On a regular basis, producers ( of anything ) are questioned on the method they would adapt to take a decision to meet a particular production target. This is as much true for white collar industries ( like software etc ) and blue collar industries ( like manufacturing etc ). There are two major constrains on which the outcome or your choice of method of production depend.

Quantity

Cost
Quantity
Quantity of production is the target to be achieved. Lets take a problem statement of a cotton factory owner who has 100 spinning machines and 150 man power trying to decide a particular quarter produce. The quantity of the production will be decided on supply and demand rules, however there is a target (X) to be achieved in time (t).
Before we jump into any sort of economic analysis, we need to be clear on the system. Some generic items would be as below.
Is there only one quantity i usually produce that make 100 people using 100 spinning machines running constantly for 8 hrs. Productivity is 1 kg cotton per hour.
Total = 8 hrs * 1 * 100 = 800 kg per day.
If my production target is 100,000 kgs this quarter, then the math goes something like this.
100,000 / 800 = 125 day = 4 months 19 days ( including holiday to be as non working ) for final production.
What if i have only 2 months to do the same thing ?
Ans : You have to increase both spinning machines and labor.
Cost
Coming to cost, it means that i set my limit on the capital i can invest or i have to spare from various resources ( loans, investors, advance capital from customers etc ).
I have allocated $10,000 for this project and i will have to finish it with the maximum amount of resources.
Isoquant (Quantity) and Isocost (Cost) analysis as i have understood, suffice this research of the companies who are trying to optimize efficiency for production of goods. Actually, my study started with the Theory of the Firm concept and eventually when i started digging deeper i have come to the mathematical models of Isocost and Isoquant which depend upon the production function.
Image courtesy : seattle.edu
If you look at the figure above the curves convex to the origin represent the isoquant lines and the tangent to the curve represents the isocost line. This optimal point is at ‘e’.
You can red more about the what the slope these lines represent and what implications can we draw from the production point of view in the here.
Coming back to production function, in plain terms it can be mentioned as below.
Q = x1 + x2 + x3 …
Q = Total quantity that can be produced
x1, x2, x3 .. are the inputs are the resources that are available to be spared. In the industrial view point the function will be modified to increase efficiency of the system.
Q = min ( x1 + x2 + x3 .. )
Well, i cannot say i have understood completely the concept of capital contribution vs labor contribution. But i can try to derive the conclusions based on my observation.
1. Capital contribution is the input that is required from the investment point of view.
2. Capital contribution involves any technological advancement costs for increasing efficiency.
3. Labor costs are also involved in the capital calculation
As seen the chart above, Q1, Q2 and Q3 are different outputs of production you can expect from a facility depending upon the capital vs labor allocation.
Depending upon the production function of the system under evaluation the implication change drastically.
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