Short Run Production Function with Two Variable Inputs

Short Run Production Function with Two Variable Inputs: We employ the notion of isoquants or iso-product curves, which are analogous to indifference curves in the theory of demand, to analyse production functions with two variable elements. As a result, before going over the production function with two variables and returns to scale, we’ll go over the notion of isoquants (or equal product curves) and their attributes.

Isoquants

Isoquants, also known as equal product curves, are related to the indifference curves used in consumer behaviour theory. An isoquant is a term that refers to all factor combinations that may provide the same amount of output.

As a result, the isoquants are contour lines that trace the locations of equal outputs. Because an isoquant indicates the permutations of inputs that may yield an equal amount of output, the producer is unconcerned with which one is used. As a result, isoquants are often referred to as equal product curves or production-indifference curves.

Short Run Production Function with Two Variable Inputs

 Factor Combinations to Produce a Specific Output Level:

To generate a product, it is assumed that two variables are used: labour and capital. The output of each of the factor combinations A, B, C, D, and E is the same, say 100 units. To begin, the supplied 100 units of output are produced by factor combination A, which consists of 1 unit of labour and 12 units of capital.

Similarly, combination B, which consists of two units of labour and eight units of capital, combination C, which consists of three units of labour and five units of capital, combination D, which consists of four units of labour and three units of capital, and combination E, which consists of five units of labour and two units of capital, are all capable of producing the same amount of output, namely 100 units. We displayed all of these combinations in Fig. 1 and obtained an isoquant by connecting them, indicating that any combination represented on it may yield 100 units of output.

Isoquants Though isoquants and indifference curves in consumer behaviour theory are similar, there is one significant distinction between the two. An indifference curve displays all combinations of two commodities that offer the same amount of happiness or value to a customer, but there is no effort to quantify the level of utility it represents.

This is because there is no way to quantify cardinal satisfaction or usefulness in an unambiguous thermos. That is why indifference curves are usually labelled with ordinal numbers such as I, II, III, and so on, indicating that a higher indifference curve represents a higher level of satisfaction than a lower one, but no information is provided as to how much one level of satisfaction is greater than another.

On the other hand, we have no trouble labelling isoquants in the physical units of output. As a physical occurrence, the production of a thing lends itself to absolute measurement in physical units. It is feasible to state how much one isoquant suggests higher or less output than another since each isoquant reflects a certain degree of production.

we’ve constructed an isoquant-map (also known as an equal-product map) with four isoquants that represent 100, 120, 140, and 160 units of output, respectively. Then, using this collection of isoquants, it’s simple to determine how much one isoquant curve’s production level differs from another.

Lines of the Ridge

If the amount utilised is too big, the marginal product of a given component may be negative. If too much labour is utilised, for example, there may be congestion and the efficiency of all labourers may be harmed. Because it covers all factor combinations that produce the same result, an isoquant will include points signifying such factor quantities.

A rational producer, on the other hand, will not work on this component of the isoquant. Drawing two lines from the origin and enclosing just those areas of the isoquants where each element has a positive marginal product shows the region of rational operation. Ridge lines are the name given to such lines. Negative marginal products occur in the positive sloped region of the isoquant.

These portions are not included in the ridge lines. Figure 3 illustrates this. Let us concentrate on isoquant Q1 spanning the range from point A to point E. We now know that when we replace labour with capital and travel from A to E, labor’s marginal productivity decreases.

But consider what happens if we continue to employ more labour after E. The isoquant Q1 rises, suggesting that in order to generate Q1 units with more labour, we must now also spend more capital. Why? Because the marginal output of labour has turned negative beyond E, we must increase the quantity of capital utilised to compensate for utilising more labour.

A similar result may be seen if we follow Q2, Q3, or Q4 from left to right. Points F, G, and H appear beyond point F. As a result of the negative marginal productivity of labour, the slopes of the isoquants turn positive.

A ridge line is a line that connects all points, such as £, F, G, and H, and symbolises the transition from stage II to stage III of manufacturing. Nobody wants to create in stage III since the same amount of output might be achieved with less of both inputs by travelling to the left along the relevant isoquant until stage II was reached.

This same line of reasoning may now be used to rule out stage I. Let’s focus our attention on isoquant Q1 once again. Assume we travel up and to the left this time, toward point A. As we do so, substituting capital for labour, capital’s marginal productivity declines, eventually becoming negative if we go beyond A. As a result, if we increase capital over A while keeping production at Q1 levels, we will need to increase labour.

From a management standpoint, this does not make sense. For their respective isoquants, points B, C, and D are equivalent to point A. We would not want to operate in that zone, which we refer to as stage I, since the marginal productivity of capital is negative beyond these points.

The ridge line R denotes the transition from stage I to stage II, while R’ marks the transition from stage II to stage III. We can see that neither stage I nor stage III are appropriate for production since at least one input’s marginal productivity is negative in those stages. We may thus infer that stage II, which is limited by the two ridge lines R1 and R2, is the sole significant zone for production. The economic region of production is the name given to this area.