The firm produces multiple products X and Y. The firm determines the optimum output and price of X and Y product when they are produced in fixed proportion.

The price theory or micro-economic models of determination are based on the assumption that a firm produces a single, homogeneous product. In actual practice, however, production of a single homogeneous product by a firm is an execution rather than a rule. Most of the firms have more than one product in their line of production. Even the most specialized forms produce a commodity in multiple models, styles and sizes, each so much differentiated from the other that each model or size of the product may be considered a different product. Various models of refrigerators, TV sets, ratio and car models are the examples, which produced by the same company may be treated as different products for at least pricing purpose.

The various models are so differentiated that consumers view them at different products and in same cases, as perfect substitutes for each other. It is, therefore, not surprising that each model or product has different AR and MR curves and that one product of the firm competes against the other product. The pricing under these conditions is known as multi-product pricing or product – line pricing. |

The major problem in pricing multiple products is that each product has a separate demand curve. But, since all of them is produced under the organization by interchangeable production facilities, they have only one inseparable marginal cost curve. If the revenue curves, AR and MR, are separate for each product, cost curves, AC and MC will inseparable. Therefore, the marginal rule of pricing cannot be applied straight a way to fix the price of each product separately. The solution is similar to the one employed to illustrate third degree price discrimination. As a discriminating monopoly tries to maximize its revenue in all its markets, so does a multi-product firm in respect of each of its products. To illustrate the multiple product pricing, let us suppose that a firm has two different products – X and Y in its line of production.

In the above figure, AR and MR curves for the two goods are shown in two segments. The marginal cost for all the products taken together is shown by the curve MC which is the factory marginal cost curve. Let us suppose that when the MRs for the individuals products are horizontally summed up, the aggregate MR (not given in the figure) passes through point E on the MC curve. If a line parallel to the X-axis is drawn from point E to the Y-axis through the MRs, the intersecting points will show the points where MX and MRs are equal for each product, as shown by the line EMR (Equal Marginal Revenue line). The points of intersection between EMR and MRs determine the output level and price for each product. The output of the two products are given as OQ1 of product X; and Q1Q2 of product B. The respective prices for the two products are P1Q1 for product X and P2Q2 for Y. these price and output combinations maximize the profit from each product and hence the overall profit of the firm.

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