Question 8.19 Choose the correct answerThe figure shows the demand and supply curves in the salt market. The government now decides to impose a sales tax of 30% on the price of salt, to be paid by the suppliers. Based on this information, read the following statements and select the correct option.

Question

BlackTom AI · Accepted Answer

When suppliers pay a per‑unit tax, their marginal cost rises by the fixed tax amount, so the supply curve shifts vertically upward by that amount.

1) Relevant concepts
- Supply expressed as price required to deliver a given quantity: P = S(Q).  
- A per‑unit tax τ paid by suppliers means they require price Pnet = S(Q) + τ to supply Q.  
- Graphically this is a parallel (vertical) upward shift of the supply curve by τ.  
- Tax incidence: the final consumer price rises by part of τ, suppliers receive the rest; quantity traded falls.

2) Step‑by‑step reasoning (algebraic)
- Let the original supply schedule be written as P = a + bQ (a linear supply with price as a function of quantity). The market equilibrium satisfies demand = supply at (P*, Q*).
- Introduce a tax τ per unit paid by suppliers. To supply quantity Q, suppliers now need Pnet = (a + bQ) + τ. The new supply relation in terms of the market price P becomes P = a + bQ + τ.
- This equation is the original supply function plus the constant τ, so at every quantity Q the required price is higher by the same amount τ. That is a parallel (vertical) upward shift of the supply curve.

3) Intermediate steps shown
- Original: P = a + bQ.
- With tax: P = a + bQ + τ = (a + τ) + bQ.
- Since τ is constant across Q, the shape and slope (b) are unchanged; only the intercept rises by τ → parallel shift.

4) Why option (b) is correct
- The statement "The supply curve shifts up in a parallel manner" exactly matches the effect of a fixed per‑unit tax paid by suppliers: the whole supply schedule moves up by the tax amount at every quantity.

5) Why the other options are incorrect
- (a) “The tax causes a fall in the quantity traded.” Although typically true, this is a consequence, not the most precise description of the immediate shift; the question asks which statement correctly describes the supply curve’s change.  
- (c) “The new equilibrium price is 30% higher than P*.” Incorrect because consumers do not generally bear the full tax; the price paid by consumers rises by only part of the tax (incidence depends on elasticities), so it will not simply be 30% higher.  
- (d) “The tax raised is 0.3 × (P × Q).” Wrong as stated: tax revenue equals tax per unit × new quantity (τ × Q′). If τ is a per‑unit amount, it is not 0.3×(P×Q) in general; if it were ad valorem the formula would be 0.3×P_consumer×Q′, not 0.3×P*×Q*.

Conclusion
Because a tax paid by suppliers increases the required price by a constant amount at every quantity, the supply curve shifts up in parallel. This confirms answer (b).

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