Difficulty: Introductory | Prerequisites: Comfort with linear equations, basic algebra, familiarity with supply and demand diagrams.
This topic covers the mechanics of finding market equilibrium when you are given demand and supply as algebraic functions, and what happens when one of those functions shifts. It also introduces the idea that when a country opens to trade at a world price below the domestic equilibrium, the gap between domestic demand and domestic supply must be filled by imports. These are the workhorses of every applied micro problem you will see for the rest of the course.
Set quantity demanded equal to quantity supplied and solve for price. When demand increases (the entire curve shifts right), the new equilibrium price rises. When a world price sits below the domestic equilibrium, quantity demanded at that price exceeds domestic supply, and the difference is imported.
Market equilibrium
The price-quantity pair where quantity demanded equals quantity supplied. No tendency for the price to change.
Think of it as the price the market settles at when nobody is interfering.
Excess demand (shortage)
When quantity demanded exceeds quantity supplied at a given price. Occurs when price is below equilibrium.
In simple terms, more people want to buy than sellers can provide.
Excess supply (surplus)
When quantity supplied exceeds quantity demanded at a given price. Occurs when price is above equilibrium.
Demand shift
A change in a non-price determinant (income, preferences, population, price of substitutes/complements) that moves the entire demand curve left or right. Not the same as a movement along the curve.
In simple terms, at every price, people now want more (rightward shift) or less (leftward shift) than before.
World price
The price at which a good trades on international markets. A small country takes this price as given.
Imports
The quantity of a good purchased from abroad. Equals domestic demand minus domestic supply at the world price, when the world price is below the domestic equilibrium price.
Think of it as the gap that foreign producers fill.
Given Q_D(P) = 3000 - 300P and Q_S(P) = 1900 + 200P:
Set demand equal to supply: 3000 - 300P = 1900 + 200P.
Collect terms: 1100 = 500P.
Solve: P* = 2.20.
To find equilibrium quantity, plug P* back into either function.
Suppose demand rises to Q_D(P) = 4000 - 300P (the intercept increases by 1000, shifting the curve right).
New equilibrium: 4000 - 300P = 1900 + 200P.
2100 = 500P, so P* = 4.20.
The equilibrium price rises from 2.20 to 4.20. Both price and quantity increase when demand shifts right along an upward-sloping supply curve.
Sometimes you are given a table of data or a description and must write out the algebraic functions yourself.
Q3 gives supply as Q_S(P) = -0.5 + 0.5P and demand as Q_D(P) = 45 - P.
Equilibrium: -0.5 + 0.5P = 45 - P. Solving gives P* = 30.33.
When a country opens to trade at a world price (here, P = 15):
Domestic demand at P = 15: Q_D(15) = 45 - 15 = 30.
Domestic supply at P = 15: Q_S(15) = -0.5 + 0.5(15) = 7.
Imports = demand - supply = 30 - 7 = 23 units.
The world price is well below the domestic equilibrium of 30.33, so domestic producers cannot serve the full market.
Equilibrium condition:
Q_D(P^*) = Q_S(P^*)For linear functions Q_D = a - bP and Q_S = c + dP:
P^* = \frac{a - c}{b + d}Import quantity when world price P_w is below domestic equilibrium:
\text{Imports} = Q_D(P_w) - Q_S(P_w)Every time a government debates a tariff or a trade deal, the import calculation above is precisely the framework being used. Domestic producers lobby for protection because they know imports fill the gap between what consumers want and what local firms supply at the world price.
Demand shifts matter for commodity markets: a population boom or rising incomes shifts demand right, pushing prices up and drawing in more supply.
Students confuse a shift of the demand curve (the whole function changes) with a movement along the curve (price changes within the same function). A shift changes the intercept; a movement changes the quantity at a new price on the same curve.
Students sometimes set demand equal to zero instead of equal to supply when finding equilibrium.
When calculating imports, students occasionally subtract in the wrong direction (supply minus demand). Imports = demand minus supply, because demand is the larger quantity at a below-equilibrium price.
Students forget that the supply function can produce negative values at very low prices. This does not mean supply is literally negative; it means the linear approximation breaks down below a certain price.
⚠️ "Solve for equilibrium" is a near-guaranteed question. Practise setting Q_D = Q_S and solving until it is automatic.
⚠️ When a demand shift is described in words (income rises, population grows), know which parameter changes and in which direction.
⚠️ Import questions test whether you can apply the equilibrium framework at a price that is not the equilibrium price.
True or False: A rightward shift in demand, with supply unchanged, raises both equilibrium price and quantity. (True.)
Fill in the blank: Imports equal ______ minus ______ at the world price. (Domestic demand minus domestic supply.)
True or False: If Q_D = 100 - 2P and Q_S = 20 + 3P, the equilibrium price is 16. (True: 100 - 2P = 20 + 3P gives 80 = 5P, P = 16.)
Fill in the blank: A change in consumer income shifts the demand ______, not a movement along it. (Curve.)
Q: Given Q_D(P) = 3000 - 300P and Q_S(P) = 1900 + 200P, find the equilibrium price.
A: Set 3000 - 300P = 1900 + 200P. This gives 1100 = 500P, so P* = 2.20.
Q: If demand shifts to Q_D(P) = 4000 - 300P with the same supply, what is the new equilibrium price?
A: 4000 - 300P = 1900 + 200P. This gives 2100 = 500P, so P* = 4.20.
Q: Domestic demand is Q_D(P) = 45 - P and domestic supply is Q_S(P) = -0.5 + 0.5P. The world price is 15. How many units are imported?
A: Q_D(15) = 30, Q_S(15) = 7. Imports = 30 - 7 = 23 units.
Q: Why does a negative intercept in a supply function not mean negative supply in practice?
A: A linear function is an approximation. Below a certain price, no firm would produce, so the approximation breaks down. Actual supply is zero at very low prices.
Equilibrium is the foundation for everything that follows: price controls, taxes, welfare analysis, and international trade all start from the baseline equilibrium and ask what happens when you disturb it. The import calculation connects directly to tariff and quota analysis. Demand shifts reappear in macroeconomics when studying aggregate demand.
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