Summary of Market Equilibrium and Price Transmission

## Introduction Regional maize markets illustrate how supply, demand and trade costs shape local prices and quantities. This material uses two South African regions, Free State (surplus producer) and Durban (deficit consumer), to show how to compute market equilibria, identify surplus/deficit regions, and determine whether interregional trade occurs given a transport cost. > **Definition:** A market equilibrium is the price and quantity where **quantity demanded equals quantity supplied**. ## Individual market equilibrium: concepts and steps To find an equilibrium in a closed market (no trade): 1. Write the demand function: quantity demanded as a function of price. 2. Write the supply function: quantity supplied as a function of price. 3. Set demand equal to supply and solve for the equilibrium price $P^*$. 4. Substitute $P^*$ into either function to get equilibrium quantity $Q^*$. > **Definition:** Consumer surplus is the area between the demand curve and the price line up to the traded quantity. Producer surplus is the area between the price line and the supply curve up to the traded quantity. ### Given demand and supply functions - Market A (Free State): - Demand: $Q_D^A = 04.00 - P$ - Supply: $Q_S^A = 05.00 + 2P$ - Market B (Durban): - Demand: $Q_D^B = 04.00 - 2P$ - Supply: $Q_S^B = 05.10 + P$ Note: The formatting of the given coefficients appears as integers with leading zeros; interpret them as ordinary numbers: $4.00$ and $5.00$, $5.10$. ## Calculations: equilibrium price and quantity ### Market A (Free State) Set demand equal to supply: $$04.00 - P = 05.00 + 2P$$ Move terms: $$04.00 - 05.00 = 2P + P$$ $$-1.00 = 3P$$ Solve for $P$: $$P = -0.333333\text{ (i.e. }-\tfrac{1}{3}\text{)}$$ Equilibrium quantity (substitute into demand): $$Q^A = 04.00 - P = 04.00 - \left(-0.333333\right)$$ $$Q^A = 04.333333\text{ (i.e. }4\tfrac{1}{3}\text{)}$$ ### Market B (Durban) Set demand equal to supply: $$04.00 - 2P = 05.10 + P$$ Move terms: $$04.00 - 05.10 = P + 2P$$ $$-1.10 = 3P$$ Solve for $P$: $$P = -0.3666667\text{ (i.e. }-\tfrac{11}{30}\text{ approximately)}$$ Equilibrium quantity (substitute into demand): $$Q^B = 04.00 - 2P = 04.00 - 2\left(-0.3666667\right)$$ $$Q^B = 04.7333334\text{ (i.e. }4.733333\text{ approx.)}$$ > **Interpretation note:** These equilibrium prices are negative in the closed-market algebra because the linear functions as given cross at negative prices. In real markets, negative prices are unusual; this algebraic result means that, with the supplied linear functions, supply exceeds demand at nonnegative prices except at negative price points. For policy or real-world interpretation, compare relative magnitudes to identify surplus/deficit rather than rely on the negative price sign alone. ## Which market is surplus and which is deficit? - A **surplus-producing** region is one where, at a common reference price (or under autarky comparison), supply exceeds local demand so the region can export. - A **deficit-consuming** region is one where demand exceeds local supply so the region must import. Using the computed equilibria under autarky (closed markets): - Free State equilibrium quantity supplied equals quantity demanded at its own (negative) price. However, the Free State was described as a surplus-producing region; compare the intercepts to see relative positions. Compare supply and demand intercepts at $P=0$ (a nonnegative reference price): - Free State at $P=0$: $Q_D^A = 4.00$, $Q_S^A = 5.00$. Supply $>$ demand by $1.00$ unit: surplus at $P=0$. - Durban at $P=0$: $Q_D^B = 4.00$, $Q_S^B = 5.10$. Here supply $>$ demand by $1.10$ units at $P=0$. But the problem statement identifies Free State as surplus-producing and Durban as deficit-consuming. To reconcile with the algebraic functions, check net positions at a common market price or interpret the given regional labels: if Free State is surplus and Durban deficit, trade should flow from Free State to Durban if transport costs allow. In shor