4 Applications of Equilibrium and Elasticity

Shifts and market equilibrium

A change in a good’s own price causes a movement along its demand or supply curve. A change in another factor—such as income, input costs, technology, or the number of buyers—can shift a curve.

To analyze a market event:

1. Identify the market and its initial equilibrium.

2. Decide whether the event affects demand, supply, or both.

3. Determine whether each affected curve shifts left, decreasing, or right, increasing.

4. Compare the new equilibrium price and quantity with the original ones.

For example, frost that damages a coffee crop reduces supply and shifts the supply curve left. If demand is unchanged, the new equilibrium has a higher price and lower quantity. The size of each change depends partly on the curves’ elasticities. If coffee demand is inelastic, consumers reduce purchases relatively little as price rises, so more of the adjustment appears as a higher price.

At a price above Equilibrium, quantity supplied exceeds quantity demanded, creating a Surplus. At a price below Equilibrium, quantity demanded exceeds quantity supplied, creating a Shortage. Unless a binding restriction prevents adjustment, these imbalances create pressure for price to move toward equilibrium.

Elasticity and seller revenue

Price elasticity measures how responsive quantity demanded or supplied is to a price change. In absolute value, demand is elastic when quantity responds proportionally more than price, inelastic when it responds proportionally less, and unit elastic when the percentage responses are equal.

A seller’s Total revenue is calculated as:

The relationship between demand elasticity and revenue gives these predictions:

• With elastic demand, a price increase tends to reduce total revenue, while a price cut tends to raise it.

• With inelastic demand, a price increase tends to raise total revenue, while a price cut tends to reduce it.

• With unit-elastic demand, a modest price change leaves total revenue roughly unchanged.

For example, if a café raises a meal’s price by $5\%$ and quantity sold falls by $10\%$, revenue falls because the decrease in sales volume outweighs the higher price. If quantity sold falls by only $2\%$, revenue rises. These predictions apply to the relevant range of the demand curve; elasticity can vary at different prices.

A supply increase, such as one resulting from a more efficient production method, generally lowers equilibrium price and raises quantity. If demand is inelastic, the price decline can be proportionally larger than the quantity increase, so sellers’ total revenue may fall. Thus, a larger harvest does not necessarily mean higher total revenue for farmers.

Taxes and who bears them

A per-unit tax creates a gap, or wedge, between the price buyers pay and the amount sellers keep. It can be represented as a leftward shift in supply: at each buyer price, sellers need a higher price to cover the tax. Compared with the no-tax equilibrium, the usual results are a higher price for buyers, a lower price received by sellers, and a lower quantity traded.

The party legally required to send the tax payment to the government does not necessarily bear most of its economic cost. Tax incidence depends on the relative elasticities of demand and supply. The less responsive, more inelastic side generally bears more of the burden because it has fewer ways to avoid the tax. If demand is relatively inelastic, buyers tend to bear more; if supply is relatively inelastic, sellers tend to bear more.

Tax revenue is calculated using the quantity sold after the tax:

For example, a tax of $\$2$ per unit with $1{,}000$ units sold raises $\$2{,}000$. If the tax reduces sales to $700$ units, revenue is $\$1{,}400$. More elastic demand or supply usually means quantity responds more strongly to the tax, limiting the amount sold and potentially lowering revenue. A tax can therefore raise revenue while also changing market behavior.

Price controls and market imbalances

A Price ceiling is a legal maximum price. It affects the market only when set below equilibrium, making it binding. At that lower price, buyers want more than sellers offer, so a shortage results. Rent limits can illustrate this: if controlled rent is below the price that would balance the market, more people may seek housing while fewer units are offered for rent.

A Price floor is a legal minimum price. It is binding when set above equilibrium. At that higher price, sellers want to offer more than buyers want to purchase, so a surplus results. A supported crop price above equilibrium can leave some output unsold unless another buyer, such as the government, purchases it.

Controls set on the other side of equilibrium are nonbinding and do not change the market outcome: a ceiling above equilibrium does not hold price down, and a floor below equilibrium does not hold it up. When a control is binding, the number of trades is limited by the short side of the market: quantity supplied under a binding ceiling or quantity demanded under a binding floor. As a result, some buyers or sellers cannot complete trades they would have made at the equilibrium price.

Elasticity helps assess the scale of these effects. If buyers or sellers respond strongly to price changes, a binding control can create a larger gap between quantity demanded and quantity supplied. The exact outcome also depends on shifts in demand and supply. For example, rising demand under an unchanged binding rent ceiling increases the shortage.