relationships between different markets: joint supply
📈 The Interaction of Demand and Supply
What is Demand?
Demand is the relationship between the price of a good and the quantity that consumers are willing to buy. Think of it like a crowd at a concert: the higher the ticket price, the fewer people want to attend.
- Higher price → lower quantity demanded.
- Lower price → higher quantity demanded.
Mathematically: $Q_d = a - bP$ (where $a,b>0$).
What is Supply?
Supply is the relationship between price and the quantity producers are willing to sell. Imagine a farmer’s market: the higher the price, the more farmers bring fresh produce.
- Higher price → higher quantity supplied.
- Lower price → lower quantity supplied.
Mathematically: $Q_s = c + dP$ (where $c,d>0$).
⚖️ Market Equilibrium
Equilibrium occurs where quantity demanded equals quantity supplied: $Q_d = Q_s$.
- Set $a - bP = c + dP$.
- Solve for $P^*$: $P^* = \dfrac{a-c}{b+d}$.
- Find $Q^*$ by substituting $P^*$ back into either equation.
At equilibrium, the market clears – no excess supply or demand.
Joint Supply: When Two Markets Share a Producer
Some producers supply goods to multiple markets. The total supply to each market depends on the price in that market and the price in the other market.
| Market | Price ($P$) | Supply Function ($Q$) |
|---|---|---|
| Market A | $P_A$ | $Q_A = \alpha + \beta P_A + \gamma P_B$ |
| Market B | $P_B$ | $Q_B = \delta + \epsilon P_B + \zeta P_A$ |
🔄 Notice the cross‑price terms ($\gamma P_B$, $\zeta P_A$). They show how a change in one market’s price affects supply in the other.
Example: Coffee and Tea
Suppose a café supplies both coffee and tea. The supply of coffee depends on its own price and on the price of tea because customers might switch between them.
- Let $Q_{coffee} = 50 + 2P_{coffee} - 1P_{tea}$.
- Let $Q_{tea} = 30 + 3P_{tea} - 0.5P_{coffee}$.
- If the price of tea rises, the café supplies more coffee (negative cross‑price coefficient).
📚 Exam Tip: Joint Supply Questions
- Identify the supply functions for each market.
- Check for cross‑price terms – they indicate joint supply.
- Show how a price change in one market shifts the supply curve in the other.
- Always label the axes and show the new equilibrium if a price changes.
Analogy: A Two‑Course Meal
Think of a restaurant offering a main dish and a side. If the price of the main dish goes up, the restaurant might offer more side dishes to keep customers happy. The side dish supply reacts to the main dish price – that’s joint supply in action!
💡 Quick Review
- Demand: $Q_d = a - bP$.
- Supply: $Q_s = c + dP$.
- Equilibrium: $Q_d = Q_s$.
- Joint supply involves cross‑price terms.
Revision
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