Model Answer
0 min readIntroduction
Market equilibrium is a fundamental concept in economics, representing a state where the quantity demanded by consumers precisely matches the quantity supplied by producers, resulting in a stable price. This equilibrium is disturbed by various external factors, including government interventions like taxation. A specific sales tax, levied per unit of a good, directly impacts the cost of production for sellers, leading to a shift in the supply curve. Understanding these shifts is crucial for analyzing how government fiscal policies affect market outcomes, influencing both prices paid by consumers and quantities exchanged in the market. The imposition of an 18% specific sales tax will alter the effective price received by sellers, thereby changing the market's equilibrium point.
Initial Market Equilibrium
Before the imposition of the sales tax, the market is in equilibrium when the quantity demanded (Qd) equals the quantity supplied (Qs).
Given the demand and supply functions:
- Qd = -500P + 5000
- Qs = 400P – 400
To find the initial equilibrium price (P_e) and quantity (Q_e), we set Qd = Qs:
-500P + 5000 = 400P – 400
Add 500P to both sides and add 400 to both sides:
5000 + 400 = 400P + 500P
5400 = 900P
P_e = 5400 / 900
P_e = 6
Now, substitute P_e = 6 into either the demand or supply function to find the equilibrium quantity:
Using Qd:
Q_e = -500(6) + 5000
Q_e = -3000 + 5000
Q_e = 2000
Using Qs:
Q_e = 400(6) – 400
Q_e = 2400 – 400
Q_e = 2000
Thus, the initial equilibrium price is 6 units and the equilibrium quantity is 2000 units.
Effect of Specific Sales Tax (18%)
A specific sales tax of 18% means that for every unit sold, the seller must pay a tax equivalent to 18% of the price. If P is the price consumers pay, the price producers receive (P_s) will be P - 0.18P. However, the question states a "specific sales tax of 18%". This implies it is an ad valorem tax, where the tax is a percentage of the price. In most economic models, an ad valorem tax on sellers shifts the supply curve upwards by a factor related to the tax rate. However, a "specific sales tax" typically refers to a fixed amount per unit. If it were a fixed amount, the supply curve would shift upward by that fixed amount. Given the 18% is a percentage, we will treat it as an ad valorem tax, meaning the tax is 18% of the *price received by the producer*. Let P be the price paid by consumers, and P_s be the price received by sellers. The tax 't' is 18% of the price consumers pay, so P_s = P - 0.18P = 0.82P. Alternatively, if the tax is levied on the seller, for every unit they sell at price P_s, the consumer pays P = P_s(1 + 0.18) = 1.18P_s. In this case, P_s = P / 1.18.
Let's assume the tax is levied on the producer, meaning the price received by the producer is lower than the price paid by the consumer. If 't' is the tax rate, and P_c is the consumer price, and P_s is the producer price, then P_c = P_s + t*P_s = P_s(1+t).
So, the new supply function (Qs') will depend on the price received by the sellers (P_s). If P is the price paid by the consumer, and the tax is 18% of this price, then the seller receives P_s = P - 0.18P = 0.82P. However, standard interpretation for an ad valorem tax on producers is that the *supply curve shifts such that for any given quantity, the price producers are willing to supply at is 1/(1-tax rate) times higher*. Or, more commonly, the producer's price P_s is related to the consumer price P by P_s = P / (1+t).
Given the phrasing "specific sales tax of 18%", let's consider the more common interpretation in such questions in competitive exams: the tax is effectively added to the price. This means if 'P_s' is the price the seller receives, the consumer pays 'P_c = P_s + T', where T is the tax amount. If the tax is a percentage of the *consumer price*, then T = 0.18 * P_c. This means P_s = P_c - 0.18 * P_c = 0.82 * P_c.
Let's assume the sales tax of 18% is levied *on the consumer price*. This means the price the sellers receive (P_s) is P times (1 - 0.18), or P_s = 0.82P, where P is the price buyers pay. Therefore, the sellers' original supply function was based on P_s. So, P = P_s / 0.82.
The new supply function should reflect the fact that for any given quantity, sellers now need a price P that covers their costs plus the tax. Or, if the tax is collected from sellers, the effective price they receive for any given market price P is P_s = P * (1 - tax rate). If the tax is 18% on the *sales price*, it implies that the price the seller gets for each unit is reduced by 18% of the final price the consumer pays. This means if P_c is the price the consumer pays, and P_s is the price the seller receives, then P_s = P_c - 0.18P_c = 0.82P_c.
Let P be the price paid by consumers. The price received by sellers, P_s, will be P / (1 + 0.18) = P / 1.18, if the tax is levied on the producers or if it is an ad valorem tax where the market price P includes the tax.
The question states "specific sales tax of 18%". In some contexts, "specific" refers to a per-unit tax, but 18% implies an ad-valorem tax. Let's assume the tax is levied *on the price paid by consumers*, and therefore, the supply curve shifts. The producers receive P - T, where T is the tax. If T = 0.18P, then the price received by producers is 0.82P. We need to express Qs in terms of P, the price consumers pay.
Original Qs = 400P_s – 400
Where P_s is the price received by the producer. With an 18% specific sales tax, the consumer pays P_c, and the producer receives P_s, where P_c = P_s + (0.18 * P_s) = 1.18 * P_s. (This is if the tax is 18% *on the producer's price* which then translates to a higher consumer price). Alternatively, if the 18% is on the consumer's final price, then P_s = P_c - 0.18P_c = 0.82 P_c.
Let's assume the tax is an ad valorem tax on the seller. This means for every P the consumer pays, the seller receives P_s = P - 0.18P. This is a common interpretation when the tax is a percentage. Therefore, the supply function, which is currently Qs = 400P – 400 (where P is implicitly the price received by sellers), needs to be adjusted. The new price received by sellers (P_s) will be related to the price consumers pay (P_c) by P_s = P_c - 0.18P_c = 0.82P_c. So, to use the original supply equation in terms of P_c, we substitute P_s with 0.82P_c.
New Qs (Qs') = 400(0.82P_c) – 400
Qs' = 328P_c – 400
Now, we find the new equilibrium by setting Qd = Qs':
-500P_c + 5000 = 328P_c – 400
5000 + 400 = 328P_c + 500P_c
5400 = 828P_c
P_c = 5400 / 828
P_c ≈ 6.5217 (New Equilibrium Price for Consumers)
Now, substitute P_c into the demand function to find the new equilibrium quantity (Qd'):
Qd' = -500(6.5217) + 5000
Qd' = -3260.85 + 5000
Qd' ≈ 1739.15 (New Equilibrium Quantity)
Let's verify this with the new supply function (Qs') using the consumer price:
Qs' = 328(6.5217) – 400
Qs' = 2141.1976 – 400
Qs' ≈ 1741.1976 (Slight rounding difference)
The equilibrium quantity should be the same for both. So, approximately 1739 units.
Price Received by Producers:
The price received by producers (P_s) after the tax is:
P_s = 0.82 * P_c
P_s = 0.82 * 6.5217
P_s ≈ 5.3478
Summary of Effects
The imposition of an 18% specific sales tax has the following effects on the market:
- Equilibrium Price (Consumer): Increases from 6 to approximately 6.52.
- Equilibrium Quantity: Decreases from 2000 to approximately 1739.
- Price Received by Producers: Decreases from 6 to approximately 5.35.
Analysis of Tax Incidence
The tax incidence refers to how the burden of the tax is shared between consumers and producers. In this case:
- Increase in Consumer Price: P_c - P_e = 6.52 - 6 = 0.52
- Decrease in Producer Price: P_e - P_s = 6 - 5.35 = 0.65
- Total Tax per Unit: P_c - P_s = 6.52 - 5.35 = 1.17. Also, 0.18 * P_c = 0.18 * 6.52 = 1.1736.
Consumers bear approximately (0.52 / 1.17) * 100 ≈ 44.4% of the tax burden.
Producers bear approximately (0.65 / 1.17) * 100 ≈ 55.6% of the tax burden.
The burden of the tax is shared between consumers and producers, with producers bearing a slightly larger share in this scenario. This distribution depends on the relative elasticities of demand and supply. A more inelastic side of the market bears a larger share of the tax burden.
| Parameter | Before Tax | After 18% Specific Sales Tax | Change |
|---|---|---|---|
| Equilibrium Price (Consumer) | 6 | ~6.52 | Increase by ~0.52 |
| Equilibrium Quantity | 2000 | ~1739 | Decrease by ~261 |
| Price Received by Producers | 6 | ~5.35 | Decrease by ~0.65 |
Conclusion
The analytical examination of the market demand and supply functions clearly illustrates the impact of a specific sales tax. The introduction of an 18% specific sales tax leads to a quantifiable increase in the equilibrium price paid by consumers and a noticeable decrease in the equilibrium quantity traded. This shift occurs because the tax effectively raises the cost of supplying goods, leading to an upward shift in the supply curve. Furthermore, the analysis reveals how the burden of the tax is distributed between consumers and producers, a phenomenon known as tax incidence. Such exercises are vital for policymakers to predict the market outcomes and welfare implications of various taxation policies, ensuring that fiscal measures achieve their intended revenue collection goals while minimizing undesirable economic distortions.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.