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: \$Qd = Qs\$.

  1. Set \$a - bP = c + dP\$.
  2. Solve for \$P^*\$: \$P^* = \dfrac{a-c}{b+d}\$.
  3. 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.

MarketPrice (\$P\$)Supply Function (\$Q\$)
Market A\$P_A\$\$QA = \alpha + \beta PA + \gamma P_B\$
Market B\$P_B\$\$QB = \delta + \epsilon PB + \zeta P_A\$

🔄 Notice the cross‑price terms (\$\gamma PB\$, \$\zeta PA\$). 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.

  1. Let \$Q{coffee} = 50 + 2P{coffee} - 1P_{tea}\$.
  2. Let \$Q{tea} = 30 + 3P{tea} - 0.5P_{coffee}\$.
  3. 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: \$Qd = Qs\$.
  • Joint supply involves cross‑price terms.