Finding Equilibrium Price and Quantity from Demand & Supply Functions

This section explains how changes in non-price determinants shift the entire demand and supply curves. For demand, changes in consumer income, prices of related goods, or other factors shift the demand curve left or right. An increase in income shifts demand right (outward), while a decrease shifts it left. Similarly, changes in input prices or prices of related goods shift the supply curve. The instructor demonstrates this with examples: increasing income from 1000 to 1200 shifts the demand curve from Qd = -2Px + 38 to Qd = -2Px + 48. These shifts represent changes in demand or supply, not movements along the curve. Understanding curve shifts is essential for analyzing how external factors affect market equilibrium.

Changes in non-price factors shift curves: demand increases (right shift) raise both price and quantity; demand decreases (left shift) lower both. Supply increases (right shift) lower price and raise quantity; supply decreases (left shift) raise price and lower quantity. These shifts represent changes in factors other than price, such as consumer income, production costs, or technology.

Demand curve shifts occur when non-price factors change: changes in consumer income, prices of related goods (substitutes and complements), tastes and preferences, or number of buyers. Supply curve shifts occur when non-price factors change: prices of inputs, technology, number of sellers, or expectations. Price changes cause movements along the curve, not shifts. Understanding these distinctions is crucial for analyzing market dynamics.

Changes in the price of a product only cause movement along the respective curve (change in quantity supplied/demanded), not a shift of the entire curve. Non-price factors cause shifts: For supply, these include taxes, input costs, technology, and number of sellers. For demand, these include consumer income, prices of related goods (substitutes and complements), tastes, expectations, and number of buyers. For example, taxes increase production costs, shifting supply left. Income increases shift demand right for normal goods but left for inferior goods. This distinction between 'change in quantity' and 'change in supply/demand' is fundamental to understanding market mechanics.

Equilibrium changes when supply or demand curves shift. Demand shifts when non-price determinants change: income, tastes, expectations, prices of substitutes/complements, or number of buyers. Supply shifts when input costs, technology, expectations, or number of sellers change. The direction of the shift (left/right) determines whether equilibrium price and quantity increase or decrease.

Governments intervene through price controls and fiscal policies. Price ceiling (harga tertinggi) sets maximum prices to protect consumers. Price floor (harga terendah) sets minimum prices to protect producers. Tax increases effective price sellers receive, reducing quantity supplied (QS = a + b(P - t)). Subsidy decreases effective price sellers receive, increasing quantity supplied (QS = a + b(P + s)). To find equilibrium, set Qd = Qs and solve algebraically. With Qd = 15 - P and Qs = 2P - 6, equilibrium is P = 7, Q = 8. With tax of 9 per unit, equilibrium becomes P = 13, Q = 2. With subsidy of 9 per unit, equilibrium becomes P = 1, Q = 14. These examples demonstrate how to calculate equilibrium with and without government interventions.

Price controls create market distortions: price ceilings below equilibrium cause shortages, while price floors above equilibrium cause surpluses. Tax incidence depends on relative elasticities - the more inelastic side bears more burden. Subsidies increase quantity transacted and reduce consumer prices while increasing producer prices. Both taxes and subsidies create deadweight loss. Extreme elasticity cases show one side bearing entire burden: perfectly elastic demand means consumers pay all taxes; perfectly inelastic demand means consumers bear all burden.

Government interventions in markets, including taxes, subsidies, price ceilings, and price floors, shift supply and demand curves to influence market equilibrium; taxes reduce demand when borne by consumers or supply when borne by producers, subsidies increase supply when given to producers or demand when given to consumers, price ceilings create shortages when set below equilibrium and require supply increases or demand reductions to restore equilibrium, while price floors create surpluses when set above equilibrium and require supply reductions or demand increases to achieve new equilibrium.

This section covers government interventions in markets. Price ceilings are maximum prices set below equilibrium to protect consumers, creating shortages when binding. Price floors are minimum prices set above equilibrium to protect producers, creating surpluses when binding. Tax incidence determines who ultimately bears the tax burden, which depends on relative elasticities of supply and demand: if demand is more elastic, buyers bear more burden; if supply is more elastic, sellers bear more burden. Subsidies are government payments to producers that increase supply, with benefit distribution depending on elasticities similar to taxes. When demand is perfectly elastic or supply is perfectly inelastic, one party bears the entire burden.

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.

To find market equilibrium in non-linear models, set the demand function equal to the supply function and solve for price; for example, given demand Qd = 4 - P² and supply Qs = 4P - 1, setting 4 - P² = 4P - 1 yields the quadratic equation P² + 4P - 5 = 0, which factors to (P + 5)(P - 1) = 0, giving P = 1 as the economically meaningful equilibrium price (rejecting the negative root), and substituting P = 1 into either function gives the equilibrium quantity Q = 3.

Market equilibrium occurs when quantity demanded equals quantity supplied (qd = qs), represented by the intersection of demand and supply curves. For non-linear functions, equilibrium is found by setting the demand function equal to the supply function and solving for the equilibrium price and quantity. In the example provided, with demand function qd = 19 - P² and supply function qs = -8 + 2P², solving 19 - P² = -8 + 2P² yields P = 3 (equilibrium price) and Q = 10 (equilibrium quantity).

To find the equilibrium point in a nonlinear supply and demand system, set the supply equation equal to the demand equation and solve for quantity (x), then substitute back to find the equilibrium price; discard any negative quantity solutions as they are economically meaningless.

In non-linear market models, equilibrium price and quantity are found by setting the demand function equal to the supply function and solving the resulting equation, which may require quadratic formula methods when the relationship between price and quantity is non-linear.

To find market equilibrium mathematically, set the supply function equal to the demand function and solve algebraically. Given Qs = 150p - 300 and Qd = 62,700 - 300p, setting them equal gives 150p - 300 = 62,700 - 300p. Solving yields 450p = 63,000, so p = 140. Substituting back into either function gives Q = 20,700. This systematic approach ensures accurate determination of equilibrium conditions.

Market equilibrium occurs when quantity supplied equals quantity demanded (QS = QD), or when price supplied equals price demanded (PS = PD). At equilibrium, the equilibrium price (P0) and quantity (Q0) are determined where supply and demand curves intersect. Price elasticity of demand (Ed) measures responsiveness of quantity demanded to price changes, calculated as Ed = (dQ/dP) × (P/Q). For linear demand Q = a - bP, Ed = -bP/Q. The absolute value determines elasticity: |Ed| > 1 indicates elastic demand, |Ed| < 1 indicates inelastic demand.

To find equilibrium price and quantity, set the quantity demanded equation equal to the quantity supplied equation and solve for price; then substitute the equilibrium price back into either equation to find the equilibrium quantity. For example, with Qd = 16 - P and Qs = -4 + P, setting them equal gives P = 10, and substituting back yields Q = 6.

Price elasticity of demand (Ep) is calculated using the formula Ep = (dq/dp) × (p/q), where dq/dp is the derivative of the demand function with respect to price, p is the initial price, and q is the initial quantity demanded; for the demand function q = 200 - 5p at p = 20, the derivative dq/dp = -5, the initial quantity q = 100, resulting in Ep = (-5) × (20/100) = -1, indicating unitary elasticity.

Price elasticity of demand is the degree of response of demand to price changes. To find equilibrium price, use the elasticity formula: percentage change in quantity divided by percentage change in price. The equilibrium price is where quantity demanded equals quantity supplied. Price elasticity of supply measures how supply responds to price changes. When elasticity equals +1, supply is unit elastic (عرض متكافئ المرونه). To graph equilibrium, plot the equilibrium price on the vertical axis and equilibrium quantity on the horizontal axis. Demand curves slope downward, while supply curves slope upward.

Point price elasticity of demand measures the responsiveness of quantity demanded to price at a specific point on the demand curve, calculated using the formula (P/Q) × (∆Q/∆P), where ∆Q/∆P is derived from the demand function's slope coefficient; for example, with demand function Q = 15,000 - 50P, at P = 100 and Q = 10,000, the elasticity equals (100/10,000) × (-50) = -0.5, indicating inelastic demand, while at P = 10 and Q = 14,500, it equals approximately -0.034, showing more inelastic demand at lower prices.