Elasticity, Price Controls, and Taxes

Elasticity recap

  • Elasticity is the sensitivity of one variable to changes in another variable. It answers: what is the percentage change in Y when X changes by 1%?
  • Formal ways to write elasticity:
    • Point/price elasticity of Y with respect to X: EY,X=∂Y∂X⋅XYE_{Y,X} = \frac{\partial Y}{\partial X}\cdot \frac{X}{Y}
    • Approximate percent-change form: EY,X≈ΔY/YΔX/XE_{Y,X} \approx \frac{\Delta Y / Y}{\Delta X / X}
  • Uses: price elasticity of demand, price elasticity of supply, income elasticity, etc.
  • Conceptual takeaway: elasticity is the mechanism by which one variable responds to changes in another; higher elasticity means greater responsiveness.

Government policies as market shocks

  • Policies discussed as shocks that alter private market equilibrium.
  • Two policies covered in this session:
    • Price controls (price ceilings and price floors)
    • Taxes (and tax incidence)
  • Key teaching: before predicting outcomes, determine if the policy is binding or non-binding (i.e., whether it actually changes the market outcome).

Price ceilings

  • Definition: a maximum price that cannot be charged above.
  • Binding vs non-binding:
    • If the ceiling is above the market equilibrium price, it is non-binding and does not change the outcome.
    • If the ceiling is below the market equilibrium price, it is binding and creates distortions (typically shortages).
Apartment market example (price ceiling)
  • Given: equilibrium price $P^* = 800$, equilibrium quantity $Q^* = 300$ apartments.
  • Ceiling: price ceiling set at $1000 (above $P^*$). Is it binding?
    • Non-binding, since the market price is already $800; quantity remains 300.
  • Visual logic: price ceiling drawn as a horizontal line at $1000; it touches the supply/demand at the existing equilibrium, no distortion.
What happens when a binding price ceiling is set below equilibrium?
  • Suppose ceiling is $500 (below the $800 equilibrium).
  • The analysis proceeds by tracing from the ceiling price to the supply curve to find $Qs$ (quantity supplied) and to the demand curve to find $Qd$ (quantity demanded).
  • Outcome: $Qd > Qs$ -> shortage.
  • Short-run vs long-run shortages (apartment example):
    • Short run shortage: e.g., 160 units.
    • Long run shortage: shortage grows to 300 units because supply and demand become more elastic in the long run (curves flatter, closer to horizontal).
  • Intuition: shortages require rationing; possible long lines and discrimination by sellers; this can be unfair and inefficient because the goods may not go to those who value them most.
  • Efficiency intuition: binding ceilings can misallocate to buyers who do not value the good the most.
  • Conceptual question from the lecture: which buyers along the demand curve value apartments the most (Area A vs Area B)? Area A (higher value) would be the ones who would pay more; price ceilings can cause misallocation away from those who value the good most.
  • Note on long-run dynamics: higher elasticity in the long run magnifies shortages because quantities adjust more.
Non-analytic notes on price ceilings in practice
  • Price controls are not inherently good or bad; their desirability depends on the market and context.
  • Real-world examples and debates include rent controls (e.g., some cities) and price controls on money (central banks influence interest rates).
  • The broader economics view: governments sometimes intervene to improve outcomes or provide justice (e.g., housing subsidies, wage subsidies) rather than pursuing pure efficiency.

Price floors (minimum prices)

  • Definition: a minimum price set by the government.
  • Binding vs non-binding:
    • If the minimum (price floor) is below the equilibrium price, it is non-binding; nothing changes.
    • If the minimum is above the equilibrium price, it is binding and causes a surplus.
Unskilled labor market example (minimum wage)
  • Baseline market: equilibrium wage $W^* = 6$ (per hour); quantity $Q^* = 500$ workers.
  • Price floor below equilibrium (e.g., $5.50): non-binding; no effect.
  • Price floor above equilibrium (minimum wage): binding; creates unemployment (labor surplus).
  • Intuition: a higher minimum wage means more workers willing to work than firms are willing to hire at that wage; unemployment occurs.
  • Economic controversy: wage policies are highly debated and context-dependent; in the US, minimum wage levels vary (e.g., California around $20/hour; in other countries, a larger share of workers may earn minimum wage). The policy’s employment effects are not uniform and depend on market power and elasticity.
  • The lecture highlights that the predictive claim that a higher minimum wage always reduces employment is not universally true; outcomes depend on market structure and elasticity.
Real-world caveats and policy nuance
  • Even if a binding floor reduces employment in some markets, it may be justified by equity or other social goals in different markets.
  • The discussion emphasizes that policy design should consider elasticity and market power.

Price controls in practice: diversity of examples

  • Tariffs as price controls (a form of policy that raises price and reduces imports; treated separately as a tax-like policy).
  • Agricultural price floors (minimum prices for agricultural products in some regions).
  • Essential medicines and subsidies (government support can take forms other than price controls, like subsidies or insurance).
  • Rent controls and housing policy (historical examples in cities like San Francisco show complexities and inefficiencies under binding ceilings).
  • Money and interest rates: central banks influence the price of money (the interest rate); this is a price control of a key aggregate in the economy.
  • Overall takeaway: price controls are tools; their desirability depends on context, and they interact with elasticity and market power.

Taxes

  • Taxes are distortionary because they change prices and thus quantities sold and bought.
  • Rationale: governments tax to fund public goods and services (hospitals, roads, defense, schools) that the private market may underprovide.
  • Tax incidence: who actually bears the tax burden (consumers vs. producers). Incidence depends on relative elasticities of demand and supply, not on whether the tax is levied on buyers or sellers.
  • The tax burden total is the tax wedge: the difference between price paid by buyers and price received by sellers equals the tax amount.
  • Graphical intuition: a tax creates a wedge between buyers’ price and sellers’ price; the distance between pb (price buyers pay) and ps (price sellers receive) equals the tax t: pb − ps = t.
Pizza market example (tax on buyers)
  • Baseline equilibrium without tax: price $P^* = 10$, quantity $Q^* = 500$ pizzas.
  • Government imposes a tax of $t = 1.50$ per pizza on buyers.
  • Demand shifts left (to reflect higher price for consumers): new equilibrium with buyers paying $Pb = 11$ and sellers receiving $Ps = 9.50$.
  • Tax wedge: $Pb - Ps = 11 - 9.50 = 1.50 = t$.
  • Incidence components:
    • Buyers’ burden: $P_b - P^* = 11 - 10 = 1.00$
    • Sellers’ burden: $P^* - P_s = 10 - 9.50 = 0.50$
  • Total tax collected = $t \times Q$; new quantity is determined by the intersection of the new demand with supply (unchanged). The distribution of the burden depends on elasticities; more elastic sides bear a smaller share of the tax.
  • Important point: placing the tax on buyers or on sellers yields the same market outcome for price to buyers, price to sellers, and quantity, because the wedge is the same and incidence redistributes depending on elasticities.
Hotel rooms example (tax on buyers; $30 per room)
  • Market characteristics: higher elasticity on the demand side than the supply side in this example (buyers are more elastic).
  • Tax on buyers: $t = 30$.
  • New equilibrium: buyers pay $Pb = 110$, sellers receive $Ps = 80$, quantity $Q = 80$ rooms.
  • Tax wedge: $Pb - Ps = 110 - 80 = 30 = t$.
  • Tax incidence calculation:
    • Buyers’ burden: $P_b - P^* = 110 - 100 = 10$
    • Sellers’ burden: $P^* - P_s = 100 - 80 = 20$
  • Incidence shares (relative): buyers bear 1/3 of the tax, sellers bear 2/3 of the tax.
  • Intuition: because demand is more elastic, buyers cannot easily avoid the tax by changing behavior other than reducing quantity demanded; but the less elastic side (supply) bears more of the burden, consistent with the general rule that the burden falls more on the side that is less elastic.
  • Summary of incidence rule: the distribution of tax burden depends on elasticities; the side with the greater elasticity bears a smaller share of the tax burden.

Practical exam insights and study tips

  • When faced with any price control question, always start by asking: Is the policy binding or non-binding?
    • If non-binding: market outcomes unchanged.
    • If binding: determine the new quantities by tracing the price line to supply and demand; identify shortages (ceilings) or surpluses (floors).
  • For taxes: identify the tax wedge and compute how much of the tax is borne by buyers and sellers using the baseline price and the new pb and ps after tax.
  • Use elasticity intuition to explain tax incidence rather than simply plugging numbers:
    • More elastic side bears less of the tax burden.
    • More inelastic side bears more burden.
  • Real-world policy nuance: price controls can be justified for equity or other social goals; their efficiency effects depend on market conditions and elasticity.
  • Key takeaway: taxes and price controls are tools with distributional and efficiency effects; understanding binding vs non-binding and elasticity is essential to predict outcomes.

Quick recap of the core ideas

  • Elasticity measures responsiveness; used to interpret how one variable responds to changes in another.
  • Price ceilings can create shortages if binding; price floors can create surpluses/unemployment if binding.
  • In practice, always check bindingness first, then determine resulting quantities and any shortages/surpluses.
  • Taxes create a wedge between price paid by buyers and price received by sellers; the tax incidence depends on relative elasticities rather than on who is legally taxed.
  • The same tax can be levied on buyers or sellers with the same market outcomes for price and quantity, but the distribution of burden changes with elasticities.
  • In all policy questions, consider both efficiency and equity implications, and the specific market context (elasticities, market power, substitutes).