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

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s