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Say's law: How does real income grow?

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joemac posted on Sat, Mar 19 2011 6:41 PM

Hi, I'm new,

From the perspective of say's law, how are real wealth and real income created. According to logic there are two ways in which real income is increased.

1)  Increase your productivity and thus your purchasing power increases

2) Others increase their productivity, industry competetion occurs, drives down prices, and thus increases your purchasing power.

But, metaphysically speaking, how does this happen? Say's law says that your purchasing power, and thus income, is determined by your ability to produce. Thus, if your producitivty increases, this should increase your purchasing power and thus your real income and thus wealth. But this is a chicken and an egg problem. Let me use an example.

Let's say all spending equals income in the economy and it is in perfect equilibrium. Each individuals real income equals his spending, and all total income equals total spending. Each individual's spending power is determined by his income, which is determined by his producitivty.

Let's a say I am a shoemaker in this situation. Given my labor, capital, land, and technology I can produce 50 shoes each week. This determined my purchasing power and thus my real income, spending and wealth, etc.

Then, my producivity increases through an new innovation and I ca now produce 100 shoes with all the same previous resources. According to basic theory this means I should become wealthier and my standard of living should increase.

But if nobody else's real income has gone up, then who can purchase my new 50 shoes? My purchasing power can only increase if other's purchase my goods. But there's nobody to purchase it.

Its like there's some missing gap here that I'm missing. In other words, how do you put say's law and economic growth together, at its deepest metaphysical level. I can't figure it out.

Help is appreciated,

Joe

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Phaedros replied on Sun, Mar 20 2011 12:35 AM

Well, right, short term. I was thinking more long term. As far as nukes go it was just an example and I guess a bad one really. I do think, though, that some form of nuclear power will become the dominant energy source for a future economy.

Tumblr The welfare of the people in particular has always been the alibi of tyrants. ~Albert Camus
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joemac:

But if I create so many new shoes, the price will fall until they all sell.

Yes.

joemac:

But where will the buyers get the money to purchase it? Any income they spend on this item will have to be taken from someone else. Everytime an individual becomes more productive and can sell more products than before (and thus become a little bit wealthier), the price will obviously fall, but spending by consumers will simply be moved from other suppliers (of other goods) towards these cheap new shoes. In other words, anyone who attempts to grow richer through increases in productivity will automatically cause someone else to become poorer.

Nominal income for the shoemaker increases, as he sells more shoes at lower prices.  However, let's assume nominal income for all other industries have decreased as households shift some expenditures from all other goods to the shoes. 

Furthermore, let's assume total income for the whole economy is fixed, and output for all other industries (except shoes) have remained unchanged.

Even though the nominal incomes for the other industries have decreased, the real incomes for these industries have actually increased, because the total output for the whole economy has increased on a constant money supply. 


Think about it another way.  Imagine a pie chart, representing total income, which the shoemaker has a share of the pie.  His increased output enlarges his share, while unchanged output of all the other industries reduces their shares.

However, even though the shares of everyone else have decreased, the total pie has become bigger, and each share of the pie is bigger too, since total output has increased for everyone.

Because total income is equal to total expenditures, these expenditures (from wages, rent, profit, and factors) will be spent on more goods than before.  Total nominal income remains the same, but total real income has increased.


Let's alter the scenario and assume that shoes are a luxury good.  Everyone else are wearing sandals, since few could afford the shoes.

Let's assume the shoemaker keep increasing his production continually, increasing supply, and reducing shoe prices.  Lower prices, means higher real income, and so more can afford the shoes. 

Because shoes are a normal good, while sandals are an inferior good, increased real income will shift expenditures from sandals to shoes.

From the pie chart, the shoe industries is winning more of its share, while the sandal industry is losing some of its share.  Because of this competition, the shoe industry increases output, while the sandal industry decreases output.

However, this scenario presents a measurement problem for measuring output.  Even though shoe output has increased, while sandal output has decreased, there is no consistent way of summing those two goods, except through prices and quantities.

It is very possible, that total output calculated may seem unchanged, when in reality the composition and quality of the goods have changed. 

This is a problem, because even though real income may seem constant, in reality the quality of life for the consumers have increased.

 

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Suggested by Micah71381

The most simple answer to your question is that you can buy your own shoes.  This probably doesn't help you visualize though so I'll try to offer a more in depth one.

You have 3 people producing goods A, B and C.  Each can produce 6 units of goods a month and, for simplicity, we'll say that the produced goods all have equivelant value (similar cost).  Each person consumes 2 units of A, B and C every month and they purchase the two goods that they don't produce.

The guy producing C all of a sudden doubles his productivity and can now produce 12 units a month.  Now the guy producing C can buy 4 units of A and B along with consuming 4 units of C.  Meanwhile, the guys producing A and B can consume 1 unit of A and B and 4 units of C.

Before:

  • Produces 6A; Consumes 2A + 2B + 2C
  • Produces 6B; Consumes 2A + 2B + 2C
  • Produces 6C; Consumes 2A + 2B + 2C

After:

  • Produces 6A; Consumes 1A + 1B + 4C
  • Produces 6B; Consumes 1A +1B + 4C
  • Produces 12C; Consumes 4A + 4B + 4C

Of course, the distribution doesn't have to be that, it could be any combination such as:

  • Produces 6A; Consumes 2B + 4C
  • Produces 6B; Consumes 6C
  • Produces 12C; Consumes 6A + 4B + 2C

This is a contrived example and doesn't take into account a lot of real world factors such as marginal utility but the point is that an increase in productivity can result in a redistribution of what people purchase.  In your shoe example, because he can double his productivity he can lower the price of his shoes which means more people will buy them and some may buy more than one or replace their shoes more frequently. This means their money isn't going to other goods they previously purchased so those now unpurchased goods are available on the market which the shoe maker can now purchase.

On a large scale there is so much changing at all times in terms of productivity that this all happens without anyone realizing it or being able to keep track of it which is why it helps to simplify the problem down to a very basic example in order to see what is really going on.  In the above example the things to note are that doubling of productivity leads to a doubling of consumption and it also leads to a doubling (on average) of the amount that everyone consumes of good C.  What the doubly productive producer consumes is unimportant, he could consume all 12C and not any A or B if he wanted.  What matters is that there are twice as many units of C in the market and he has twice the purchasing power he used to.

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You made 50 more shoes. Since we assume there was demand for more shoes that did not get met [which is why you made those extra shoes in the first place] then peopl ewill buy them. But they did not buy them until now because they were too expensive. So you sell the shoes for less. What you lose in cheaper shoe prices you gain in selling more shoes.

You can now buy more things because you have more money. But this wealth spreads to everyone. Because they have the same shoes at a lower price. And some people went from barefoot to shod.

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This is an excellent barter example Micah71381 has provided.  Here are my modifications:

Producer Output Produced Output Saved Expenditures (from others) Income (to Producer) Consumption Gains Loses
A 6A 2A 4A 2B + 2C 2A + 2B + 2C    
B 6B 2B 4B 2A + 2C 2A + 2B + 2C    
C 6C 2C 4C 2A + 2B 2A + 2B + 2C    

Income (to producer) is what you received from the trade.  Expenditures (from others) is what you give to the trade.

Expenditures are simply the Output you produced minus the Output you saved for yourself.  In other words:


Expenditures = Output Produced - Output Saved

 

Producer Output Produced Output Saved Expenditures (from others) Income (to Producer) Consumption Gains Loses
A 6A 1A 5A 2B + 5C 1A + 2B + 5C 3C 1A
B 6B 1B 5B 2A + 5C 2A + 1B + 5C 3C 1B
C 12C 2C 10C 3A + 3B 3A + 3B + 2C 1A + 1B None

Let's say Produce C doubles his output from 6C to 12C (refer to the above table).  Here is the breakdown of effects:

  1. Producer C expenditures (from others) have increased from 4C to 10 C.  Producer C still saves 2C for himself.
     
  2. Income for Producer C has increased from 2A + 2B to 3A + 3B.
     
  3. Because Income must equal Expenditures, increased expenditures by Producer C means increased income to Producer A and Produce B.  Producer A income has increased 2B + 2C to 2B + 5C.  Producer B incomes has increased from 2A + 2C to 2A + 5C.
     
  4. Even though Producer A and Producer B Output has remain unchanged at 6A and 6B, respectively, their income has increased by 3C, respectively.  But Produce A and Producer B gives up one unit from savings in trade to Producer C.
     

Net effect is this: 

  • Producer C increases his consumption (gains) by 1A + 1B, while he loses nothing.
     
  • Producer A increases his consumption (gains) by 3C, while decreases his consumption (loses) by 1A. 
     
  • Producer B increases his consumption (gains) by 3C, while decreases his consumption (loses) by 1B.

In summary, Producer C increases his Income by increasing his productivity, but through his increased Income, he must also increase his Expenditures, which then increases the incomes of Producer A and Producer B.

Even though Producer A and Producer B loses something, they gain in trade with more of something else.

If you have any more questions, feel free to ask.

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It looks like Think Blues example adds in the component of reducing the value (cost) of C due it an increase in supply.  5C are worth 3A or 3B (5:3 ratio) now that the supply is higher versus the 1:1 ratio when the supplies were equal.

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If this is some sort of personal attack I'd ask you refrained from making them and handled it via private messages.

It was meant as a joke... apparently, it wasn't funny, so: I'm sorry Caley... no offense meant.

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joemac replied on Wed, Mar 23 2011 7:51 PM

Thanks Micah and Think Blue.

I've been staring at your posts for three days and still can't figure it out. I think this is similar to the difference between absolute and comparative advantage, which is what econ books start with. I never understood that either. But I still can't figure it out.

Also, there's difference between your two tables. In Micah's consumption stays the same as production, but in Think Blue's they are different for each worker. Think Blue's numbers are confusing because their Expenditures are differnet from their Income. How can how much he gives away be different from what he gets.

Is that because unlike Micah, Think Blue's table says that in nominal terms expenditure-income are different do to changes in prices, but in real terms they are of course the same. He's starting to inclue prices and money.

Still very confused, but working on it!

Thanks for your help! 

Joe

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Think Blue's example takes into account marginal utility whereas mine does not.  Mine was meant to be about as simplified as you can get, assuming all goods are of equal value and marginal utility does not exist (you derive the same utility from the first widget as the 1000th widget).

Is there a particular part of our examples you don't understand that we can perhaps shed some light on?

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Hi joemac,

I probably made it more complex than it has to be.  To provide better clarity, perhaps we can start with Micah's example first, and walk through the steps of the problem, from start to finish?

Let us know what you'd like to do.

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joemac replied on Wed, Mar 23 2011 8:20 PM

thinking about Micah's post....

In it, one day C becomes more productive and goes into the market with 10 shoes (having saved 2 for himself). Your table assumed that these extra goods will be desired. It assumes that A & B will lower their previous consumption of their own goods and buy all of C's new stuff. But what if they tell him that they don't want his new stuff?

Then his new increase in productivity will have been for nothing. Your table allows for only two possibilities of an increase in productivity, 1) C will consume all of his own new shoes, or 2) All three will change their desired distribution of consumption.

For 1) no one needs that many shoes and also the entire reason to produce is to exchange it for other stuff, but this leads to 2) there is no reason that A or B will necessarily want the newly produced shoes

Or, take an extreme, let's say C's productivity skyrockets and he makes 100 shoes. Then (2) would be impossible because A & B only have 6 worth of purchasing power each, and (1) is impossible for what I explained in the last paragraph

Ergo, the original problem I had with all of this.....!

Thanks, Joe

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This is where Think Blue's example comes into play.  He takes into consideration marginal utility whereas I do not.  My example takes place in a world without marginal utility so it doesn't' properly extend to the real world, though it simplifies things a lot.  It sounds like you grasp the concept in a world without marginal utility so you should focus on Think Blue's example instead.

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In Think Blue's example A is not willing to trade 1A for 1C after he already has 2C.  However, he is willing to trade 1A for 3C after the first two C.  That is, he already has two pairs of shoes, enough for his needs and he would rather have a 2nd A than a 3rd shoe.  If the shoemaker (C) were to offer him 3 shoes (3C) in exchange for another A, he would be willing to give up one A for 3 shoes (3C).

If production suddenly jumped 1000 fold it may required 500 shoes for him to be willing to trade for 1A because after the first few shoes, he just doesn't really need any more.  This is what marginal utility is all about.  After you have 1 of something, you want another less than you wanted the first.  For some goods this falls off very quickly (cars) while for others it can be a slow decline (food).

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joemac:

For 1) no one needs that many shoes and also the entire reason to produce is to exchange it for other stuff, but this leads to 2) there is no reason that A or B will necessarily want the newly produced shoes

Like what Micah said, this has something to do with the law of diminishing marginal utility.  From my example, think about it this way.

Let's say Producer A makes televisions, so for a period of time he makes 6 TV's (represented as 6A in the above table).  He doesn't need all 6 TV's, so he'll keep 2 TV units for his personal use, and trade away the 4 remaining TV units.

From his perspective, the 6th TV is less valuable than the 5th TV, and the 5th TV is less valuable than the 4th TV, and so on.  Each and every TV he gives away from his stock of units, the nth - 1 unit becomes more valuable than the nth unit, until he has one TV unit left, which he'd be the most reluctant to give away.

For the 6th and 5th unit of A (that is TV units), he trades for 2 units of B, so the trade is 2A for 2B.

This is leaves 4A remaining in stock.

Here is where the price of C comes in.  If the price is 1A for 1C, then Producer A would give Producer C the 4th and 3rd units of A.

However, if the price is 3A for 5C (that is 1A for 1.66C), then Producer A would give Producer C the 2nd unit of A, as well as the 3rd and 4th unit.

This means he's willing to give up the 2nd unit of A for an extra 3 units of C, whereas before he'd give up the 3rd and 4th unit of A for 1 unit of C each.

For each remaining unit left, Producer A raises the price he is willing to sell Producer C for the nth -1 in his stock.

joemac:

Or, take an extreme, let's say C's productivity skyrockets and he makes 100 shoes. Then (2) would be impossible because A & B only have 6 worth of purchasing power each, and (1) is impossible for what I explained in the last paragraph

Then Producer A would be unwilling to sell the 1st unit of A (the very last unit of A) at any price, even if Producer C offers him 100 C for that one unit.

For Producer A, watching television is priceless!! 
 

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joemac:

In Micah's consumption stays the same as production, but in Think Blue's they are different for each worker. Think Blue's numbers are confusing because their Expenditures are differnet from their Income. How can how much he gives away be different from what he gets.

Is that because unlike Micah, Think Blue's table says that in nominal terms expenditure-income are different do to changes in prices, but in real terms they are of course the same. He's starting to inclue prices and money.

Income and expenditure model is confusing within barter.  Instead, let's replace the word "Income" with "Bought", and replace the word "Expenditure" with "Sold".

Here is the logic:

  1. Increased output by Producer C means increased sales (more things sold).  More C units are sold.
     
  2. Increased sales means increases in what Producer C purchases (more things bought).  More A and B units are bought.
     
  3. Increased purchases by Producer C of A and B units means increased sales for Producer A and B.  More A and B units are sold.

Conclusion:  Increased output, increases the sales for Producer C, which increases the sales for everyone else (Producer A and B).

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