Multi-product firms are firms that produce more than one good. As multiproduct firms are dealing with multiple products, they have to deal with allocating inputs more properly in order to obtain a higher level of output. This is a greater problem than the one single-product firms face, the maximization of profit problem, since multiproduct firms must allocate their factors not only to produce one good but multiple goods.
The production analysis can be extended to include multiproduct firms. There is a possibility that two products can be jointly produced in varying proportions by a single production process. In the case of joint products, the production of two or more products is technically dependent on each other. This we can explain with the help of the production possibility curve.
Production Possibility Curve:
A Production Possibility Curve (PPC), sometimes called Production Possibility Frontier or Transformation Curve, is a curve which shows different possibilities of two goods that can be produced with the available resources and given technology. We know that resources are very much limited and have alternative uses.
Suppose a firm decides to produce two goods that are rice and cloth; the more cloth the firm produces, the less rice it would be able to produce. So by, utilizing more resources in the production of cloth means the lesser resources would be available for the production of rice and vice versa.
Assumptions of Production Possibility Curve:
- The amount of productive resources is given and remains fixed (i.e. resources can be shifted from the production of one good to another).
- Resources are neither unemployed nor under-employed but utilized efficiently.
- The economy is working at full employment level and trying to achieve the maximum possible level of production.
- There is no change in technology.
The Production Possibility Curve is a curve which shows different possibilities of two goods that can be produced with the available resource and given technology.
In Figure 4, rice is measured on X-axis and cloth on Y-axis. On one extreme, we are utilizing all our resources in the production of cloth, and on the other extreme, we are utilizing all our resources in the production of rice alone.
Between these two extreme points, there are many possibilities of rice and cloth which a firm can produce. By joining all production possibilities points, we derive Production Possibility Curve. It is also known as Production Possibility Boundary.
With the given resources and available technology, all the points within and on the boundary of the production possibility curve are attainable combinations. All the points on the production possibility boundary represent efficient utilization of resources.
It implies that the production of one good can be increased only by decreasing the resources from the production of other goods. All the points within the production possibility curve represent inefficient utilization of resources. Thus, resources remain under-utilized inside the production boundary.
Slope of Production Possibility Curve:
The Production Possibility Curve is negatively sloped and “bowed outward”. In short, as larger and larger quantities of resources are transferred from the production of one output to another, the addition to the production of second product declines. The slope of the production possibility curve is known as marginal opportunity cost. The marginal opportunity cost refers to the loss of good Y that we need to sacrifice in order to produce one (1) more unit of good X.
Marginal Opportunity Cost = Slope of PPC = ΔY/ΔX
As we move from left to right on the production possibility curve, its slope increases. The increasing slope implies that when we are withdrawing resources from the production of Y to produce more and more of good X, the loss of output of good Y for each additional unit of good X tends to increase.
Iso Revenue Lines:
An iso-revenue is defined as the locus of product combinations that will earn the same revenue. In other words, all the combinations of rice and cloth lying on this line give the same revenue when sold in the market.
At any given fixed price, the iso-revenue line would be a straight line. The higher the iso-revenue line higher is the revenue earned by selling larger combinations of two goods. For a given fixed price, the iso-revenue lines are parallel to one another. The slope of the iso-revenue line is equal to the ratio of the price of the product.
Slope of the Iso-revenue Line = 𝑃𝑥/𝑃𝑦
Where,
𝑃𝑥 is the price of good X, and
𝑃𝑦 is the price of good Y.
Optimum Combination:
The aim of the producer is to maximise profit. The revenue would be maximum when the given production possibility curve is tangent to the iso-revenue line. At this point, the marginal rate of transformation, i.e. the slope of the production possibility curve, is equal to the ratio of prices of commodities X and commodity Y.
𝑃𝑥/𝑃𝑦 = 𝑀𝑅𝑇𝑥𝑦
And the second condition required for an optimum combination of two products is that the production possibility curve must be concave from below.
Read More- Microeconomics
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