Supply, Demand Curves and Price Elasticity

How Shapes of Supply and Demand Curves Matter

• Shapes of supply and demand curves dictate a shock's effect on equilibrium price and quantity.
• The supply of avocados is contingent on the price of avocados and fertilizer costs.
• Fertilizer is a major input in avocado production.
• An increase in fertilizer prices shifts the avocado supply curve leftward.
• The impact on equilibrium price/quantity depends on the demand curve's shape.

Sensitivity of Quantity Demanded to Price

• Knowing how much quantity demanded falls as the price increases is important in predicting the effect of a shock in a supply and demand model.
• Elasticity is the percentage change in one variable responding to a percentage change in another.
• Price elasticity of demand (ε) is the percentage change in quantity demanded, given percentage change in price, at a point on the demand curve.
• Formally, ε = (%ΔQ/%Δp) = (ΔQ/Q) / (Δp/p) = (ΔQ/Δp) * (p/Q), where Δ signifies change.
• Example: A 1% increase in price leads to a 3% decrease in quantity demanded; the elasticity of demand is e = -3%/1% = -3.
• Along a linear demand curve, given Q = a - bp, then -b is the ratio of fall in quantity to the rise in price: -b = ΔQ/Δp.
• Elasticity of demand = ε = (ΔQ/Δp) * (p/Q) = -b(p/Q).
• Categories of elasticity include relative elasticity (|Ep| > 1), relative inelasticity (0 < |Ep| < 1), and unitary elasticity (|Ep| = 1).
• Extreme cases are perfect elasticity (|Ep| = ∞) and perfect inelasticity (|Ep| = 0).
• Estimated demand curve for U.S. corn is Q = 15.6 - 0.5p, where Q is quantity in billion bushels/year, p is price in dollars/bushel.
• To find elasticity of demand at p = $7.20 per bushel: Substitute b, p, Q (where Q = 12) into the elasticity equation.
• Elasticity of demand at this point is ε = -b(p/Q) = -0.5 * (7.20/12) = -0.3.
• Elasticity of demand varies along most demand curves and is different at every point along a downward-sloping linear demand curve.
• Elasticities are constant along horizontal and vertical linear demand curves.
• Along a horizontal demand curve (perfectly elastic demand), elasticity is infinite, people are willing to buy at any price less than or equal to p*.
• If the price increases even slightly above p*, demand falls to zero.
• A small increase in price equals an infinite drop in quantity demanded along a horizontal demand curve.
• Along a vertical demand curve, elasticity is zero, which equals perfectly inelastic demand.
• If the price goes up, the quantity demanded is unchanged with perfectly inelastic demand.
• A demand curve is vertical for essential goods that people feel they must have and will pay anything to get.
• A diabetic's demand curve for insulin is perfectly inelastic below p* and perfectly elastic at p*, which is the maximum price the individual can afford to pay.
• A diabetic cannot afford to pay more than p*, and they buy nothing at higher prices.
• A diabetic's demand curve is perfectly elastic up to Q* units at a price of p*.
• Any shock that changes the equilibrium price will affect an industry's revenue.
• If revenue rises or falls when equilibrium price rises is determined by the elasticity of demand.
• With elastic demand, a higher price reduces revenue, and the opposite happens with inelastic demand.

Demand Elasticities Over Time

• Demand elasticities can vary between the short-run and long-run.
• The difference depends on substitution and storage opportunities.
• Elasticities for most goods tend to be larger in the long run.
• For easily storable or durable goods, the reverse is true:
• Coffee: short run is -0.2, long run is -0.33.
• Kitchen and household appliances: -0.63
• Meals at restaurants are at -2.27
• Airline travel in the US equals -1.98
• U.S. oil demand: short run is -.06, long run is -0.45.

Other Elasticities

• Income elasticity measures the percentage change in quantity given percentage change in income.
• Formally, ε = (%ΔQ/%ΔY) = (ΔQ/Q)/(ΔY/Y) = (ΔQ/ΔY) * (Y/Q), where Y stands for income.
• Example: A 1% increase in income leads to a 3% increase in quantity demanded, the income elasticity of demand is x = 3%/1% = 3.
• There are three situations relating to income elasticity of demand, quantity demanded of the product increases as income rises, indicating a positive income elasticity of demand and thus a normal good.
• As income rises, the quantity demanded of the product remains unchanged and the income elasticity of demand is equal to zero.
• The quantity demanded decreases as income rises, thus illustrating negative income elasticity of demand and an inferior good.
• Treating children as a consumption good finds that its income elasticity is negative yet close to zero.
• Number of children demanded is not very sensitive to income.
• The estimated demand function for avocados is Q = 104 - 40p + 20pt + 0.01Y.
• The quantity is measured in millions of lbs/month, avocado and tomato prices in dollars/lb, and average monthly income in dollars.
• Cross-price elasticity considers the effects on the quantity of one product given the changing price of another.
• Formally: (%ΔQ/%Δpo) = (ΔQ/Q) / (Δpo/po) = (ΔQ/Δpo) * (po/Q), where po is the price of another good.
• Example: A 1% increase in the price of a related good results in a 3% decrease in quantity demanded, the cross-price elasticity of demand is = -3%/1% = -3.
• If cross-price elasticity is negative, goods are considered complements.
• If the cross-price elasticity is positive, goods are substitute.
• Ex > 0: Increasing the iPhone X price leads to increase in quantity demanded for Samsung S11; a substitution effect occurs.
• Ex = 0: Increasing the iPhone price leads to no changes in quantity demanded of Lamb Doner, which are unrelated goods.
• Ex 0.5 (in absolute value).
• The estimated demand function for avocados is Q = 104 - 40p + 20pt + 0.01Y.

Sensitivity of Quantity Supplied to Price

• Elasticity of supply is similar to demand, but considers how much supply changes with price.
• Formally, η = (%ΔQ/%Δp) = (ΔQ/Q) / (Δp/p) = (ΔQ/Δp) * (p/Q), Q= quantity supplied.
• A 1% increase in price results in a 2% increase in quantity supplied, the elasticity of supply is η = 2%/1% = 2.
• Along a linear supply curve Q = g + hp, h is the slope or h = ΔQ/Δp.
• The elasticity of supply is η = (ΔQ/Δp) * (p/Q) = h*(p/Q).
• Estimated function for corn = Q = 10.2 + 0.25p.
• Q is quantity of corn supplied in billion bushels per year and p is the price of corn in dollars per bushel.
• If p = $7.20 and Q = 12, the elasticity of supply is: η = (ΔQ/Δp) * (p/Q) = 0.25 * (7.20/12) = 0.15.
• Supply elasticities may differ in the short-run and the long-run depending on the ability to convert fixed inputs into variable inputs.
• Firms' long-run supply elasticity is generally greater than short-run elasticity.

Effects of a Sales Tax

• Sales taxes affect equilibrium prices and quantity as well as tax revenue.
• Equilibrium price and quantity do not depened on whether the government collects a specific tax from the suppliers or their customers.
• Producers dont paass along to customers any taxes collected from producers, that is, do consumers pay the entire tax?
• Comparable ad valorem and specific taxes does not have equivalent effects on equilibrium prices and quantities and on tax revenue.
• An ad valorem tax is for every dollar the consumer spends, and the government keeps a fraction, a, which is the ad valorem tax rate.
• A specific tax (or unit tax) is where a specified dollar amount, t, is collected per unit of output.
• If the government sets a new specific tax of t and raises the tax from 0 to t, so the change in the tax is At = t - 0 = t.
• The incidence of a tax on consumers is the share of the tax that consumers pay.
• Incidence of the tax that falls on consumers is Δp/Δt, the amount by which the price to consumers rises as a fraction of amount tax increases.
• Tax incidence on customers depends on the elasticities of supply and demand.
• Price customers pay increases by Δp = (η/(η-ε))Δt.
• If ε = -0.3 and η = 0.15, a change of a tax of Δt = $2.40 causes the price buyers pay to rise by Δp = (η/(η-ε))Δt = (0.15/(0.15−[-0.3])) * $2.40 = 80¢.
• The incidence of tax that consumers pay = Δp/Δt = η/(η-ε).
• The incidence of the corn tax on consumers = 0.15/.15−[−0.3] =1/3.