Finding Equilibrium Price and Quantity with Linear Demand and Supply

In market equilibrium, consumer surplus is calculated as the area below the demand curve and above the equilibrium price (a triangle), while producer surplus is the area above the supply curve and below the equilibrium price (a trapezoid when the supply curve intersects the quantity axis); total surplus is the sum of both. For example, with demand Qd = 200 - 2P and supply Qs = 140 + 2P, equilibrium occurs at P = 20 and Q = 180, yielding consumer surplus of 16,200 and producer surplus of 3,200, for a total surplus of 19,400.

Consumer surplus (CS) is calculated as 1/2 × (maximum willingness to pay - equilibrium price) × equilibrium quantity. For this problem: CS = 1/2 × (100 - 73.33) × 53.33 = 711.81 triệu đồng. Producer surplus (PS) is calculated as 1/2 × (equilibrium price - minimum acceptable price) × equilibrium quantity: PS = 1/2 × (73.33 - 20) × 53.33 = 1,422.04 triệu đồng. Total social surplus equals CS + PS = 2,133.85 triệu đồng.

Consumer Surplus (CS) is the area above the equilibrium price and below the demand curve, representing the benefit consumers receive from paying less than their maximum willingness to pay. Producer Surplus (PS) is the area below the equilibrium price and above the supply curve, representing the benefit producers receive from receiving more than their minimum acceptable price. Total Social Welfare (NSB) equals CS + PS, representing the total benefit to society from market transactions.

Consumer surplus is the area between the demand curve and the equilibrium price, calculated as half the base times height (0.5 × equilibrium quantity × (maximum willingness to pay - equilibrium price)). Producer surplus is the area between the supply curve and the equilibrium price, calculated as half the base times height (0.5 × equilibrium quantity × (equilibrium price - minimum acceptable price)). Social welfare is the sum of consumer surplus and producer surplus, representing total economic welfare in the market.

Find equilibrium by setting supply equal to demand, solve for x (equilibrium quantity), substitute back to find equilibrium price. Consumer surplus = ∫₀^xg (D(x) - P(x)) dx. Producer surplus = ∫₀^xg (P(x) - S(x)) dx. These formulas calculate total economic welfare by integrating the difference between willingness to pay/receive and actual market price.

Government intervention through price controls can create significant market distortions. Price ceilings (maximum prices) set below equilibrium cause shortages as consumers demand more while producers supply less. Price floors (minimum prices) set above equilibrium cause surpluses as producers supply more while consumers demand less. Both interventions reduce total welfare by creating deadweight loss, where the market fails to produce the socially optimal quantity of goods and services.

This comprehensive section covers government interventions in markets. It begins with price floors and ceilings: binding floors (above equilibrium) create surplus; binding ceilings (below equilibrium) create shortage. The section then transitions to taxation theory, explaining that neither buyers nor sellers bear the entire tax burden—distribution depends on demand and supply elasticities. Perfectly elastic supply means sellers bear none; perfectly inelastic demand means consumers bear all. The mathematical framework involves finding equilibrium, imposing taxes on demand or supply, solving for new quantities and prices, and analyzing welfare effects. This establishes the analytical foundation for evaluating government policy interventions.

Price ceilings and floors have opposite price effects but similar quantity reductions—both lower equilibrium quantity and create deadweight loss. Price ceilings create shortages; price floors create surpluses. Quotas also lower quantities and raise prices. Consumer surplus decreases with price floors and quotas, while being ambiguous with price ceilings. Producer surplus decreases with price ceilings and is ambiguous with price floors. Governments implement these interventions to help specific groups despite efficiency losses.

Government interventions alter market outcomes through price controls and transfers. A price floor above equilibrium creates surplus, reduces quantity traded, and generates deadweight loss. A tax creates a wedge between consumer and producer prices, shifting demand downward. With equal elasticities, tax burden splits equally; government collects tax revenue equal to tax per unit times quantity traded. A subsidy shifts supply downward, increasing quantity traded. Consumers pay less, producers receive more, but government expenditure creates net cost. Deadweight loss occurs in all interventions as mutually beneficial trades are prevented. The burden distribution depends on relative elasticities: less elastic side bears more burden.

Government interventions in free markets include taxation (which shifts supply or demand curves and creates tax burdens shared between buyers and sellers based on elasticities), price ceilings (maximum prices that create shortages when binding and lie below equilibrium), and price floors (minimum prices that create surpluses when binding and lie above equilibrium); the effectiveness of these policies depends on whether they are binding relative to the market equilibrium price.

Price elasticity measures how responsive quantity is to price changes. For supply curves: steep (near vertical) curves are price inelastic (quantity doesn't change much with price), while flat (near horizontal) curves are price elastic (quantity changes significantly). A perfectly elastic supply curve is horizontal (완전 탄력), while a perfectly inelastic supply curve is vertical (완전 비탄력). The same principles apply to demand curves. When demand increases, the effect on equilibrium depends on supply elasticity: if supply is perfectly inelastic, price rises while quantity stays unchanged; if supply is perfectly elastic, price stays unchanged while quantity increases.

Elasticity measures responsiveness to price changes. Perfectly elastic demand/supply has horizontal curves (infinite responsiveness). Perfectly inelastic demand/supply has vertical curves (no responsiveness). Elastic demand/supply curves are downward/upward sloping. Elasticity determines how equilibrium price and quantity change when curves shift.

Price elasticity measures responsiveness to price changes: (1) Demand elasticity - when demand elasticity (absolute value) exceeds supply elasticity, the market tends toward equilibrium, (2) Supply elasticity - when supply curve slope is steeper than demand curve slope, the market exhibits different equilibrium characteristics. These concepts help predict market behavior and price movements.

The slope of the demand curve (ΔQ/ΔP) is inversely related to price elasticity. A flatter demand curve indicates lower slope and higher elasticity, meaning consumers are more responsive to price changes. A steeper demand curve indicates higher slope and lower elasticity, meaning consumers are less responsive to price changes. This relationship helps visualize how responsive demand is at different points along the curve.

Elasticity measures how one economic variable responds to changes in another, with price elasticity of demand calculated as the percentage change in quantity demanded divided by the percentage change in price (using the midpoint method to ensure direction invariance), and price elasticity of supply calculated similarly but without absolute value since price and quantity supplied move in the same direction; values greater than 1 indicate elastic responsiveness while values less than 1 indicate inelastic responsiveness.