<p>It is because saving <strong>is investment expenditure</strong>, they must be  equivalent in standard macro models. To explain this forget about CGE models for a second, they are set up in this way because all macroeconomics is set up in this way.</p>
<p>In macroeconomics by definition income = expenditure. This is definitional. For closed economy by definition income (Y):</p>
<p><span class="math-container">$$Y \equiv C+ I + G \tag{1}$$</span></p>
<p>where <span class="math-container">$C$</span> is expenditure on <em>consumption</em> (which is what you likely confused with expenditure in general), <span class="math-container">$I$</span> is expenditure on investment (public plus private saving), and <span class="math-container">$G$</span> is government expenditure (see more details in Blanchard et al Macroeconomics a European Perspective).</p>
<p>Now <span class="math-container">$I$</span> will by definition be equal to public and private saving since private saving <span class="math-container">$S_p$</span> is by definition income not consumed after taxes: <span class="math-container">$S_{p} = Y-T-C$</span>. Public saving <span class="math-container">$S_G$</span> is by definition any difference between taxes and government spending <span class="math-container">$S_G = T-G$</span>. Together then all saving must be:</p>
<p><span class="math-container">$$S= S_p+S_G = Y-T-C+T-G=Y-C-G$$</span></p>
<p>Now this must be equal to investment since just by rearranging equation 1 we find that investment is:</p>
<p><span class="math-container">$$Y-C-G =I \implies S=I$$</span></p>
<p>Hence the reason why the CGE imposes restriction that income is equal to expenditure is not that there should be no saving (although there might be simplified models where saving will be 'turned off' to make it easier for students). It is because expenditure and income are macroeconomically equivalent even in presence of saving (which is just investment spending).</p>

CC BY-SA 4.0
2020-12-13T17:31:39.487Z
Thank you for this well-thought out response! This actually makes more sense. You're correct--I confused expenditure in general with consumption spending in particular.
Andrew Plummer
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2020-12-14T03:10:57.463Z
Consider the Robinson Crusoe economy where one man lives alone in the wilderness or Commonwealth territory. He uses labor to produce a mix of consumption and investment goods. The allocation of labor in production determines the level of investment. There is no financial saving. I don't think it makes sense to say saving equals investment or expenditure equals income in this toy model because there is no money or finance relations. To state that expenditure equals income the classical factors of production are labor, land, and capital. Expenditure equals income as wages, rent, and profit.
SystemTheory
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2020-12-14T03:23:08.837Z
@SystemTheory they are by definition equal, as proven mathematically. I think issue here is that since you are not an economist you might be unfamiliar with  terminology used in economics. In economics saving does not have the same meaning as saving in common English. In economics saving is by definition difference between income and consumption. This holds even in Robinson Crusoe economy. Investment is only possible if income/output is not immediately consumed, if Robinson Cruse catches 5 fish but eats only 4 in economics that would be saving and that extra fish would be inventory investment
1muflon1
CC BY-SA 4.0
2020-12-14T15:00:00.113Z
@1muflon1 I studied engineering where definitions relate to a social custom known as a measurement procedure. The logic for definition of income equals expenditure is that all expenses are made for investment, consumption, or government and all income is a factor payment called wages, rent, profit, taxes. Then if it is logical to say that expense payments equal income receipts the definition holds expenses = income in aggregate economy. If the logic does not hold the definition is invalid. Robinson Crusoe does not have to save consumption goods he only needs enough to subsist so he can invest.
SystemTheory
CC BY-SA 4.0
2020-12-14T15:16:35.513Z
@SystemTheory but all expenses will be equal to income. Again in Robinson Crusoe economy where 5 fish are caught but only 4 consumed by definition consumption expense  is 4 and investment expense 1. Accumulating inventory is considered inventory investment in economics. Now in same Robinson Crusoe economy the factor income to labor is 5 fish. So the income is 5 fish and all expenditure (consumption 4 fish, investment 1 fish) again gives you 5 fish. So the definition is valid. If it wouldn’t there would have to be inconsistency in the math above which is just pure logic applied to definitions.
1muflon1
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2020-12-14T15:21:56.227Z
@1muflon1 In a two person economy Crusoe would spend say 3 hours of labor to catch 5 fish. If he eats 4 there is 1 left over which will spoil if there is only 1 person in economy and cannot be an investment activity. In a two person economy Crusoe can create a consumption goods surplus, say getting 8 fish, he can share 4 fish with Friday, and Friday can work 8 hours labor on an investment project. Crusoe and Friday can vote or agree (socialism) how to allocate labor to consumption and investment while subsisting without saving anything first. Saving may be a flawed concept in economic logic.
SystemTheory
CC BY-SA 4.0
2020-12-14T15:25:59.667Z
@SystemTheory no it would be an investment with 100% depreciation rate. Even capital spoils over long periods of time so according to your logic that is not an investment? Look the problem here clearly is that you are not familiar with the terminology because this is not logical issue. Let me give you analogy your argument is basically equivalent to telling biologist that dolphins should not be mammals but fish because they live in water and have fins and most people understand fish as animal that lives in water and has fins but that is not biological definition of fish.
1muflon1
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2020-12-14T15:32:43.540Z
@1muflon1 So investment has two meanings in economics. The meaning I am evoking is the allocation of labor to produce capital (buildings, plant, property, equipment used in the production of more goods). So Friday might make fishing poles as a capital investment while Crusoe catches fish without poles to furnish consumption goods to himself and Friday until the fishing poles are finished. The other meaning of investment is consumption goods inventory held in the production sector before transfer to households for consumption. Labor is allocated to capital projects or consumer goods production.
SystemTheory
CC BY-SA 4.0
2020-12-14T15:32:55.207Z
@SystemTheory also in your example that sharing of 4 fish with Friday would be saving and investment spending for Robinson Crusoe since in this case he hired Friday to build some capital goods which also counts as investment but investment is not just that.
1muflon1
CC BY-SA 4.0
2020-12-14T15:35:18.757Z
@SystemTheory no investment does not have two meanings but there are different types of investments that all counts as investments - you can have capital investment and also inventory investment they are both part of total investment. Of course you scan subdivide investment into infinitely many subcategories but those are not different meanings. Just because you can subdivide fish into salmon, tuna etc that does not mean fish has multiple meanings. Fish and investment are umbrella terms. Even consumption can be subdivided into necessities, luxury etc that is not same as having multiple meaning
1muflon1
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2020-12-14T15:44:07.693Z
@1muflon1 The logic should be simple. Regardless of how many people exist in the Commonwealth there is an allocation of labor to making a mix of goods. Some of these goods are classified as investment and others as consumption based on some criteria imposed by econometric theories. Production allocates labor to a mix of goods called investment and consumption. If there is savings in a period it always equals the allocation of labor to investment by the community. This means savings is just the allocation of labor to whatever you call investment as opposed to whatever you call consumption.
SystemTheory
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2020-12-14T16:02:51.433Z
@SystemTheory that does not make any sense whatsoever. There are multiple factors of production so why should be investment defined in terms of allocation of labor? Also it has to be defined in terms of income because labor or other factors of production are not homogeneous. 1 labor hour of Harvard scientist is not equivalent in economic terms to 1 labor hour of someone who did not finished elementary. The current definition already covers all income allocated to investment.
1muflon1
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2020-12-14T17:06:15.180Z
@1muflon1 In a 1 person economic model, as in a Commonwealth population with no property rights or monetary customs, there are no factor payments to classify as wages, rent, profits, taxes, etc. The economic decision is to allocate hours of labor each day to produce a mix of capital and consumption goods. Workers who produce consumer goods must make a surplus to share with workers who produce capital goods or provide other social services or government services. A valid accounting model must be introduced to state definitions such as expenditure equals income and saving equals investment.
SystemTheory
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2020-12-14T17:09:53.440Z
@SystemTheory maybe engineering has different definitions of wages profits etc but in economics there are wages, rents and profits even in 1 person economy. If Robinson Crusoe builds a fishing rod (capital) then part of his income (fish he will catch) will be rent and part of it that depends on labor will be wage. In economics definition of rents and wages etc does not depend on whether there are property rights or not or whether surplus is shared or not. Yes I agree we need a valid system of definition to account for it and we already have that in economics
1muflon1
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2020-12-14T18:34:27.603Z
@1muflon1 Conventional logic of expenditure and income is built from assumptions about social accounting and payment customs. In the simplest economy consumption occurs only in the household sector. Consolidate production, finance, and government into another sector that I call The Company Town. Let Crusoe work 10 hours a day for the Crusoe Company Town (CCT). He draws wages 100{mu} money units. If CCT marks up the price of output goods above the cost of wages then Crusoe household pays say 110{mu} for the output. So definitions of income and expenditure depend on payment and finance customs.
SystemTheory
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2020-12-14T19:03:01.520Z
@SystemTheory no they obviously do not. Every science has its definition. Definition of mammal, or fish or bird does not depend on customs in fact often scientific definitions are completely different from ordinary definitions. For example, in physics moon is by definition a satellite but when people talk about satellites they mean artificial satellites. Economic definitions obviously do not reflect finance customs in fact definitions between economics and finance are often diametrically opposed. For example, profit has completely different meaning in finance/accounting and economics
1muflon1
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2020-12-14T19:15:51.157Z
@1muflon1 Economic definitions and models must be coherent or logical or reasonable within the social context. Arguments which state that Crusoe is playing the same game without money as he would with money and finance are not coherent. Without money Crusoe allocates labor to produce either capital projects or consumption goods. With money and finance he incorporates the Crusoe Company Town which then pays the wage bill to Crusoe Household. The wage bill will not be sufficient to save financially and purchase the consumption goods at markup prices over wages let alone pay taxes or rent to CCT.
SystemTheory
CC BY-SA 4.0
2020-12-14T19:25:11.290Z
@SystemTheory but wages, profits, taxes etc in economics have absolutely nothing to do with money. In economics wage is by definition return to labor whether it is in the form of money or in kind and no matter where the return arisen from. You can make further distinction between monetary wages and non monetary wages - some models do that - **but by definition** even Robinson Crusoe is getting income and makes spending - if you want you can further split it into monetary and non monetary income/spending but this is just definitional. I am puzzled why it is so hard for you to understand that
1muflon1
CC BY-SA 4.0
2020-12-14T19:26:26.210Z
terminology exists and is used in a science. You said you are engineer.  As part of your engineering training you never learned that in physics for example temperature or stress or flow  have precise definition that do not necessary coincide with common usage?
1muflon1
CC BY-SA 4.0
2020-12-14T20:59:32.627Z
@1muflon1 Definitions in physics/engineering are with reference to methods of measurement and calculation. Crusoe only devotes labor hours to production of goods. We can measure the labor hours. We may classify the output of his labor effort as capital, inventory, or consumption. We may say that he earns wages as return on labor and profits as return on capital. We may say that he saves and invests when he decides to devote more labor to capital and inventory and less labor to make output for current consumption. Yet consumption is his only real income and labor is his only real expense.
SystemTheory
CC BY-SA 4.0
2020-12-14T21:05:22.017Z
@SystemTheory but you can measure empirically how much output/income is created by the capital use and how much by labor use. Wage is the return that can be attributed to the use of labor and rent the output/income from use of capital. So this is all measurable - in fact there is whole literature that measures how much an employee earn as a return to their human capital and how much just by labor there hundreds of studies on that and there are also studies that decompose firm accounting profits to returns to capital and entrepreneurial labor.
1muflon1
CC BY-SA 4.0
2020-12-14T21:07:33.527Z
@SystemTheory in your Robinson Crusoe economy we just need to observe what the production function of the Crusoe is - that can be done by setting up experiments - those experiments would be difficult but it is feasible that can exactly tell us what the composition of real income of Crusoe is in terms of rent/wages/profit etc.
1muflon1
CC BY-SA 4.0
2020-12-14T21:25:44.843Z
@1muflon1 I agree production with capital stock may boost output in future periods above what would be output from labor without capital. Capital has no use outside production so the real income is consumption by society. Rent would be a claim on consumption income due to owners of capital but for Robinson Crusoe or socialist production this factor payment would be distributed to all households as an increasing share of future real consumption. Crusoe or a social group do not have to save before investment only allocate labor hours and capital to produce a mix of capital and consumption goods.
SystemTheory
CC BY-SA 4.0
2020-12-14T21:31:02.703Z
@SystemTheory no in economics real income is defined as your whole output no matter if it is consumed or just thrown away. You might define welfare in terms of consumption but for income that is nonsensical. Also there is no such thing in economics as consumption income. Also what does this has to do with socialism? That is just red herring. This discussion is about whether in economics saving is equal to investment expenditure. Also in economics producing investment goods is also by definition saving so in your example they have to save by definition
1muflon1
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2020-12-14T22:22:24.553Z
@1muflon1 Thanks this discussion is long so maybe I will formulate a question. I want to isolate economic production and consumption from political systems with different property and finance relations. Consolidated production function would be the economic heart of any system. It uses land, labor, and capital as economic inputs to produce investments and services as economic outputs. Investments are capital and inventory of new houses or household goods before transfer to household sector for consumption. Wage bill is set below markup price of output so finance makes income equal expenditure.
SystemTheory
CC BY-SA 4.0
2020-12-14T22:27:25.810Z
@SystemTheory I don’t see any question here however note that for example nothing in the answer above and in the definitions above assumes private property or any economic system. In fact the equations above were at center of the economic models that people in centrally planes economies/socialistic economies used in their input output tables. So the above output/income and spending definitions can be used for any economy no matter what institutional arrangements it is set up as.
1muflon1
CC BY-SA 4.0
2020-12-15T00:26:14.600Z
@1muflon1 In balance sheet accounting the assets, liabilities, and equity or net worth are stated in money units {mu} so one can write the equation assets equal liabilities plus net worth. If there are no money units then assets are items with economic value in excess of one year plus claims to legal ownership or the right to control the use of those items. Liabilities are some type of legal obligation equivalent to payment in money units but without money units one cannot subtract liabilities from assets to find net worth. I wonder how the economist writes equations without common units?
SystemTheory
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2020-12-15T01:04:50.137Z
@SystemTheory in economic models without money everything is being tracked in relative terms. You will select one good to be  numeraire and all prices are tracked relative to that good. If you ever studied physics this is similar to the theory of relativity where during calculations you select some frame of reference and calculate everything relative to the observer in that frame of reference.
1muflon1
CC BY-SA 4.0
2020-12-15T14:12:37.490Z
This comment thread isn't really valuable anymore. Can you guys take this somewhere else, please? @1muflon1 is correct. What he has provided is just an economic definition--something learned in introductory economics courses. Please move your debate somewhere else.
Andrew Plummer
CC BY-SA 4.0
2020-12-15T14:17:32.300Z
@Andrew yes, I wont be discussing this here anymore. I should have ignored the off topic comment and just flagged it as an irrelevant but I always like to presume that people are actually trying to learn here and hence sometimes I let myself get baited into off topic discussions.
1muflon1
CC BY-SA 4.0
2020-12-15T19:39:52.427Z
@Andrew I understand your intolerance however do not accept your assertion. A definition or "term of art" is only correct or incorrect with reference to a context. It is not enough to say that "income equals expenditure" by definition. One must provide the context to measure income, to measure expenditure, and to apply common units on both sides of the equation, so one can verify in context that the definition is valid or not valid.
SystemTheory
CC BY-SA 4.0
2020-12-13T16:25:43.697Z
2020-12-13T16:39:01.343Z
2020-12-13T16:39:01.343Z
1muflon1
<p>I'm reading up on CGE models and one clearing condition that must be met is that Expenditure must equal income.</p>
<p>This seems odd to me because I thought households allocate income to savings and expenditure.</p>

CC BY-SA 4.0
2020-12-13T15:03:56.000Z
Maybe it is a model without savings, how are we supposed to know? There are very many CGE models, especially since they are widely used around the world by governments that have designed there own special versions. But a simple model would potentially ignore savings. Introducing savings can quickly become very complex because this opens the question of dynamic optimzation unless one simply assumes fixed saving rates.
Jesper Hybel
CC BY-SA 4.0
2020-12-13T15:20:55.743Z
Thanks! I didn't realize that there were many CGE models, but, yes, that makes sense. I think I'm just confused because in the paper I'm reading the authors write that they assume households allocate income between expenditure and savings but then one of their market clearing conditions states that Expenditure must equal Income.
Andrew Plummer
CC BY-SA 4.0
2020-12-13T16:37:02.780Z
@JesperHybel no this is actually common condition in most macro models because macroeconomically spending = income even with the presence of saving (since they are investment expenditure)
1muflon1
CC BY-SA 4.0
2020-12-13T18:08:45.180Z
True my mistake. You are right.
Jesper Hybel
<macroeconomics>
Why Should Expenditure Equal Income in Computable General Equilibrium (CGE) models?
Andrew Plummer
# Why Should Expenditure Equal Income in Computable General Equilibrium (CGE) models?

(Asked by: username_0 on 2020-12-13)

I'm reading up on CGE models and one clearing condition that must be met is that Expenditure must equal income.

This seems odd to me because I thought households allocate income to savings and expenditure.

**Tags:** macroeconomics
> **Comments:**
> **username_1**: Maybe it is a model without savings, how are we supposed to know? There are very many CGE models, especially since they are widely used around the world by governments that have designed there own special versions. But a simple model would potentially ignore savings. Introducing savings can quickly become very complex because this opens the question of dynamic optimzation unless one simply assumes fixed saving rates.  
> **username_0**: Thanks! I didn't realize that there were many CGE models, but, yes, that makes sense. I think I'm just confused because in the paper I'm reading the authors write that they assume households allocate income between expenditure and savings but then one of their market clearing conditions states that Expenditure must equal Income.  
> **username_2**: @JesperHybel no this is actually common condition in most macro models because macroeconomically spending = income even with the presence of saving (since they are investment expenditure)  
> **username_1**: True my mistake. You are right.  

---

## 1 answers

### Answer by username_2 on 2020-12-13. Score: 1 | Accepted answer

It is because saving **is investment expenditure**, they must be equivalent in standard macro models. To explain this forget about CGE models for a second, they are set up in this way because all macroeconomics is set up in this way.

In macroeconomics by definition income = expenditure. This is definitional. For closed economy by definition income (Y):

$$Y \equiv C+ I + G \tag{1}$$

where $C$ is expenditure on *consumption* (which is what you likely confused with expenditure in general), $I$ is expenditure on investment (public plus private saving), and $G$ is government expenditure (see more details in Blanchard et al Macroeconomics a European Perspective).

Now $I$ will by definition be equal to public and private saving since private saving $S\_p$ is by definition income not consumed after taxes: $S\_{p} = Y-T-C$. Public saving $S\_G$ is by definition any difference between taxes and government spending $S\_G = T-G$. Together then all saving must be:

$$S= S\_p+S\_G = Y-T-C+T-G=Y-C-G$$

Now this must be equal to investment since just by rearranging equation 1 we find that investment is:

$$Y-C-G =I \implies S=I$$

Hence the reason why the CGE imposes restriction that income is equal to expenditure is not that there should be no saving (although there might be simplified models where saving will be 'turned off' to make it easier for students). It is because expenditure and income are macroeconomically equivalent even in presence of saving (which is just investment spending).

> **Comments:**
> **username_0**: Thank you for this well-thought out response! This actually makes more sense. You're correct--I confused expenditure in general with consumption spending in particular.  
> **username_3**: Consider the Robinson Crusoe economy where one man lives alone in the wilderness or Commonwealth territory. He uses labor to produce a mix of consumption and investment goods. The allocation of labor in production determines the level of investment. There is no financial saving. I don't think it makes sense to say saving equals investment or expenditure equals income in this toy model because there is no money or finance relations. To state that expenditure equals income the classical factors of production are labor, land, and capital. Expenditure equals income as wages, rent, and profit.  
> **username_2**: @SystemTheory they are by definition equal, as proven mathematically. I think issue here is that since you are not an economist you might be unfamiliar with  terminology used in economics. In economics saving does not have the same meaning as saving in common English. In economics saving is by definition difference between income and consumption. This holds even in Robinson Crusoe economy. Investment is only possible if income/output is not immediately consumed, if Robinson Cruse catches 5 fish but eats only 4 in economics that would be saving and that extra fish would be inventory investment  
> **username_3**: @1muflon1 I studied engineering where definitions relate to a social custom known as a measurement procedure. The logic for definition of income equals expenditure is that all expenses are made for investment, consumption, or government and all income is a factor payment called wages, rent, profit, taxes. Then if it is logical to say that expense payments equal income receipts the definition holds expenses = income in aggregate economy. If the logic does not hold the definition is invalid. Robinson Crusoe does not have to save consumption goods he only needs enough to subsist so he can invest.  
> **username_2**: @SystemTheory but all expenses will be equal to income. Again in Robinson Crusoe economy where 5 fish are caught but only 4 consumed by definition consumption expense  is 4 and investment expense 1. Accumulating inventory is considered inventory investment in economics. Now in same Robinson Crusoe economy the factor income to labor is 5 fish. So the income is 5 fish and all expenditure (consumption 4 fish, investment 1 fish) again gives you 5 fish. So the definition is valid. If it wouldn’t there would have to be inconsistency in the math above which is just pure logic applied to definitions.  
> **username_3**: @1muflon1 In a two person economy Crusoe would spend say 3 hours of labor to catch 5 fish. If he eats 4 there is 1 left over which will spoil if there is only 1 person in economy and cannot be an investment activity. In a two person economy Crusoe can create a consumption goods surplus, say getting 8 fish, he can share 4 fish with Friday, and Friday can work 8 hours labor on an investment project. Crusoe and Friday can vote or agree (socialism) how to allocate labor to consumption and investment while subsisting without saving anything first. Saving may be a flawed concept in economic logic.  
> **username_2**: @SystemTheory no it would be an investment with 100% depreciation rate. Even capital spoils over long periods of time so according to your logic that is not an investment? Look the problem here clearly is that you are not familiar with the terminology because this is not logical issue. Let me give you analogy your argument is basically equivalent to telling biologist that dolphins should not be mammals but fish because they live in water and have fins and most people understand fish as animal that lives in water and has fins but that is not biological definition of fish.  
> **username_3**: @1muflon1 So investment has two meanings in economics. The meaning I am evoking is the allocation of labor to produce capital (buildings, plant, property, equipment used in the production of more goods). So Friday might make fishing poles as a capital investment while Crusoe catches fish without poles to furnish consumption goods to himself and Friday until the fishing poles are finished. The other meaning of investment is consumption goods inventory held in the production sector before transfer to households for consumption. Labor is allocated to capital projects or consumer goods production.  
> **username_2**: @SystemTheory also in your example that sharing of 4 fish with Friday would be saving and investment spending for Robinson Crusoe since in this case he hired Friday to build some capital goods which also counts as investment but investment is not just that.  
> **username_2**: @SystemTheory no investment does not have two meanings but there are different types of investments that all counts as investments - you can have capital investment and also inventory investment they are both part of total investment. Of course you scan subdivide investment into infinitely many subcategories but those are not different meanings. Just because you can subdivide fish into salmon, tuna etc that does not mean fish has multiple meanings. Fish and investment are umbrella terms. Even consumption can be subdivided into necessities, luxury etc that is not same as having multiple meaning  
> **username_3**: @1muflon1 The logic should be simple. Regardless of how many people exist in the Commonwealth there is an allocation of labor to making a mix of goods. Some of these goods are classified as investment and others as consumption based on some criteria imposed by econometric theories. Production allocates labor to a mix of goods called investment and consumption. If there is savings in a period it always equals the allocation of labor to investment by the community. This means savings is just the allocation of labor to whatever you call investment as opposed to whatever you call consumption.  
> **username_2**: @SystemTheory that does not make any sense whatsoever. There are multiple factors of production so why should be investment defined in terms of allocation of labor? Also it has to be defined in terms of income because labor or other factors of production are not homogeneous. 1 labor hour of Harvard scientist is not equivalent in economic terms to 1 labor hour of someone who did not finished elementary. The current definition already covers all income allocated to investment.  
> **username_3**: @1muflon1 In a 1 person economic model, as in a Commonwealth population with no property rights or monetary customs, there are no factor payments to classify as wages, rent, profits, taxes, etc. The economic decision is to allocate hours of labor each day to produce a mix of capital and consumption goods. Workers who produce consumer goods must make a surplus to share with workers who produce capital goods or provide other social services or government services. A valid accounting model must be introduced to state definitions such as expenditure equals income and saving equals investment.  
> **username_2**: @SystemTheory maybe engineering has different definitions of wages profits etc but in economics there are wages, rents and profits even in 1 person economy. If Robinson Crusoe builds a fishing rod (capital) then part of his income (fish he will catch) will be rent and part of it that depends on labor will be wage. In economics definition of rents and wages etc does not depend on whether there are property rights or not or whether surplus is shared or not. Yes I agree we need a valid system of definition to account for it and we already have that in economics  
> **username_3**: @1muflon1 Conventional logic of expenditure and income is built from assumptions about social accounting and payment customs. In the simplest economy consumption occurs only in the household sector. Consolidate production, finance, and government into another sector that I call The Company Town. Let Crusoe work 10 hours a day for the Crusoe Company Town (CCT). He draws wages 100{mu} money units. If CCT marks up the price of output goods above the cost of wages then Crusoe household pays say 110{mu} for the output. So definitions of income and expenditure depend on payment and finance customs.  
> **username_2**: @SystemTheory no they obviously do not. Every science has its definition. Definition of mammal, or fish or bird does not depend on customs in fact often scientific definitions are completely different from ordinary definitions. For example, in physics moon is by definition a satellite but when people talk about satellites they mean artificial satellites. Economic definitions obviously do not reflect finance customs in fact definitions between economics and finance are often diametrically opposed. For example, profit has completely different meaning in finance/accounting and economics  
> **username_3**: @1muflon1 Economic definitions and models must be coherent or logical or reasonable within the social context. Arguments which state that Crusoe is playing the same game without money as he would with money and finance are not coherent. Without money Crusoe allocates labor to produce either capital projects or consumption goods. With money and finance he incorporates the Crusoe Company Town which then pays the wage bill to Crusoe Household. The wage bill will not be sufficient to save financially and purchase the consumption goods at markup prices over wages let alone pay taxes or rent to CCT.  
> **username_2**: @SystemTheory but wages, profits, taxes etc in economics have absolutely nothing to do with money. In economics wage is by definition return to labor whether it is in the form of money or in kind and no matter where the return arisen from. You can make further distinction between monetary wages and non monetary wages - some models do that - **but by definition** even Robinson Crusoe is getting income and makes spending - if you want you can further split it into monetary and non monetary income/spending but this is just definitional. I am puzzled why it is so hard for you to understand that  
> **username_2**: terminology exists and is used in a science. You said you are engineer.  As part of your engineering training you never learned that in physics for example temperature or stress or flow  have precise definition that do not necessary coincide with common usage?  
> **username_3**: @1muflon1 Definitions in physics/engineering are with reference to methods of measurement and calculation. Crusoe only devotes labor hours to production of goods. We can measure the labor hours. We may classify the output of his labor effort as capital, inventory, or consumption. We may say that he earns wages as return on labor and profits as return on capital. We may say that he saves and invests when he decides to devote more labor to capital and inventory and less labor to make output for current consumption. Yet consumption is his only real income and labor is his only real expense.  
> **username_2**: @SystemTheory but you can measure empirically how much output/income is created by the capital use and how much by labor use. Wage is the return that can be attributed to the use of labor and rent the output/income from use of capital. So this is all measurable - in fact there is whole literature that measures how much an employee earn as a return to their human capital and how much just by labor there hundreds of studies on that and there are also studies that decompose firm accounting profits to returns to capital and entrepreneurial labor.  
> **username_2**: @SystemTheory in your Robinson Crusoe economy we just need to observe what the production function of the Crusoe is - that can be done by setting up experiments - those experiments would be difficult but it is feasible that can exactly tell us what the composition of real income of Crusoe is in terms of rent/wages/profit etc.  
> **username_3**: @1muflon1 I agree production with capital stock may boost output in future periods above what would be output from labor without capital. Capital has no use outside production so the real income is consumption by society. Rent would be a claim on consumption income due to owners of capital but for Robinson Crusoe or socialist production this factor payment would be distributed to all households as an increasing share of future real consumption. Crusoe or a social group do not have to save before investment only allocate labor hours and capital to produce a mix of capital and consumption goods.  
> **username_2**: @SystemTheory no in economics real income is defined as your whole output no matter if it is consumed or just thrown away. You might define welfare in terms of consumption but for income that is nonsensical. Also there is no such thing in economics as consumption income. Also what does this has to do with socialism? That is just red herring. This discussion is about whether in economics saving is equal to investment expenditure. Also in economics producing investment goods is also by definition saving so in your example they have to save by definition  
> **username_3**: @1muflon1 Thanks this discussion is long so maybe I will formulate a question. I want to isolate economic production and consumption from political systems with different property and finance relations. Consolidated production function would be the economic heart of any system. It uses land, labor, and capital as economic inputs to produce investments and services as economic outputs. Investments are capital and inventory of new houses or household goods before transfer to household sector for consumption. Wage bill is set below markup price of output so finance makes income equal expenditure.  
> **username_2**: @SystemTheory I don’t see any question here however note that for example nothing in the answer above and in the definitions above assumes private property or any economic system. In fact the equations above were at center of the economic models that people in centrally planes economies/socialistic economies used in their input output tables. So the above output/income and spending definitions can be used for any economy no matter what institutional arrangements it is set up as.  
> **username_3**: @1muflon1 In balance sheet accounting the assets, liabilities, and equity or net worth are stated in money units {mu} so one can write the equation assets equal liabilities plus net worth. If there are no money units then assets are items with economic value in excess of one year plus claims to legal ownership or the right to control the use of those items. Liabilities are some type of legal obligation equivalent to payment in money units but without money units one cannot subtract liabilities from assets to find net worth. I wonder how the economist writes equations without common units?  
> **username_2**: @SystemTheory in economic models without money everything is being tracked in relative terms. You will select one good to be  numeraire and all prices are tracked relative to that good. If you ever studied physics this is similar to the theory of relativity where during calculations you select some frame of reference and calculate everything relative to the observer in that frame of reference.  
> **username_0**: This comment thread isn't really valuable anymore. Can you guys take this somewhere else, please? @1muflon1 is correct. What he has provided is just an economic definition--something learned in introductory economics courses. Please move your debate somewhere else.  
> **username_2**: @Andrew yes, I wont be discussing this here anymore. I should have ignored the off topic comment and just flagged it as an irrelevant but I always like to presume that people are actually trying to learn here and hence sometimes I let myself get baited into off topic discussions.  
> **username_3**: @Andrew I understand your intolerance however do not accept your assertion. A definition or "term of art" is only correct or incorrect with reference to a context. It is not enough to say that "income equals expenditure" by definition. One must provide the context to measure income, to measure expenditure, and to apply common units on both sides of the equation, so one can verify in context that the definition is valid or not valid.  

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