Optimum use of two variable inputs
In this article, we cover basic concept, assumptions, and equilibrium conditions in different two types of approaches regarding the optimal employment of two variable inputs. So let's start the topic.
Concept
The optimum use of two variable inputs is the long term phenomenon in economics. It is also known as the producer's equilibrium. The optimum employment of two variable inputs means finding the best combination of Labour and Capital which will produce certain level of output at lowest cost or maximum level of output at given cost.
We have to be aware about isoquants and isocost line to find the equlibrium point.
Isoquant
Isoquant is a curve that shows various combination of labour and capital which produce same level of output. Group of isoquant curves are called isoquant map.
Isocost line
Isocost line is a line that shows various combination of labour and capital that a firm can employ at a given budget.
Assumptions
This theory of optimal use of two variable inputs is based on following assumptions.
1.The objective of the producer is to maximize the profit.
2. The producer is rational.
3. The producer uses only two inputs i.e Labour and Capital.
4. Price of labour and capital are fixed.
5. All units of labour and capital are homogeneous.
6.There is perfect competition market for labour and capital.
7. There is existence of isocost line in case of cost minimization and isoquant map in case of output maximization.
Equilibrium Condition
There are basically two condition for equilibrium which are as follows.
1. Isoquant tangents to the isocost line.
2. Isoquant is convex to the origin at the tangency point.
There are two types of cases to explain this theory which are as follows:
1. Cost given
2. Output given
1. Cost given
In this case, we have to find out the best combination of labour and capital for maximizing the level of output at a given cost or budget. For that, we have to look at the point where given isocost line touches the highest isoquant. We can also explain this approach with the help of following figure.
In the above figure, x-axis and y-axis represents units of labour and units of capital respectively. The line AB is the given isocost line. IQ1, IQ2 and IQ3 are the various isoquant curves which produce deferent level of output. They are together called isoquant map. The Isocost line AB tangents to IQ3 at point E which meets both condition of the equilibrium. Therefore the point E is the equilibrium point which determine the optimal combination of Labour and Capital i.e OL1 And OK1 respectively.
The rational producer wants to produce at highest IQ3 but he can not because of limited cost or budget.The isocost line also tangets to the point M and N of IQ1 which produce lower level of output than IQ2 at same cost. So, a rational producer doesn't produce at the IQ1. Therefore the producer has to produce at IQ3 level of output at point E where OL1 units of labour and OK1 units of capital can be employed.
2. Output given
In this case, we have to find out the best combination of labour and capital for minimizing the cost at a given level of output. For that, we have to look at the point where given isoquant touches the lowest isocost line. We can also explain this approach with the help of following figure.
In the above figure, x-axis and y-axis represents units of labour and units of capital respectively. The line A1B1, A2B2, and A3B3 are the isocost lines which represent different cost outlays. Higher isocost line shows higher cost outlays and lower isocost line shows lower cost outlays. IQ curve represents the given isoquant curve which produces given level of output. The isocost line A2B2 tangents to the Isoquant curve IQ at a point E. This is the equilibrium point as it meets the both conditions for equilibrium. Therefore the optimum combination of labour and capital are OL1 and OK1 respectively.
The producer has two alternatives i.e point M and N which lies in higher isocost line. That means firm can produce same level of output but at higher cost. A rational producer doesn't produce at point M and N. The producer wants to produce at lower isocost line but he can not produce given level of output at this cost outlays. Therefore the producer has to produce given level of output at A2B2 cost outlays at point E where OL1 units of labour and OK1 units of capital can be employed.
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