Joint product pricing
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In microeconomics, joint product pricing is the firm's problem of choosing prices for joint products, which are two or more products produced from the same process or operation, each considered to be of value. Pricing for joint products is more complex than pricing for a single product. To begin with, there are two demand curves. The characteristics of each could be different. Demand for one product could be greater than for the other. Consumers of one product could be more price elastic than consumers of the other (and therefore more sensitive to changes in the product's price).
To complicate things further, both products, because they are produced jointly, share a common marginal cost curve. There are also complexities in the production function. Their production could be linked in the sense that they are bi-products (referred to as complements in production) or in the sense that they can be produced by the same inputs (referred to as substitutes in production). Further, production of the joint product could be in fixed proportions or in variable proportions.
When setting prices in such a complex situation, microeconomic marginal analysis is helpful. In a simple case of a single product, the price is set at that quantity demanded where the marginal cost equals the marginal revenue. This is what is done when joint products are produced in variable proportions. Each product is treated separately. It might even be possible to construct separate cost functions. In the diagram below, to determine optimal pricing for joint products produced in variable proportions, one finds the intersection point of marginal revenue (product A) with the joint marginal cost curve. That quantity is then extended up to the demand curve for product A, which yields the profit-maximizing price for product A (point Pa in the diagram). The same is done for product B, yielding price point Pb1.
If the products are produced in fixed proportions (e.g., cow hides and cow steaks), then one of the products will likely be produced in quantities different from the profit-maximizing amount considered separately. In fact, the profit-maximizing quantity and price of the second half of the joint product will be different from the profit-maximizing amount considered separately. In the diagram, product B is produced in greater amounts than the profit-maximizing amount considered separately and sold at a lower price (point Pb2) than the profit-maximizing price considered separately (point Pb1). Although the price is lower and the output is higher, the marginal cost is also higher. Yet this is a profit-maximizing solution to this situation. The quantity of product B supplied is increased to the point where marginal revenue becomes zero (i.e., where the marginal revenue curve intersects the horizontal axis).