Per-unit Taxes, Incidence, and Subsidies — Study Notes

Per-unit taxes, incidence, and subsidies — study notes

  • Per-unit taxes (examples mentioned)
    • 40¢ per unit on something (a per-unit tax).
    • $2 per unit tax example for gasoline referenced in the explanation.
    • $7 per car is another per-unit-style tax example (tax assessed per unit of a car, i.e., per car).
  • Key concept: a per-unit tax creates a gap t between what consumers pay and what sellers receive
    • Let the price paid by consumers be pd and the price received by sellers be ps.
    • The tax per unit is t, and the fundamental relation is
      pd - ps = t
    • If there is a tax on a good, the government collects revenue equal to the tax per unit times the quantity sold:
      R = t imes Q^ where Q^ is the equilibrium quantity after the tax.
  • How the tax is remitted (who pays the tax) affects which curve shifts
    • If the tax is remitted by the seller (the seller pays the tax to government), the supply curve shifts up by t.
    • If the tax is remitted by the buyer (the buyer bears the tax amount), the demand curve shifts down by t.
    • In either case, the post-tax market clears at a new equilibrium where the gap between consumer price and seller price is t, and the quantity is reduced relative to the pre-tax equilibrium.
  • Concrete numerical example (illustrative, follows the transcript’s numbers)
    • Initial (no tax) equilibrium: price p0 = 3 ext{,} ext{ quantity } Q0 = 6.
    • Tax per unit: t = 2.
    • Post-tax equilibrium (tax remitted by either side):
    • Price paid by consumers: p_d = 4
    • Price received by sellers: p_s = 2
    • Market quantity: Q^* = 4
    • Government tax revenue:
      R = t imes Q^* = 2 imes 4 = 8
    • Graphically, the tax revenue is represented as a rectangle with height t = 2 and base Q^* = 4, area = 8.
  • Different taxes and which party remits the tax
    • If a tax is paid by the buyer (e.g., a license tax on a used car transfer, like Ontario’s 75 transfer tax), the effect is to shift the demand curve downward by t.
    • If a tax is remitted by the seller (e.g., a grocery-store tax), the effect is to shift the supply curve upward by t.
    • In all cases, the tax creates a gap of size t between what consumers pay and what firms receive.
  • Substituting a tax with a subsidy (the reverse) and the equivalent price gap
    • A per-unit subsidy is the opposite of a tax: the government pays part of the cost, effectively raising the price to sellers relative to price to buyers.
    • In the subsidy setting, the price paid by consumers is typically lower than the price received by firms by the subsidy amount s:
      pd = ps - s ext{ or } ps = pd + s
    • Government must fund the subsidy; total cost to government is
      C = s imes Q^*
    • Example from transcript (education subsidy at a university):
    • Initial equilibrium (no subsidy): p0 = 3{,}000, Q0 = 6 (in course pricing terms).
    • Subsidy per course: s = 2{,}000 (government pays this amount per course).
    • New equilibrium with subsidy: price paid by students (consumers) is reduced, price received by the university (sellers) is higher, and quantity increases.
    • Post-subsidy example numbers: ps = 4{,}000 and pd = 2{,}000; quantity Q^* = 8.
    • Cost of subsidy: C = s imes Q^* = 2{,}000 imes 8 = 16{,}000
    • The economic effect can be visualized as a rectangle with height s = 2{,}000 and base Q^* = 8, area = 16{,}000.
  • Elasticity and tax/subsidy incidence
    • Elasticity matters for two reasons:
      1) How much revenue the government collects from a tax (tax incidence and revenue depend on elasticities of supply and demand).
      2) How the burden or benefit of the tax/subsidy is distributed between buyers and sellers (incidence).
    • Intuition: If demand is very inelastic (consumers respond little to price changes) and supply is elastic, buyers bear more of the tax; if supply is very inelastic and demand is elastic, sellers bear more of the tax.
    • The transcript emphasizes the following conventions:
    • When demand is inelastic and supply is elastic, consumers tend to bear a larger share of the tax burden.
    • When supply is inelastic and demand is elastic, producers tend to bear a larger share of the tax burden.
    • The general rule: the more inelastic side of the market bears the larger share of the tax burden.
    • Visualization aid from the transcript: two figures compare elasticity on the demand and supply sides, with one showing a flat (elastic) demand curve and a steep (inelastic) supply curve, and the other showing the opposite. The left scenario tends to shift more burden to sellers; the right scenario tends to shift more burden to buyers, depending on which side is more inelastic.
  • Incidence under elasticity in two-curve diagrams (summary from the transcript)
    • If demand is elastic and supply is inelastic, the tax burden tends to fall more on sellers (since sellers can’t adjust quantity much but consumers’ price sensitivity is high).
    • If demand is inelastic and supply is elastic, the tax burden tends to fall more on buyers (consumers bear most of the higher price due to inelastic demand).
    • The key phrase used: “If you’re slow to respond to price changes (inelastic), you pay most of the tax.”
    • The slogan-like intuition:
    • For a tax, the less responsive side pays more; for a subsidy, the outcome depends on which side is more elastic, influencing who benefits more.
  • Subsidies vs taxes: policy intuition and real-world examples
    • Subsidy benefits can be unevenly distributed depending on elasticity:
    • When supply is inelastic and demand is elastic, the subsidy largely benefits consumers (students) because the price they pay falls substantially while producers don’t gain much in price.
    • When supply is elastic and demand is inelastic, the subsidy largely benefits producers (universities) because the price they receive rises significantly with little reduction in quantity.
    • The transcript emphasizes the practical moral: subsidies are generally beneficial in policy arguments, whereas taxes are harmful or distortionary, but the distributional effects depend on elasticity and market structure.
    • Everyday example used in class discussions: education subsidies (e.g., tuition subsidies) and how they affect students versus universities.
    • Another analogy used: a bear vs. cookie analogy to describe taxes and subsidies behavior (tax as a bear that can “eat” the consumer’s breakfast if you hesitate; subsidy as a friendly cookie provider that you can take advantage of by “snoozing” and still gaining benefit).
  • Two related tax concepts mentioned
    • Sales tax: a tax applied at the point of sale, typically collected from the buyer by the seller; the tax revenue accrues to the government and depends on price and quantity; can be partly absorbed by buyers or sellers depending on elasticities.
    • Excise tax: a per-unit tax imposed on specific goods (often sin foods, tobacco, gasoline, etc.), usually intended to discourage consumption of those goods; closely tied to the per-unit tax analysis above.
  • What the math teaches about policy design
    • For unit taxes (or per-unit taxes), the incidence and revenue depend on elasticities, and it matters who remits the tax for the final price to consumers and price received by producers.
    • For unit subsidies, the cost to the government grows with how elastic both curves are; subsidies can be very expensive if both sides are highly elastic.
    • The same tax can be implemented in two ways (shift the supply curve or shift the demand curve) with the same post-tax gap, yet the distributional outcomes differ depending on which side is remitting the tax.
  • Practical considerations and reflections from the lecture
    • Policy relevance: sin taxes (liquor, cigarettes, gasoline) rely on inelastic demand to minimize quantity reductions while raising revenue; subsidies (e.g., education) can lead to large costs to the government if demand and supply are highly elastic.
    • The persistence of the lesson: elasticity matters for both revenue and burden sharing; different products have different elasticities, so the same tax or subsidy can have very different effects depending on the product.
    • The instructor’s practical tips for students (study habit and workload):
    • Treat University of Toronto as a full-time job when taking courses; for five courses, aim for about six hours per week per course (roughly 30 hours per week total).
    • Suggested study cadence: about one hour per course per day, plus additional time for assignments and posting in online forums.
    • Plan: rotate between courses to maintain steady study blocks (e.g., one hour on Course A, then one hour on Course B, etc.).
  • Quick reference formulas and concepts to memorize
    • Tax per unit: per-unit tax t
    • Price to consumers vs price to sellers: pd, ps with relation
      pd - ps = t
    • Government revenue from a unit tax:
      R = t imes Q^*
    • For subsidies with subsidy amount s: price relationship
      pd = ps - s ext{ or } ps = pd + s
    • Government cost of subsidy:
      C = s imes Q^*
    • Elasticity idea: the more inelastic the demand or supply, the more burden falls on that side for a tax; the more elastic the sides, the more distortion and lower revenue (for taxes) or higher cost (for subsidies).
  • Final takeaway themes
    • A unit tax creates a price gap but does not automatically determine who loses the most; the allocation of burden depends on elasticities.
    • The identical tax outcome (gap size) can have different incidence depending on whether the tax is remitted by sellers vs buyers.
    • Subsidies can yield large welfare gains for some groups but come with significant budget costs, especially when both sides are elastic.
    • Real-world examples (gasoline, cigarettes, education) illustrate how elasticity matters in policy design and revenue generation.
  • Quick study tips mentioned
    • Expect to answer questions that ask you to analyze who pays more under a unit tax or who benefits more under a subsidy by looking at elasticity (demand and supply).
    • Remember the two key roles elasticity plays in unit taxes/subsidies: (i) revenue potential for the government; (ii) distribution of burden/benefit between buyers and sellers.
    • Build intuition with simple numerical examples (like the 3–6–4–2–8 numbers above) to see how tax or subsidy shifts affect price, quantity, and revenue.
  • Closing note from the instructor
    • Practice the economic intuition and be ready to apply it to policy questions like why certain goods are taxed (or subsidized) and how the burden shifts with different elasticities; also be prepared to relate these ideas to ethical and practical implications in public policy.