Multi-Product Firm and Production Possibility Curve

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:

1. The amount of productive resources is given and remains fixed (i.e. resources can be shifted from the production of one good to another).
2. Resources are neither unemployed nor under-employed but utilized efficiently.
3. The economy is working at full employment level and trying to achieve the maximum possible level of production.
4. 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/𝑃_𝑦

Where,

𝑃_𝑥 is the price of good X, and

𝑃_𝑦 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.

𝑃_𝑥/𝑃_𝑦 = 𝑀𝑅𝑇_𝑥𝑦

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

1. Microeconomics: Definition, Meaning and Scope
2. Methods of Analysis in Economics
3. Problem of Choice & Production Possibility Curve
4. Concept of Market & Market Mechanism in Economics
5. Concept of Demand and Supply in Economics
6. Concept of Equilibrium & Dis-equilibrium in Economics
7. Cardinal Utility Theory: Concept, Assumptions, Equilibrium & Drawbacks
8. Ordinal Utility Theory: Meaning & Assumptions
9. Indifference Curve: Concept, Properties & Shapes
10. Budget Line: Concept & Explanation
11. Consumer Equilibrium: Ordinal Approach, Income & Price Consumption Curve
12. Applications of Indifference Curve
13. Measuring Effects of Income & Excise Taxes and Income & Excise Subsidies
14. Normal Goods: Income & Substitution Effects
15. Inferior Goods: Income & Substitution Effects
16. Giffen Paradox or Giffen Goods: Income & Substitution Effects
17. Concept of Elasticity: Demand & Supply
18. Demand Elasticity: Price Elasticity, Income Elasticity & Cross Elasticity
19. Determinants of Price Elasticity of Demand
20. Measuring Price Elasticity of Demand
21. Price Elasticity of Supply and Its Determinants
22. Revealed Preference Theory of Samuelson: Concept, Assumptions & Explanation
23. Hicks’s Revision of Demand Theory
24. Choice Involving Risk and Uncertainty
25. Inter Temporal Choice: Budget Constraint & Consumer Preferences
26. Theories in Demand Analysis
27. Elementary Theory of Price Determination: Demand, Supply & Equilibrium Price
28. Cobweb Model: Concept, Theorem and Lagged Adjustments in Interrelated Markets
29. Production Function: Concept, Assumptions & Law of Diminishing Return
30. Isoquant: Assumptions and Properties
31. Isoquant Map and Economic Region of Production
32. Elasticity of Technical Substitution
33. Law of Returns to Scale
34. Production Function and Returns to Scale
35. Euler’s Theorem and Product Exhaustion Theorem
36. Technical Progress (Production Function)
37. Multi-Product Firm and Production Possibility Curve
38. Concept of Production Function
39. Cobb Douglas Production Function
40. CES Production Function
41. VES Production Function
42. Translog Production Function
43. Concepts of Costs: Private, Social, Explicit, Implicit and Opportunity
44. Traditional Theory of Costs: Short Run
45. Traditional Theory of Costs: Long Run
46. Modern Theory Of Cost: Short-run and Long-run
47. Modern Theory Of Cost: Short Run
48. Modern Theory Of Cost: Long Run
49. Empirical Evidences on the Shape of Cost Curves
50. Derivation of Short-Run Average and Marginal Cost Curves From Total Cost Curves
51. Cost Curves In The Long-Run: LRAC and LRMC
52. Economies of Scope
53. The Learning Curve
54. Perfect Competition: Meaning and Assumptions
55. Perfect Competition: Pricing and Output Decisions
56. Perfect Competition: Demand Curve
57. Perfect Competition Equilibrium: Short Run and Long Run
58. Monopoly: Meaning, Characteristics and Equilibrium (Short-run & Long-run)
59. Multi-Plant Monopoly
60. Deadweight Loss in Monopoly
61. Welfare Aspects of Monopoly
62. Price Discrimination under Monopoly: Types, Degree and Equilibrium
63. Monopolistic Competition: Concept, Characteristics and Criticism
64. Excess Capacity: Concept and Explanation
65. Difference Between Perfect Competition and Monopolistic Competition
66. Oligopoly Market: Concept, Types and Characteristics
67. Difference Between Oligopoly Market and Monopolistic Market
68. Oligopoly: Collusive Models- Cartel & Price Leadership
69. Oligopoly: Non-Collusive Models- Cournot, Stackelberg, Bertrand, Sweezy or Kinked Demand Curve
70. Monopsony Market Structure
71. Bilateral Monopoly Market Structure
72. Workable Competition in Market: Meaning and Explanation
73. Baumol’s Sales Revenue Maximization Model
74. Williamson’s Model of Managerial Discretion
75. Robin Marris Model of Managerial Enterprise
76. Hall and Hitch Full Cost Pricing Theory
77. Andrew’s Full Cost Pricing Theory
78. Bain’s Model of Limit Pricing
79. Sylos Labini’s Model of Limit Pricing
80. Behavioural Theory of Cyert and March
81. Game Theory: Concept, Application, and Example
82. Prisoner’s Dilemma: Concept and Example