Assuming a unitary elastic demand and supply, a tax on the sellers of coffee:

Question

BlackTom AI · Accepted Answer

With unitary (elasticity = 1) demand and unitary supply, a per‑unit tax imposed on sellers reduces the equilibrium quantity traded.

1) Relevant knowledge points and concepts
- Price elasticity of demand/supply measures percent change in quantity for a 1% change in price.
- Tax incidence depends on relative elasticities: the more inelastic side bears more of the tax.
- A per‑unit tax on sellers shifts the supply curve upward (or, equivalently, reduces the price sellers receive by the tax) and generally reduces equilibrium quantity unless one side is perfectly elastic or perfectly inelastic in special ways.

2) Step‑by‑step reasoning
- Represent unitary demand and supply with simple functional forms: demand Q = A / Pb (elasticity −1 with respect to buyer price Pb), supply Q = B · Ps (elasticity +1 with respect to seller price Ps).
- Before tax equilibrium: A / P* = B · P* → A = B · P*^2 → P* = sqrt(A/B), Q* = sqrt(A·B).
- Introduce a per‑unit tax t on sellers: sellers receive Ps = Pb − t. New equilibrium satisfies A / Pb = B · (Pb − t).

3) Calculations (intermediate steps)
- Solve A / Pb = B(Pb − t) → A = B · Pb · (Pb − t) = B(Pb^2 − t Pb).
- Rearranged quadratic: B Pb^2 − B t Pb − A = 0. The positive root gives Pb (buyers’ price) after tax.
- Numerical example: pick A = 100, B = 1, t = 2.
  - Before tax: P* = sqrt(100/1) = 10, Q* = 10.
  - After tax: Pb^2 − 2 Pb − 100 = 0 → Pb = [2 + sqrt(4 + 400)]/2 = (2 + 20.099)/2 ≈ 11.0495.
  - Sellers receive Ps = Pb − t = 11.0495 − 2 = 9.0495.
  - New quantity Q = A / Pb = 100 / 11.0495 ≈ 9.0495 < 10, so quantity falls.

4) Why the correct answer is correct
- The tax shifts supply, raising the price buyers pay and lowering the net price sellers receive; with unitary elasticities, quantity must fall because both sides respond proportionally to price changes. The numeric example shows quantity decreases from 10 to ≈9.05.

5) Why other options are incorrect
- “Increases the size of the coffee market”: wrong — taxes reduce supply (or effective supply) so quantity falls, not rises.
- “Has no effect on the size of the coffee market”: wrong — only specific extreme elasticities (perfectly elastic/inelastic combinations) could leave quantity unchanged; unitary elasticities do not.
- “Will be paid entirely by sellers of coffee”: wrong — incidence splits according to elasticities; with equal elasticities the burden is shared (approximately equally), not entirely on sellers.

6) Conclusion
The analysis and calculations show the tax reduces the equilibrium quantity traded, confirming the correct answer: decreases the size of the coffee market.

Assuming a unitary elastic demand and supply, a tax on the sellers of coffee:单项选择题

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