Additional notes for Marx—Schemes of reproduction

I: Assumptions:

Economy is divided into two Departments

Dept I: Capital Goods

Dept II: Consumer goods

Due to labour mobility rate of exploitation (s/v) must be the same in both Departments (assumed to be 100%)

Capital to labour (c/v) ratios are fixed in each Department

II: Case of Simple Reproduction (no capital accumulation):

All c is spent on capital goods, all v and s is spent on consumer goods

Dept I:    4000c + 1000v + 1000s = 6000

Dept II:  2000c + 500v +500s = 3000

The 2 departments balance—all v and s are spent on the output of Dept II and all c on the output of Dept I

Total demand for Dept I output = 4000 + 2000 = 6000

Total Demand for Dept II output = 1000 + 1000 +500 + 500 = 3000

This could just carry on period after period—no growth.

III: Case of Expanded Reproduction (with capital accumulation)

Have to start from an initial point where there is some excess capacity in the capital goods industry.

Dept I:  4000c + 1000v + 1000s = 6000

Dept II: 1500c + 750v + 750s = 3000

Capitalists in Dept I decide to accumulate (and not spend on consumption) half of their s.

So 500s in Dept I will get spent on 400c and 100v (fixed proportions) instead of on 500 of the output of Dept II.

So the demand for capital goods in Dept I will now be 4000 + 400 = 4, 400

And the Dept I demand for consumption goods will be 1000 + 500 + 100 = 1,600

That means the total demands of Depts I and II will not match the outputs

Total Demand for Capital Goods = 4,400 from Dept I + 1,500 from Dept II = 5, 900 (not 6,000)

Total Demand for Consumption Goods = 1,600 from Dept I + 1,500 from Dept II = 3,100 (not 3,000)

In other words there is an excess supply of capital goods and an excess demand for consumption goods

For the demands and outputs to match there would also have to be some exactly matching capital accumulation going on in Dept II.

If capitalists in Dept II accumulate 150s in the form of 100c and 50v then the

Dept II demand for capital goods will rise by 100 from 1,500 to 1,600

Dept II demand for consumption goods will fall by 100 (-150 +50) from 1,500 to 1,400

Now everything balances:

Total demand for capital goods = 4,400 + 1,600 = 6,000

Total demand for consumption goods = 1,600 + 1,400 = 3,000

Now at the beginning of the next period this will give us a new starting point as follows:

Dept I:  4,400c + 1,100v + 1,100s = 6,600

Dept II: 1,600c + 800v + 800s = 3,200

Could again assume capitalists in Dept I accumulate half their s and go through the process again and again.

This will show an economy growing in balance.

But Marx’s point is that the economy can easily get out of balance creating a “crisis” and liquidations until balance is restored.  This is the problem of steady growth.