9/10: Supply, Demand, and Equilibrium

Supply and Its Determinants

• Supply is the relationship between quantity supplied and price.
• Other factors can shift the supply curve:
  • Changes in expected prices
  • Number of suppliers
  • Technology improvements
  • Taxes/Subsidies
  • Natural disasters (typically reduce supply due to destruction)
• Technology improvements
  • Lower input costs → higher supply (shift right) or, at every quantity, willingness to sell at a lower price
• Subsidies
  • Government payments to sellers reduce production costs → increase supply (shift right)
  • Removing subsidies lowers supply
• Price changes cause movements along the supply curve, not shifts
  • Higher price → higher quantity supplied (movement along curve)
  • The supply curve reflects the minimum price producers are willing to accept; higher willingness to produce at a given quantity corresponds to higher prices
• Substitutes in production
  • Armchairs vs sofas are substitutes in production
  • If armchair price rises, firms shift production toward armchairs, reducing sofa supply (sofa supply shifts left)
• Real-world intuition
  • Negative shocks (e.g., disasters) typically decrease supply; positive changes (e.g., tech, subsidies) increase supply

Market Equilibrium

• Equilibrium occurs where buyers’ plans and sellers’ plans coincide
  • Demand curve shows quantity demanded at each price
  • Supply curve shows quantity supplied at each price
• Equilibrium price and quantity
  • $P^<em>$ is the price where $Q^d(P^</em>) = Q^s(P^*)$
  • $Q^*$ is the corresponding traded quantity
• Non-equilibrium adjustments
  • If price is pushed above equilibrium, a surplus appears; price tends to fall back toward equilibrium
  • If price is below equilibrium, a shortage appears; price tends to rise back toward equilibrium

Inverse vs Regular Demand and Supply

• Inverse curves plot price as a function of quantity:
  • Inverse demand: $p = f_d(q)$
  • Inverse supply: $p = f_s(q)$
• Regular curves plot quantity as a function of price:
  • Demand: $q = g_d(p)$
  • Supply: $q = g_s(p)$
• Either approach yields the same equilibrium; solving with inverse curves is just another path
• When solving, you typically get the equilibrium by equating the two price equations or by equating the two quantity equations

Finding Equilibrium from Schedules

• Given demand and supply schedules, plot or convert to equations
• Solve for equilibrium price and quantity
  • Option A (regular): set $Q^d(p) = Q^s(p)$ and solve for $p^<em>$, then find $Q^</em>$ by plugging back
  • Option B (inverse): set $p<em>d(q) = p</em>s(q)$ and solve for $q^<em>$, then compute $p^</em>$ from either inverse curve
• Both approaches yield the same equilibrium

Example: Baja Blast (Demand + Supply)

• Equilibrium from schedule: $P^* = 2, \, Q^* = 21$
• If price is set at $P = 3$:
  • Demand quantity: $Q^d = 14$
  • Supply quantity: $Q^s = 31.5$
  • Surplus: $Q^s - Q^d = 31.5 - 14 = 17.5$
  • Traded quantity: $14$ (the quantity buyers want to buy)
• Market mechanism moves price toward equilibrium to resolve the surplus

Example: Soybeans (Algebraic Equilibrium)

• Given inverse curves:
  • Inverse demand: $p = 12 - frac{1}{2} q$
  • Inverse supply: $p = frac{1}{6} q$
• Solve for equilibrium by equating them:
  • $frac{1}{6} q = 12 - frac{1}{2} q$
  • igl( frac{1}{6} + frac{1}{2}igr) q = 12 \ frac{2}{3} q = 12 \ q^* = 18
  • Price: $p^* = frac{1}{6} imes 18 = 3$
• Equilibrium: $P^* = 3, \, Q^* = 18$
• Reassuringly, solving with regular curves yields the same result

Practical Takeaways

• Equilibrium is where quantity supplied equals quantity demanded
• Shifters move the entire supply curve; price changes move along the curve
• Substitutes in production can shift supply between goods (e.g., sofas vs armchairs)
• Inverse and regular curves are two valid representations; choose based on given data
• When given schedules, you can find equilibrium by solving either with the regular equations or the inverse equations