Firms often produce multiple related products. When products are substitutes, increasing production of one reduces demand for the other. When complementary, increasing one boosts demand for the other. Profit maximization requires jointly determining prices and output levels. A firm should produce quantities where the marginal revenue from each product equals marginal cost. It prioritizes producing profitable products up to the point where the least profitable product's marginal cost equals marginal revenue. Joint products have interconnected production and demand. Firms maximize profits by setting marginal revenue of each joint product equal to their shared marginal cost.

2. INTRODUCTION:
• Most modern firms produce a variety of products
rather than a single product.
• The products sold by a firm may be interrelated
as substitutes or complements.
• Generally, organizations produce more than one
product in their line of production.Even a single
product of an organization can differ in styles
and sizes.

3. Meaning:
• For example, a refrigerator manufacturing
organization produces refrigerators in different
colours, sizes, and features.
• Similarly, an automobile organization manufactures
vehicles in different colours, sizes, and mileage.
The pricing in case of multiple products is called
multiple product pricing.

4. • In the pricing of interrelated products, a firm needs
to consider the effect of a change in the price of
one of its products on the demand for the others.
• The reason for this is that a reduction in the price of
a product leads to a reduction in the demand for a
substitute product sold by the same firm, and to an
increase in the demand for complementary
products.

5. • Thus, profit maximization requires that the
output levels and prices of the various products
produced by the firm be determined jointly
rather than independently.

6. For a two-product (A and B) firm, the marginal
revenue functions of the firm are:
A B
A
A A
TR TR
MR
Q Q
 
 
 
B A
B
B
TR TR
MR
QB Q
 
 
 

7. • From the two equations above, we see that the
marginal revenue for each product has two
components,
1. one associated with the change in the total
revenue from the sale of the product itself,
2. and the other associated with the change in
the total revenue from the other product.

8. • The second term on the right-hand side of each
equation, thus, reflects the demand
interrelationships.
• For example: the term(
𝚫TRB
𝚫QA
) in equation 1
measures the effect on the firm’s revenues from
product B resulting from the sale of an additional
unit of product A by the firm.

9. • Similarly, (
𝜟TRA
𝜟QB
) in equation 2 measures the
effect on the firm’s total revenue from
product A resulting from the sale of an
additional unit of product B by the firm.

10. • If the second term on the right-hand side of
each equation is positive, indicating that
increased sales of one product stimulates sales
of the other, the two products are
complementary.
• If, on the other hand, second term in each
equation is negative, indicating that increased
sales of one product leads to reduced sales of
the other, the two products are substitutes.

11. Plant Capacity Utilisation:
• A multi-product firm using a single plant should
produce quantities where the marginal revenue
(MRi) from each of its k products is equal to the
marginal cost (MC) of production.

12. • The quantity produced of the more profitable
products is then determined by the point at
which their marginal revenue equals the
marginal revenue and marginal cost of the last
unit of the least profitable product produced by
the firm. The price of each product is then
determined on its respective demand curve.
• This process is shown in figure 1.

13. Optimal outputs and Prices of Multiple
Products by a firm:

14. • Figure 1 shows the situation of a firm selling
three products(A, B, and C) with respective
demand curves DA, DB, and DC, and
corresponding revenue curves MRA, MRB,
and MRC. The firm maximizes profits when
MRA=MRB= MRC=MC. This is shown by points
EA, EB, and EC, where the equal marginal
revenue curve, at the level at which MRc=MC,
crosses the MRA, MRB, and MRC curves.

15. • Thus, QA=60 and PA=₹16; QB=90 (from 150-60)
and PB=₹15; and QC=180 (from 330-150) and
PC=₹14. Note that each successive demand
curve is more elastic and that the price of each
successive product is lower, while its MC is
higher.

16. Optimal Pricing of Joint Products
Produced in Fixed proportions:
• The products produced by a firm can be related not
only in demand but also in production.
• Production interdependence arises when products are
jointly produced.
• Products can be jointly produced in fixed or variable
proportions.
• An example of joint production with variable proportions
is provided by petroleum refining, which results in
gasoline, fuel oils etc…

17. Joint Products in Fixed Proportions:

18. • In both panels, DA and MRA, and DB and MRB
refer, respectively, to the demand and marginal
revenue curves for products A and B, which
are jointly produced in fixed proportions.
• The total marginal revenue (MRT) curve is
obtained from the vertical summation of the
MRA and MRB curves.

19. • When the marginal cost of the jointly produced
production package is MC (see the left panel),
the best level of output of products A and B is
40 units and is given by point E, at which
MRT=MC. At Q=40,PA= ₹12 on DA and PB= ₹5
on DB.

20. • on the other hand, with MC’ (see the right
panel), the best level of output of the joint
product package is 60 units and is given by
point E’, at which MRT=MC’. Q=60,P’A= ₹10 on
D’A, but since MRB is negative for QB>45, the
firm sells only 45 units of product B at
PB’=₹4.50 (at which TRB is maximum at
MRB=0) and disposes of the remaining 15 units
of product B.

21. Optimal Pricing and Output of Joint
Products Produced in Variable
Proportions:
• The case of products that are produced jointly
in fixed proportions is possible, more common
is the case of products that are jointly
produced in variable proportions.
• We can determine the profit-maximizing
combination of products that are jointly
produced in variable proportions with the aid of
figure 3.

22. .
Pricing of Multiple Products

23. • The curved lines are product transformation
curves showing the various combinations of
products A and B that the firm can produce at
each level of total cost (TC).
• The curvature arises because the firm’s
productive resources are not perfectly
adaptable in the production of products A and B
that give rise to the same total revenue (TR) to
the firm when sold at constant prices.

24. • The tangency point of an isorevenue to a TC
curve gives the combination of products A
and B that leads to the maximum profit for
the firm for the specific TC. The overall
maximum profit of the firm is = ₹40. this is
earned by producing and selling 80A and
120B with TR=₹240 and TC=₹200.

25. References:
1. Managerial Economics, principles and worldwide
applications, eighth edition(2019) , Dominick salvatore,
siddhartha K.Rastogi.
2. Modern Microeconomics,second edition(2017)
A.Koutsoyiannis.
3. Advanced economic theory: Microeconomic analysis,
Nineteenth edition, H.L.Ahuja.
4. Various Online sources.