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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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joemac:
Now, all I have to do is figure out how all this works with money! Will be back with more really annoying questions!

If you can get it with real goods in a barter system, money is even easier...because remember money is just a commodity too...it just happens to be a commodity that gets value from its utility as a facilitator of trade...a "medium of exchange".

So when you say the "price" of something goes down in terms of dollars due to increased productivity, what you're really saying is that the value of that good relative to the value of the currency has gone down...therefore, the purchasing power of the money has increased.  This means that everyone who holds that money is able to buy more stuff with the same amount of money...they are, for our purposes here, wealthier.

It's great to see that you're so interested in learning this and putting such effort into it as well as making progress.  The best read for you at this point might be Peter Schiff's How an Economy Grows and Why it Crashes.  It goes into this as well as many other basic economic concepts in a very easy-to-follow way.  It's an update and expansion of his father's book of a similar title.  You'll have to check out a library or bookstore to get Peter's updated book, but his father's version is available in pdf here, and our own Nielsio posted a nice reading of it here.

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joemac replied on Thu, Mar 31 2011 8:23 PM

My little model here on my paper (took 6 hours to figure out) shows that when productivity increases for the butcher, his marginal cost of production goes down and so the price relative to other goods of meat goes down. In response to the movement down their demand curves, the baker and the tailor request far more than before of meat. As a result the butcher has more bread and clothes than before and the other two have more meat. Here are my numbers...

Relative prices: Meat $100 - Bread $183 - Clothes $225

                  Incomes   Spending 
Butcher     $8500       $8500 

Baker        $7500        $7500

Tailor        $5000        $5000

I simply convert any of the incomes into the price of one of the three goods to compare their incomes in terms of the goods.

NGDP  is $21,000. No cash balances are ever held. So the demand for money is zero.

What is the money supply? Can this info be put int terms of the equation of exchange MV = PQ, or into the cambridge k, M = kY?

I will try to go from here and figure out how this transforms when productivity for the butcher goes up. Will take some time smiley

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joemac:

I simply convert any of the incomes into the price of one of the three goods to compare their incomes in terms of the goods.

NGDP  is $21,000. No cash balances are ever held. So the demand for money is zero.

What is the money supply? Can this info be put int terms of the equation of exchange MV = PQ, or into the cambridge k, M = kY?

The problem is that transition from barter to money can't be done without an intermediate step.  Money is a commodity just like any other good.

In the former British colonies in America, some of them use tobacco as a form of money.  Tobacco had its direct use for consumption, and its indirect use as a medium of exchange for exchanging other goods.

For the barter model, introduce Producer D as a tobacco farmer, who supplies tobacco to Producer A, B, and C, and then establish appropriate exchange ratios for good D with respect to goods A, B, and C. 

Have each producer consume some of the tobacco himself, but have some leftover for trade.

Remove direct barter exchange among Producers A, B, and C, and replace it with indirect exchange.  For example, let's say Producer A wishes to trade with Producer B.  Instead of a direct exchange of good A for good B, this will happen:

  1. Producer A trades with Producer D, exchanging good A for good D.
     
  2. Producer A trades with Producer B, exchanging good D for good B.
     
  3. Producer B trades with Producer A, exchanging good D for good A

Money supply is that total amount of good D in existence.  For your purposes, the Equation of Exchange (MV = PQ) is more appropriate, since the Cambridge equation (M (1/k) = PY) is simply a derivation of the Equation of Exchange.

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Can you help me understand the difference between the two?

The Fisher equation is MV = Y and the cambridge k us M = kY

Let's say k = 1/12, that means that on average moneyholdings are 8% of nominal income. Why does that mean that the veolcity of each dollar is 12? Weird.

Thanks.

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joemac:

Can you help me understand the difference between the two?

The Fisher equation is MV = Y and the cambridge k us M = kY

Equation of Exchange (per Fisher, et al.) is:

MV = PQ

But sometimes economists substitute quantity Q for real output Y:

MV = PY

Therefore PY is nominal output, while Y by itself is real output.


For the Cambridge Equation, velocity V is defined as:

V = 1 / k

Therefore plug the above back into the Equation of Exchange:

M * (1/k) = PY


joemac:

Let's say k = 1/12, that means that on average moneyholdings are 8% of nominal income. Why does that mean that the veolcity of each dollar is 12? Weird.

Yes.

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