stretch

In the previous post we saw how an increase in owners’ compensation can lead, even while keeping wages intact, to a decrease in what workers can buy -i.e., their real wages diminish.

Now we’ll take a look at a possible way to solve this issue: stretching the workday. We’ll bring more products into the market by making employees work longer hours in exchange for the same total wage, 8F per day of labor, while the owners receive 3 and 2 times this amount, respectively.

The aggregate demand of the social arrangement will remain at 56 foodies, corresponding to the total income generated by wages and salaries. By the same token, all product enters the market to be sold completely. In this case, workers can satisfy entirely the needs of their families.  We can derive the following relationships:

Q = p · t,

where Q is the quantity produced of a certain product (bread, milk) in a given working-time, t, and p is the hourly productivity. Moreover, the quantities produced of each product are related by

Qm = (C2 · Qb)/((Qb · W) – C1)

where C1, C2 are the costs of producing the respective products and W is what I’ve called the wage-to-price index of affordability, or a measure of the buying power of wages:

W = b + m,

indicating the limit that wages put on the relative prices of products so that workers can acquire them.

In the scenario under consideration, the hourly-productivity of bread production is 3b while 3 glasses of milk are produced in one hour.

PB WHr HrW P OC (F/Hr) OC (/HrW) GM WHr HrW P OC (F/Hr) OC (/hrW) TWKHr
20 6.67 1.20 1.60 3.60 3 60.00 20.00 0.40 0.40 0.80 2 26.67
22 7.33 1.09 1.45 3.27 3 44.00 14.67 0.55 0.55 1.09 2 22.00
24 8.00 1.00 1.33 3.00 3 36.00 12.00 0.67 0.67 1.33 2 20.00
26 8.67 0.92 1.23 2.77 3 31.20 10.40 0.77 0.77 1.54 2 19.07
28 9.33 0.86 1.14 2.57 3 28.00 9.33 0.86 0.86 1.71 2 18.67
30 10.00 0.80 1.07 2.40 3 25.71 8.57 0.93 0.93 1.87 2 18.57
32 10.67 0.75 1.00 2.25 3 24.00 8.00 1.00 1.00 2.00 2 18.67
34 11.33 0.71 0.94 2.12 3 22.67 7.56 1.06 1.06 2.12 2 18.89
36 12.00 0.67 0.89 2.00 3 21.60 7.20 1.11 1.11 2.22 2 19.20
38 12.67 0.63 0.84 1.89 3 20.73 6.91 1.16 1.16 2.32 2 19.58
40 13.33 0.60 0.80 1.80 3 20.00 6.67 1.20 1.20 2.40 2 20.00
42 14.00 0.57 0.76 1.71 3 19.38 6.46 1.24 1.24 2.48 2 20.46
48 16.00 0.50 0.67 1.50 3 18.00 6.00 1.33 1.33 2.67 2 22.00
52 17.33 0.46 0.62 1.38 3 17.33 5.78 1.38 1.38 2.77 2 23.11
56 18.67 0.43 0.57 1.29 3 16.80 5.60 1.43 1.43 2.86 2 24.27
60 20.00 0.40 0.53 1.20 3 16.36 5.45 1.47 1.47 2.93 2 25.45

PB: pieces of bread; WHr: working hours; HrW: hourly wage; P: price; OC: owner’s compensation; GM: glasses of milk; TWKHr: total working hours

We can derive the following relationship:

Price = [Total Cost/Total Wage] * [Hourly Wage/Hourly Productivity]

or,

Price = [Total Cost/Total Wage] * [Wage Cost per Unit]

The following tables illustrate these results when the expected return of owners decreases:

 

PB WHr HrW P OC (F/Hr) OC (/HrW) GM WHr HrW P OC (F/Hr) OC (/hrW) TWKHr
20 6.67 1.20 1.60 3.60 3 60.00 20.00 0.40 0.40 0.80 2 26.67
22 7.33 1.09 1.45 3.27 3 44.00 14.67 0.55 0.55 1.09 2 22.00
24 8.00 1.00 1.33 3.00 3 36.00 12.00 0.67 0.67 1.33 2 20.00
26 8.67 0.92 1.23 2.77 3 31.20 10.40 0.77 0.77 1.54 2 19.07
28 9.33 0.86 1.14 2.57 3 28.00 9.33 0.86 0.86 1.71 2 18.67
30 10.00 0.80 1.07 2.40 3 25.71 8.57 0.93 0.93 1.87 2 18.57
32 10.67 0.75 1.00 2.25 3 24.00 8.00 1.00 1.00 2.00 2 18.67
34 11.33 0.71 0.94 2.12 3 22.67 7.56 1.06 1.06 2.12 2 18.89
36 12.00 0.67 0.89 2.00 3 21.60 7.20 1.11 1.11 2.22 2 19.20
38 12.67 0.63 0.84 1.89 3 20.73 6.91 1.16 1.16 2.32 2 19.58
40 13.33 0.60 0.80 1.80 3 20.00 6.67 1.20 1.20 2.40 2 20.00
42 14.00 0.57 0.76 1.71 3 19.38 6.46 1.24 1.24 2.48 2 20.46
48 16.00 0.50 0.67 1.50 3 18.00 6.00 1.33 1.33 2.67 2 22.00
52 17.33 0.46 0.62 1.38 3 17.33 5.78 1.38 1.38 2.77 2 23.11
56 18.67 0.43 0.57 1.29 3 16.80 5.60 1.43 1.43 2.86 2 24.27
60 20.00 0.40 0.53 1.20 3 16.36 5.45 1.47 1.47 2.93 2 25.45

 

PB WHr HrW P OC (F/Hr) OC (/HrW) GM WHr HrW P OC (F/Hr) OC (/hrW) TWKHr
20 6.67 1.20 1.40 3.00 2.5 40.00 13.33 0.60 0.60 1.20 2 20.00
22 7.33 1.09 1.27 2.73 2.5 33.00 11.00 0.73 0.73 1.45 2 18.33
24 8.00 1.00 1.17 2.50 2.5 28.80 9.60 0.83 0.83 1.67 2 17.60
26 8.67 0.92 1.08 2.31 2.5 26.00 8.67 0.92 0.92 1.85 2 17.33
28 9.33 0.86 1.00 2.14 2.5 24.00 8.00 1.00 1.00 2.00 2 17.33
30 10.00 0.80 0.93 2.00 2.5 22.50 7.50 1.07 1.07 2.13 2 17.50
32 10.67 0.75 0.88 1.88 2.5 21.33 7.11 1.13 1.13 2.25 2 17.78
34 11.33 0.71 0.82 1.76 2.5 20.40 6.80 1.18 1.18 2.35 2 18.13
36 12.00 0.67 0.78 1.67 2.5 19.64 6.55 1.22 1.22 2.44 2 18.55
38 12.67 0.63 0.74 1.58 2.5 19.00 6.33 1.26 1.26 2.53 2 19.00
40 13.33 0.60 0.70 1.50 2.5 18.46 6.15 1.30 1.30 2.60 2 19.49
42 14.00 0.57 0.67 1.43 2.5 18.00 6.00 1.33 1.33 2.67 2 20.00
48 16.00 0.50 0.58 1.25 2.5 16.94 5.65 1.42 1.42 2.83 2 21.65
52 17.33 0.46 0.54 1.15 2.5 16.42 5.47 1.46 1.46 2.92 2 22.81
56 18.67 0.43 0.50 1.07 2.5 16.00 5.33 1.50 1.50 3.00 2 24.00
60 20.00 0.40 0.47 1.00 2.5 15.65 5.22 1.53 1.53 3.07 2 25.22

 

PB WHr HrW P OC (F/Hr) OC (/HrW) GM WHr HrW P OC (F/Hr) OC (/hrW) TWKHr
20 6.67 1.20 1.20 2.40 2 30.00 10.00 0.80 0.80 1.60 2 16.67
22 7.33 1.09 1.09 2.18 2 26.40 8.80 0.91 0.91 1.82 2 16.13
24 8.00 1.00 1.00 2.00 2 24.00 8.00 1.00 1.00 2.00 2 16.00
26 8.67 0.92 0.92 1.85 2 22.29 7.43 1.08 1.08 2.15 2 16.10
28 9.33 0.86 0.86 1.71 2 21.00 7.00 1.14 1.14 2.29 2 16.33
30 10.00 0.80 0.80 1.60 2 20.00 6.67 1.20 1.20 2.40 2 16.67
32 10.67 0.75 0.75 1.50 2 19.20 6.40 1.25 1.25 2.50 2 17.07
34 11.33 0.71 0.71 1.41 2 18.55 6.18 1.29 1.29 2.59 2 17.52
36 12.00 0.67 0.67 1.33 2 18.00 6.00 1.33 1.33 2.67 2 18.00
38 12.67 0.63 0.63 1.26 2 17.54 5.85 1.37 1.37 2.74 2 18.51
40 13.33 0.60 0.60 1.20 2 17.14 5.71 1.40 1.40 2.80 2 19.05
42 14.00 0.57 0.57 1.14 2 16.80 5.60 1.43 1.43 2.86 2 19.60
48 16.00 0.50 0.50 1.00 2 16.00 5.33 1.50 1.50 3.00 2 21.33
52 17.33 0.46 0.46 0.92 2 15.60 5.20 1.54 1.54 3.08 2 22.53
56 18.67 0.43 0.43 0.86 2 15.27 5.09 1.57 1.57 3.14 2 23.76
60 20.00 0.40 0.40 0.80 2 15.00 5.00 1.60 1.60 3.20 2 25.00

not enough

Operating under the previous conditions, let’s see what happens when prices are not restricted by the income of workers.

Workers will continue to receive the same daily wage, 8F, to satisfy the needs of their families, while the owners receive 3 and 2 times this amount, respectively. As before, when we take into account the total income of the social arrangement,

24b + 24m = 56F

and

b + m = 2.33

Then, at a minimum,

24b = 32F and b =/> 1.33F

24m = 24F and m =/> 1F

The companies will now, at least, avoid a loss by selling to the higher income consumers -in this case, the owners-, but the workers won’t be able to satisfy their families’ needs in their totality.

 

A slight twist

Now we’ll introduce a slight variation to our two producers model. One of the owner’s companies -let’s choose Richard’s- will pay him more for his services, increasing his buying power as a consumer.  Savings continue to be impossible for workers, whose wages just cover the minimum needs. Productivity remains at 24 pieces of bread and 24 glasses of milk for an 8-hour working day. The market will clear as before.

The production-costs, or expenses, of Richard’s company increase to 32F while Robert’s stay at 24F, a total of 56F, which is the total income of the social arrangement, and since we’re not considering reserves yet, the money available for demand.

For Richard’s company to make a profit, its revenue after sales must be greater than 32F, which means than Robert’s company would obtain less than 24F after sales, or a loss. If Robert wants to avoid this, which is the case in this study, the 24 glass of milk his company produces must sell for at least 24F, or one foody per glass of milk. Now Richard’s in trouble, for his company must sell 32F in bread to avoid a loss, charging at least 1.33F per piece. Then

b + m = 2.33F

Remember, however, the workers: each receives 8F per working day to cover the basic needs of their families, 4 pieces of bread and 4 glasses of milk:

8b + 8m = 16F,

and

b + m = 2F.

This means that, when we’re dealing with basic, necessary products, under the conditions here imposed, prices are determined by the income of workers -i.e., wages.

We also see that 24b +24m = 48F or less, which means that, even though both companies can sell all the product at different price-ratios, the sum of unit-prices is 2F, what we’ll call the wage-to-price index of affordability, and the aggregate price is 48F, leading to an aggregate loss of 8F. Both or either company will sustain a loss.

two producers model

Let’s take a look at a very simple social arrangement where capitalist relationships are established:

a) the tools and materials are owned by two businessmen, Richard and Robert, whose companies produce bread and milk, respectively;

b) production -the process of elaboration of bread and extraction of milk- is carried out by two workers, David and George. David works for Richard and George for Roberts in exchange for wages.

capitalism production distribution

The total population equals 16 persons divided into 4 families. For the sake of simplicity, in this first model each family consists of an equal number of members, 4.

A currency that we’ll call “the foody” (F) will operate as means of exchange. Wages, salaries and products will be paid in foodies

The following assumptions, conditions and restrictions will apply:

a) the time frame is one economic day;

b) production will satisfy the total demand of the population. Assume that each person needs at least 1 piece of bread and 1 glass of milk daily to survive;

c) the 2 workers receive the same wage -one foody per hour (1F/hr). This compensation allows them to satisfy their families’ minimum needs: 4 pieces of bread and 4 glasses of milk per family;

d) the working day is at least 8 hours;

e) owners receive a salary for their administrative and managerial work in the firm, twice the wages of the employees, so each owner receives 16 foodies. They consume what the company produces and acquire it in the market -i.e., they buy their own product;

f) Twenty four pieces of bread and 24 glasses of milk reach the market;

g) workers are unable to save, so their wages are 100% destined to satisfy the needs of their families;

h) owners don’t save either -i.e., their salaries go fully into consumption;

i) neither company generates a profit -revenues equal costs;

j) the market clears, everything is sold.

The wages of David and George are the same, enough (remember: they don’t save) to buy 4 pieces of bread and 4 glasses of milk each:

w1= 4b + 4m = 8F

w2 = 4b + 4m = 8F

where b and m are the prices of one piece of bread and one glass of milk, respectively.

The salaries of the owners is:

s1 = 8b + 8m = 16 F

s2 = 8b + 8m = 16F

The consumption of each worker’s family is:

CW1 = 4b + 4m = 8F

CW2 = 4b + 4m = 8F

The consumption of each owner’s family is:

CO1 = 8b + 8m = 16F

CO2 = 8b + 8m = 16F

Richard company’s production-cost is

pc1 = 24F

and Robert company’s production-cost is

pc2 = 24F

Richard company’s revenue is

R1 = 24b

and Robert company’s revenue is

R2 = 24m

Because nobody saves, all income from work  is spent: 48 foodies are spent in bread and milk. Thus

24b + 24m =48F or b + m = 2F

Since neither company produces neither a profit nor a loss,

24b = 24F and 24m = 24F

Therefore,

b = m = 1F

 

 

 

 

 

the method

This is a study of the world, concerning the real, what really happens. As in any inquiry, there will be assumptions not to be taken as reality, which will help to clarify certain issues and establish points of departure. The objective is to move from simple scenarios to more complex ones, testing the assumptions, introducing imperfections, making the model resemble more and more a real capitalist economy.