Joint Supply: When Two Goods Are Produced Together
What is Joint Supply? The Core Concept
Imagine you are a farmer raising a cow. Your main goal might be to produce beef. But from that same cow, you will also get leather for jackets, bones for gelatin, and fat (tallow) for candles or soap. You cannot produce just the beef without also producing these other items. This is the essence of joint supply: two or more goods that are produced together from a single origin or process. They are "joint" because their production is linked; they come as a package.
These goods are often called co-products or by-products. While sometimes used interchangeably, there is a subtle difference. A co-product is usually a second output that has significant value, like leather from a cow. A by-product is often a secondary output with lesser economic value, like the bones used for stock. However, the distinction can blur as technology and markets change. For example, sawdust was once a low-value by-product of lumber mills, but it is now a valuable co-product used for particleboard and fuel pellets.
The Mathematics of Joint Supply: A Simple Model
We can represent the joint supply relationship with a simple formula. Think of $Y$ as the main production process (like raising a cow or refining crude oil). This process yields two goods, $A$ and $B$, in relatively fixed proportions.
This fixed proportion is a key feature. If farmers want to produce more beef to meet high demand, they must raise more cows, which automatically means they will also produce more leather, even if the demand for leather hasn't changed. This simple relationship is what creates fascinating ripple effects across different markets.
Key Characteristics and Market Effects
Goods in joint supply have three main characteristics that set them apart:
1. Fixed Proportion of Output: The ratio in which the goods are produced is often determined by nature or technology. You cannot custom-order a cow that gives only beef with no hide.
2. Derived Supply: The supply of one co-product is derived from the decision to produce the primary product. The supply of leather is derived from the decision to raise cattle for beef.
3. Price Interdependence: This is the most important effect. The market price of one co-product can dramatically affect the supply and price of the other. Let's see why.
| Production Process (Y) | Primary Co-Product (A) | Secondary Co-Product (B) | Economic Impact |
|---|---|---|---|
| Crude Oil Refining | Gasoline | Heating Oil, Asphalt, Plastics | High demand for gasoline increases supply of other products, potentially lowering their prices. |
| Wheat Milling | Wheat Flour | Bran, Wheat Germ | Flour production determines supply of bran for animal feed, affecting its cost. |
| Livestock (Sheep) | Lamb/Mutton Meat | Wool | A drop in wool prices may not reduce sheep numbers if meat demand is strong. |
| Sawmill Operation | Lumber (Planks) | Sawdust, Wood Chips | Lumber demand drives the supply of chips for paper and sawdust for fuel. |
The Beef and Leather Connection: A Practical Case Study
Let's dive deeper into the classic example of cattle to see joint supply in action. The cattle-raising industry is motivated by the total revenue it can get from all the co-products of a cow. This is called the joint product revenue.
Now, imagine a new fashion trend makes leather jackets extremely popular. The demand for leather soars, driving up the price of leather hides. What happens?
1. Direct Effect: Leather producers make more money from each hide.
2. Joint Supply Effect: To get more leather, more cows must be raised and processed. This automatically increases the supply of beef.
3. Market Consequence: The increased supply of beef, assuming demand for beef stays the same, will lead to a fall in the price of beef. So, a price increase for leather can cause a price decrease for beef! This inverse relationship in their prices is a classic sign of goods in joint supply.
The opposite can also happen. If people eat less beef (demand falls), fewer cows are raised, leading to a shortage of leather and higher leather prices for consumers. This case study shows how markets for seemingly unrelated goods like food and fashion are intimately connected through the production process.
Joint Supply vs. Alternative Production Concepts
It's easy to confuse joint supply with other economic ideas. Let's clarify the differences.
Joint Supply vs. Complementary Goods: Complementary goods are linked in consumption, not production. For example, peanut butter and jelly are consumed together. If the price of peanut butter drops, demand for jelly might rise because people buy them as a pair. In joint supply, the link is in production. Beef and leather are produced together, but you don't have to consume them together.
Joint Supply vs. Substitute Goods: Substitute goods can replace each other in consumption, like butter and margarine. An increase in the price of butter causes people to buy more margarine. In joint supply, the goods are not substitutes; you cannot use leather as a substitute for beef in a recipe!
Joint Supply vs. Multi-Product Firms: A company like Samsung makes both phones and televisions. These are separate production processes using different factories and materials. This is diversification, not joint supply. In true joint supply, the multiple outputs are technologically inseparable from a single process.
Important Questions
Q1: If goods are in joint supply, does a high price for one always cause a high price for the other?
Q2: Can technology change a joint supply relationship?
Q3: How does joint supply affect producers' decisions and resource allocation?
Conclusion
Joint supply is a fundamental economic concept that reveals the hidden connections in our world. From the food we eat to the fuel in our cars, many products arrive on the market not as isolated items but as part of an inseparable pair or group from a common origin. Understanding this link helps explain why the price of wool might fall when people eat more lamb, or why a boom in construction (increasing lumber demand) can make paper (from wood chips) more plentiful. It teaches us about efficiency, as producers seek uses for every output, and about market interdependence, where a shock in one industry can ripple unpredictably into another. By recognizing joint supply, we gain a clearer, more connected view of how our global economy truly works.
Footnote
1 Co-Products: Two or more goods produced simultaneously from a single production process, where each has significant economic value (e.g., gasoline and diesel fuel from crude oil).
2 By-Products: Secondary outputs generated during the production of a primary good. They may have lower economic value initially but can become valuable over time (e.g., sawdust from lumber mills).
3 Derived Supply: The supply of a co-product that is not independently planned but results from the decision to supply the primary product. The supply of leather is derived from the supply of beef.
4 Joint Product Revenue ($TR$): The total income a producer receives from selling all the outputs of a joint production process. It is the sum of the revenues from each co-product and is the key determinant for production decisions.