an activity occurring over time, a flow variable, whereas savings refers to something that exists at any one time, a stock variable.
Good point Oliver.
I presumed he meant “saving” given the context.
Many posts above djb says:
“and I am proposing that savings does not “always equal investment”, that this supposed “tautology” is incorrect”
This suggests he is using “savings” to mean “saving”.
I’m wondering now if djb means “savings” or “saving” when he says “savings”?
Henry,
I think we have two issues here.
1. Double entry always has two ways of defining each entry.
2. The second issue: if we have a measurement of economic activity (meaning “exchanges”) occurring between two dates, we have a single measurement.
That single measurement is composed of two accounting categories, income and expense, but each (income and expense) is a proxy for the fact that an exchange (with value) has occurred.
Next consider that the producers of the GDP measurement have decided that an exchange-of-ownership-of-inventory should be counted towards GDP. The production of that inventory results in income for many people but the income frequently occurs in the prior GDP period. How do you (as the producer of a GDP measurement) do the accounting for this contingency?
I think the answer is to have the terms “investment” and “savings”. This allows GDP to measure “transactions” (in terms of money) with the further breakdown into categories of “investment” and “savings” to fulfill the requirements of double entry accounting for inventory.
Nick, Your example shows that (a software engineer might say) micro and macro are at two different levels of abstraction. This is somewhat complicated, so naturally it’s hard at first to see how to resolve them.
Roger,
“The production of that inventory results in income for many people but the income frequently occurs in the prior GDP period.”
I would say:
The income derived from the production of the inventory is added to GDP in the prior period. That added inventory is of course defined as investment.
All that is taken account of (i.e. added to income) in the current period (when the inventory change occurs) is the profit/loss the inventory change yields for the inventory owner. And the profit/loss = sale value – inventory change. So the sale value is added to income and the inventory change is deducted from income. If the good is a consumption good then consumption is incremented by the sale value and investment is decremented by the change in inventory (disinvestment).
“I think the answer is to have the terms “investment” and “savings”.
Isn’t the problem with that, that given the definition Oliver provided in a prior post, “investment” is a flow item and “savings” a stock item. GDP only accounts for flow items.
Did I understand you correctly?
Henry,
Before I began writing this reply, I took a quick look at BEA’s guide to NIPA (referenced in an earlier comment). They use the phrase “estimates of consumption of fixed capital (CFC)”. The bureau seems to have struggled with this issue continuously, changing their procedures occasionally.
Briefly, the problem of measuring consumption for cars illustrates. A car is built in one time period, sold in a second period, and resold many times over many periods. When is the car “consumed”? When is the labor used to build the car “consumed”? When is the related consumption of car and labor measured in GDP? And does the GDP increment consist of consumption or investment/savings?
You write “…………. “investment” is a flow item and “savings” a stock item. GDP only accounts for flow items.”
Yes, I think GDP accounts for flow items but GDP also seems to count changes in stock items. Again, a car may be the best example, but what I think is correct may NOT be the way BEA does things. So I think – if a car is built, the labor used in construction should add to GDP, increasing also the investment and savings measure. If the car is sold in a second measuring period, this should add to GDP again, this time increasing the consumption measure.
Did we double count the car? Yes, I think so. Will we double count the car again when it resells in even later time periods? Yes, I think so. Does BEA make an adjustment for consumption to reduce this double (or multiple ) counting? Yes, I think so but I don’t know how they do it.
I think the breakdown between consumption and investment/savings is adequately complex to allow subjective choices. GDP is more a political measurement and less an accounting report.
Roger,
Regarding assets like second hand cars which can be traded, the profit or loss made by the owner selling the asset makes its way into the income statement (i.e. GDP).
Yes, I would agree that if the car was made in a prior period and not sold in that period, its cost would be added to GDP as change to inventory (i.e. investment). If it is sold in a subsequent period what is effectively booked to income (GDP) is the profit/loss (= sale – inventory change) made by the owner of the vehicle who sells the vehicle.
well, henry, i am saying new production is part of what is left over and that gets added to the total wealth = total capital = total savings
it is not counted as income but should be counted as savings (new wealth)
it is the only way to get new wealth or new capital, call it what you want
there is an additional part of savings that is income
and that is the part of the savings that equals investment
this is not new wealth, this is simply preservation of the investment
simple example, say the investment is all currency, it does its work gets added as part of the income with consumption being the other part of income and via multiplier effect you get total income
now people do not spend all their income, they spend some, save some and at the end of the process the currency has neither been created nor destroyed, it continues to exist as “savings” “in someones pocket”
so this part of the savings, that which is the preservation of the investment, actually is the same money as the investment money and it is left over at the end of the given period as savings
but is not new wealth, so it does count as income, because it is actually the same money as the investment money which of course counts as part of income
so this part of the savings counts as income but not as new wealth
whereas the savings that comes from net production counts as new wealth but not income…. at least not part of I + g – t + c + [ex – im]
Roger,
“I think time is already in the equation. Consumption(t1) is the consumption measured as a sum-of-transactions between measurement t0 and t1 (with a time period between the two measurements). If this is correct, then your equation should read:
Consumption(t1) + Investment(t1) + Government spending(t1) + Net eXports (t1) = GDP(t1) = Consumption(t1) + Taxes(t1) + Saving(t1)”
I am trying to get this into an equation of exchange type format (MV = PQ).
Consumption(t1) + Investment(t1) + Government Spending(t1) + Net exports(t1) = PQ : This is the goods portion of the equation
Consumption(t0) + Taxes(t0) + Saving(t0) = MV : This is the money portion of the equation
The reason I added the two different time parameters ( t0 and t1 ) was to recognize that there is a time delay ( t1 – t0 ) between when money as income is received (MV) and when it is spent on goods / services (PQ). This method allows us to recognize that income received from the sale of consumption goods at time t0 is not identical to money spent on consumption goods at time t1.
Frank R.,
OK, I think I understand your intent to show that income received in period one can be spent in period two.
As we have proceeded through these comments (Nick, thanks for this post!) I have become more keenly aware that GDP is intended to be a measure of INCOME and production within one time period.
If I understand correctly, the BEA is trying to get a measure of income rather than a sum of all transactions. So, to express it mathematically, let M be Money and G be all goods and labor. I (apparently) incorrectly thought GDP was the sum of the G terms in the sequence
M = G = M = G = M = G =……… (apparently incorrect)
where I show three of a much larger number of G’s.
Instead, I now think that GDP is intended to be an estimate of the value of NEW production, some of which is destined to become residual inventory at the end of the period. To express this mathematically, we need the additional term NG standing for New Goods (which would include labor used in the period). Then we would have the sequence
M = NG = M = NG = M = G = M = NG = M = G = M = G = ……….
GDP here would be the sum of the NG terms, with the sum of the G terms uncounted in GDP. I think there is an adjustment in GDP for depreciation. Clearly there is an added increment of income that comes from the ownership of existing homes, an increment treated as rent.
The sequence illustrates the time delay (I think) you were trying to demonstrate. The sequence would unfold over a period of time, each using money as the exchange facilitator.
I need to tweak my (personal) estimation of the role used machinery (including used cars) plays in the GDP measurement.
JKH said: “I think it’s more effective to illustrate this first with the very simplest closed model without government, which is:
Y = C + I = C + S
The other sectors are relatively simple adjustments after this basic conceptual form”
I think so too.
Y = C + I and
Y = C + S
“An important point: macro S consists of the sum of a lot of micro positive and micro negative s’s, depending on the micro drilldown of units that can save”
A really important point here too.
“For a closed economy, we know that national saving equals national investment, and investing in newly-produced goods counts towards GDP. And “saving” means anything we do with our income other than paying taxes and spending on newly-produced consumption goods. So if I take $100 from my pay and stick it under the mattress, does that count towards GDP?”
JKH, let’s skip the taxes. Foreign sector = 0, gov’t sector = 0, private S = 0, and private I = 0. The person saves $100 and puts it under the mattress (does not invest). I believe the person is asking what happens if someone saves but does not invest and no other entity invests. Private I = 0, so private S needs to = 0. If the person micro saves, then other entity(ies) will micro dissave so private S stays = 0.
Also it seems likely that C will fall if no entity borrows or issues stock.
Are those right? Thanks!
Nick: I was not going to comment on this I=S debate and the philosophy of national income identities until you mentioned Hayek. Hayek is always an excellent palliative for too-Keynesian thinking. As for I=S: in a robinson crusoe economy, not only does I=S, but I is identical to S. Hayek tells the story (in Pure Theory of Capital) of Robinson spending all his waking hours climbing trees to gather bananas. 10 hours per day allows him to gather 10 bananas to be satisfied for the day. Obviously his income is his consumption. Robinson realizes that if he spends only 7.5 hours of his time on gather bananas and now spends 2.5 hours of his time on fashioning a stick to knock the bananas from the tree he will consequently, in future (emphasis!), be able to spend only 2.5 hours of the day on gathering the same number (10) of bananas as the stickless-gathering. Robinson will in all future periods (ignoring stick-depreciation) have 7.5hours freed up time(emphasis!).
Everyone should see perfectly easily that in this story, the “saving” of 2.5 hours of Robinson’s labour-time (priced at 25% of the daily banana-gathering or 2.5 bananas) is perfectly identical to robinson’s “investment”. (this is a different thing from ‘hoarding’, which as you know, consumed the keynians and Howtrey in the interwar period)
As for the fixation on the national income identity: the day before making the stick: Y (10 bananas) = C (10 bananas);
In order to appreciate the theory of the national income identity, we have to face the fact that on the stick-making day, strictly speaking: Y(7.5 bananas) = C (7.5 bananas). we are very tempted to throw S on the right hand side of the equation. it is obvious that S=I in this case and we can logically “price” S and I at 2.5 bananas. But what does the national income identity measure? “actual” income “actually” taken from the tree on the stick-making day in question (only 7.5 bananas)? if so we omit the notional saving and investment from the right hand side of the equation.
recall that the early theorists on capital seemed to solve this problem by conceiving of “advances” (savings from past periods) which were actually paid to the stick-making robinson on the stick-making day (2.5 bananas) for his stick-making work. So under the ‘advance’ theory of the national income identity we would be back to Y (10 bananas) = C(7.5 bananas) + I (2.5 bananas advanced to robinson from past period savings).
ECC (Carleton MA 88)
“…on the stick-making day…….Y(7.5 bananas) = C (7.5 bananas). ”
I would say his income on stick making day clearly was :
Y = 7.5 bananas + 1 stick.
How you would value the production of one stick for income accounting purposes in a non-monetary economy is another question.
What motivated RCs behaviour is also another question all together. He could see the possibility of producing 10 bananas in 2.5 hours leaving 7.5 hours for other activities. The value of future production for him was significantly greater than the loss of 2.5 bananas while making the stick.
on the macro level saving is determined by all the output purchases that weren’t consumption (that includes inventories of consumption goods). focusing on an individual’s choice to save 100 dollars is misleading because we don’t know if any non-final consumption output has been purchased. Incidentally Marx makes this point when he criticizes Smith for breaking down all national income into “revenue” in volume two of capital.