In a monopoly market, the demand and cost curves are given by : p = 200 – 8q and c = 25 + 10q Suppose that the government imposes a tax of ₹ 10 per unit. How will equilibrium price and quantity be affected ?

A monopoly market, characterized by a single seller, holds significant market power, allowing it to influence both price and quantity. Governments often intervene in such markets through regulations or taxes to address potential inefficiencies or redistribute surplus. This intervention can profoundly alter the monopolist's profit-maximizing decisions, impacting the equilibrium price and quantity. Understanding these effects is crucial for policymakers aiming to achieve specific economic objectives, such as consumer welfare or revenue generation, without inadvertently causing market distortions. The imposition of a per-unit tax directly raises the monopolist's marginal cost, leading to a recalculation of its optimal output and pricing strategy. Understanding the Monopoly Equilibrium In a monopoly, the firm maximizes profit by producing at a quantity where marginal revenue (MR) equals marginal cost (MC). The price is then determined from the demand curve at that quantity. 1. Pre-tax Equilibrium Given the demand curve: p = 200 – 8q From the demand curve, we can derive the total revenue (TR): TR = p * q = (200 – 8q) * q = 200q – 8q^2 Now, we find the marginal revenue (MR) by taking the derivative of TR with respect to q: MR = d(TR)/dq = 200 – 16q Given the total cost curve: c = 25 + 10q Now, we find the marginal cost (MC) by taking the derivative of c with respect to q: MC = d(c)/dq = 10 To find the pre-tax equilibrium quantity (q_pre), we set MR equal to MC: MR = MC 200 – 16q = 10 190 = 16q q_pre = 190 / 16 = 11.875 units Now, substitute q_pre back into the demand curve to find the pre-tax equilibrium price (p_pre): p_pre = 200 – 8 * (11.875) p_pre = 200 – 95 p_pre = ₹ 105 Impact of a Per-Unit Tax When the government imposes a tax of ₹ 10 per unit, the total cost for the monopolist increases by ₹ 10 for each unit produced. This directly affects the marginal cost. 2. Post-tax Equilibrium The new total cost curve (c') will be: c' = 25 + 10q + 10q = 25 + 20q Now, we find the new marginal cost (MC') by taking the derivative of c' with respect to q: MC' = d(c')/dq = 20 The marginal revenue (MR) remains the same: MR = 200 – 16q To find the post-tax equilibrium quantity (q_post), we set MR equal to MC': MR = MC' 200 – 16q = 20 180 = 16q q_post = 180 / 16 = 11.25 units Now, substitute q_post back into the original demand curve to find the post-tax equilibrium price (p_post): p_post = 200 – 8 * (11.25) p_post = 200 – 90 p_post = ₹ 110 Summary of Impact Let's compare the equilibrium price and quantity before and after the tax: Parameter Before Tax After Tax Change Equilibrium Quantity (q) 11.875 units 11.25 units Decreased by 0.625 units Equilibrium Price (p) ₹ 105 ₹ 110 Increased by ₹ 5 Conclusion on Impact: The imposition of a ₹ 10 per unit tax leads to a decrease in the equilibrium quantity produced by the monopolist from 11.875 units to 11.25 units. It also results in an increase in the equilibrium price from ₹ 105 to ₹ 110. It is important to note that while the tax imposed was ₹ 10, the price only increased by ₹ 5. This indicates that the monopolist has absorbed some part of the tax, and passed on the remaining part to the consumers. The incidence of tax is shared between the producer and the consumer. The analysis demonstrates that a per-unit tax significantly alters a monopolist's market outcomes. By increasing the marginal cost, such a tax compels the monopolist to reduce output and raise prices. In this specific scenario, a ₹10 per-unit tax resulted in a decrease in equilibrium quantity by 0.625 units and an increase in equilibrium price by ₹5. This outcome highlights the complex interplay between government intervention and market dynamics, where the tax burden is often shared between producers and consumers, depending on the elasticity of demand and supply. Such policy tools, while generating revenue, also impact consumer welfare and market efficiency.

Why does the price not increase by the full amount of the tax?

The price does not increase by the full amount of the tax because the monopolist faces a downward-sloping demand curve. If the monopolist were to pass on the entire tax to consumers, the quantity demanded would fall significantly, potentially leading to lower overall profits. Therefore, the monopolist absorbs a portion of the tax to maintain a relatively higher sales volume.

Monopoly and Unit Tax: Price & Quantity Impact | UPSC Mains ECONOMICS-PAPER-I 2025

Model Answer

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Introduction

A monopoly market, characterized by a single seller, holds significant market power, allowing it to influence both price and quantity. Governments often intervene in such markets through regulations or taxes to address potential inefficiencies or redistribute surplus. This intervention can profoundly alter the monopolist's profit-maximizing decisions, impacting the equilibrium price and quantity. Understanding these effects is crucial for policymakers aiming to achieve specific economic objectives, such as consumer welfare or revenue generation, without inadvertently causing market distortions. The imposition of a per-unit tax directly raises the monopolist's marginal cost, leading to a recalculation of its optimal output and pricing strategy.

Understanding the Monopoly Equilibrium

In a monopoly, the firm maximizes profit by producing at a quantity where marginal revenue (MR) equals marginal cost (MC). The price is then determined from the demand curve at that quantity.

1. Pre-tax Equilibrium

Given the demand curve: p = 200 – 8q

From the demand curve, we can derive the total revenue (TR):

TR = p * q = (200 – 8q) * q = 200q – 8q^2

Now, we find the marginal revenue (MR) by taking the derivative of TR with respect to q:

MR = d(TR)/dq = 200 – 16q

Given the total cost curve: c = 25 + 10q

Now, we find the marginal cost (MC) by taking the derivative of c with respect to q:

MC = d(c)/dq = 10

To find the pre-tax equilibrium quantity (q_pre), we set MR equal to MC:

MR = MC
200 – 16q = 10
190 = 16q
q_pre = 190 / 16 = 11.875 units

Now, substitute q_pre back into the demand curve to find the pre-tax equilibrium price (p_pre):

p_pre = 200 – 8 * (11.875)
p_pre = 200 – 95
p_pre = ₹ 105

Impact of a Per-Unit Tax

When the government imposes a tax of ₹ 10 per unit, the total cost for the monopolist increases by ₹ 10 for each unit produced. This directly affects the marginal cost.

2. Post-tax Equilibrium

The new total cost curve (c') will be:

c' = 25 + 10q + 10q = 25 + 20q

Now, we find the new marginal cost (MC') by taking the derivative of c' with respect to q:

MC' = d(c')/dq = 20

The marginal revenue (MR) remains the same: MR = 200 – 16q

To find the post-tax equilibrium quantity (q_post), we set MR equal to MC':

MR = MC'
200 – 16q = 20
180 = 16q
q_post = 180 / 16 = 11.25 units

Now, substitute q_post back into the original demand curve to find the post-tax equilibrium price (p_post):

p_post = 200 – 8 * (11.25)
p_post = 200 – 90
p_post = ₹ 110

Summary of Impact

Let's compare the equilibrium price and quantity before and after the tax:

Parameter	Before Tax	After Tax	Change
Equilibrium Quantity (q)	11.875 units	11.25 units	Decreased by 0.625 units
Equilibrium Price (p)	₹ 105	₹ 110	Increased by ₹ 5

Conclusion on Impact:

The imposition of a ₹ 10 per unit tax leads to a decrease in the equilibrium quantity produced by the monopolist from 11.875 units to 11.25 units.
It also results in an increase in the equilibrium price from ₹ 105 to ₹ 110.
It is important to note that while the tax imposed was ₹ 10, the price only increased by ₹ 5. This indicates that the monopolist has absorbed some part of the tax, and passed on the remaining part to the consumers. The incidence of tax is shared between the producer and the consumer.

Conclusion

The analysis demonstrates that a per-unit tax significantly alters a monopolist's market outcomes. By increasing the marginal cost, such a tax compels the monopolist to reduce output and raise prices. In this specific scenario, a ₹10 per-unit tax resulted in a decrease in equilibrium quantity by 0.625 units and an increase in equilibrium price by ₹5. This outcome highlights the complex interplay between government intervention and market dynamics, where the tax burden is often shared between producers and consumers, depending on the elasticity of demand and supply. Such policy tools, while generating revenue, also impact consumer welfare and market efficiency.

Answer Length

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In a monopoly market, the demand and cost curves are given by : p = 200 – 8q and c = 25 + 10q Suppose that the government imposes a tax of ₹ 10 per unit. How will equilibrium price and quantity be affected ?

Model Answer

Introduction

Understanding the Monopoly Equilibrium

1. Pre-tax Equilibrium

Impact of a Per-Unit Tax

2. Post-tax Equilibrium

Summary of Impact

Conclusion

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