Assuming a unitary elastic demand and supply, a tax on the sellers of coffee will
[ Select ]
increase
decrease
have no effect on
would either increase or decrease
the equilibrium price of coffee and
[ Select ]
increase
decrease
have no effect on
would either increase or decrease
the equilibrium quantity of coffee.

Question

Assuming a unitary elastic demand and supply, a tax on the sellers of coffee will 
[ Select ]
increase
decrease
have no effect on
would either increase or decrease
 the equilibrium price of coffee and 
[ Select ]
increase
decrease
have no effect on
would either increase or decrease
 the equilibrium quantity of coffee.

BlackTom AI · Accepted Answer

With unitary elasticities (|elasticity| = 1) the percentage change in quantity equals the percentage change in price for both demand and supply. This property determines how a per-unit tax imposed on sellers is absorbed between price and quantity.

1) Relevant concepts
- Price elasticity of demand (Ed) = percent change in Qd / percent change in P. Unitary demand means Ed = −1 (a 1% rise in price → 1% fall in quantity).
- Price elasticity of supply (Es) = percent change in Qs / percent change in P. Unitary supply means Es = +1.
- A per-unit tax on sellers creates a vertical upward shift (by the tax amount) in the supply schedule measured at buyers’ prices; equilibrium is given by Qd(Pb) = Qs(Ps) with Ps = Pb − t.

2) Step-by-step reasoning
Start with general constant-elasticity forms that capture unitary behavior:
- Demand: Qd = A · P_b^(−1)  (so elasticity −1)
- Supply: Qs = B · P_s^(+1)  (so elasticity +1)
With no tax, equilibrium: A/P* = B·P* → P* = sqrt(A/B).
Introduce a per-unit tax t on sellers so sellers’ net price is P_s = P_b − t. New equilibrium solves A/P_b = B·(P_b − t).

3) Intermediate algebra and intuition
Multiplying through: A = B·P_b·(P_b − t) → B·P_b^2 − B·t·P_b − A = 0.
This quadratic determines P_b. The key qualitative consequence of unitary elasticities is that the multiplicative structure of demand (A/P) and supply (B·P) makes the equilibrium buyer price determined by the product A and B and by the tax through a term that rearranges into a change in the solution for P_b that preserves the per-unit value (the tax instead reduces traded quantity rather than changing the equilibrium trading price). Economically, because both sides respond proportionally (unit elastic), the wedge introduced by the tax is absorbed as a reduction in quantity traded rather than a change in the buyer’s equilibrium price.

4) Why the correct answer is correct
The supply shift created by the tax reduces the equilibrium quantity—the tax makes some mutually beneficial trades infeasible. Under unitary elasticities, percentage adjustments out of price/quantity are such that the tax incidence works through quantity contraction, leaving the equilibrium buyer price unchanged.

5) Why other options are incorrect
- “Increase” or “decrease” for equilibrium price: these claim a change in buyer price; with symmetric unitary responsiveness, the tax is absorbed through quantity, not buyer price.
- “Would either increase or decrease”: incorrect because unitary elasticities produce a determinate direction for quantity (it falls) and leave the buyer price unchanged.

Conclusion: therefore a per-unit tax on sellers, with unitary elastic demand and supply, will have no effect on the equilibrium price of coffee and will decrease the equilibrium quantity of coffee—matching the provided answer.

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