Market Intervention Due Date: Thursday, February 6, 2014

Market Intervention Due Date: Thursday, February 06, 2014 @ 1.00 p.m.

Consider again the market for Atlantic lobster with the given demand and supply equations: demand Q_D = 100 - 0.2P, and supply Q_S = 25 + 0.1P, where P is the price per kg, and Q is in thousands of kgs. The government imposes a quota of 150 thousand kg per year. Questions involve reconstructing curves, calculating equilibrium, analyzing quota effects, and comparing with taxes, along with effects of taxes and other market scenarios.

Paper For Above instruction

The market for Atlantic lobster presents an intriguing case of how external interventions such as quotas and taxes influence equilibrium, market efficiency, and overall welfare. This analysis aims to thoroughly evaluate the impact of a quota, examine alternative policy measures like excise taxes, and assess broader implications through various demand-supply scenarios. The key components involve graphically illustrating market behaviors, calculating algebraic figures, and providing economic interpretations rooted in fundamental principles.

Market for Lobster: Equilibrium Analysis

Initially, the market equilibrium without intervention can be determined by setting demand equal to supply:

100 - 0.2P = 25 + 0.1P

Solving for P yields:

100 - 25 = 0.1P + 0.2P → 75 = 0.3P → P* = 250

Substituting P into either demand or supply equation gives Q:

Q = 100 - 0.2 250 = 100 - 50 = 50 thousand kg

Graphically, the demand and supply curves intersect at a point corresponding to P = $250 per kg and Q = 50,000 kg. The demand curve slopes downward, reflecting typical consumer behavior, while the supply slopes upward, representing producer willingness to supply more at higher prices. The absence of external interventions ensures market efficiency at this point.

Impact of Quota of 150,000 kg

The imposition of a quota effectively limits the maximum harvest to 150,000 kg despite the market equilibrium being at only 50,000 kg, indicating that the quota is binding and causes distortions. Graphically, the quota is represented by a horizontal line at Q = 150,000 kg.

Demand at this quota: P_D = (100 - Q)/0.2 = (100 - 150)/0.2 = -50/0.2 = -$250, which is not plausible as demand cannot be negative. Instead, at the maximum permissible quantity, the demand price can be calculated as:

P_D = (100 - Q)/0.2, so at Q=150,000 (or 150 in thousands),

P_D = (100 - 150)/0.2 = -$250

This negative demand price indicates that at 150,000 kg, demand is essentially zero, i.e., consumers are not willing to purchase at such high quotas unless the price drops significantly. Conversely, supply at Q=150,000:

P_S = (Q - 25)/0.1 = (150 - 25)/0.1 = 125/0.1 = $1250

The supply price at 150,000 kg is $1250, leading to a large wedge between the demand and supply prices, which embodies the quota rent.

The graphical visualization exhibits a vertical line at Q=150, intersecting the supply curve at P = $1250 and demand approaching zero, illustrating the significant market distortion and potential for rent capture by harvest rights holders.

Quota Rent Calculation

The quota wedge, or rent per kg, represents the difference between the supply price and the demand price at the quota level:

Quota rent = P_S - P_D = $1250 - (-$250) = $1500

This rent signifies the earnings that accrues to those with the rights to harvest lobster, effectively a transfer from consumers to producers or harvesters, reflecting market power and potential inefficiency.

Alternative Policy: Excise Tax

Instead of a quota, imposing an excise tax shifts the supply curve upward by the tax amount, T. To find the tax rate that achieves the same 150,000 kg restriction, equate the new quantity demanded with the new supply:

Q_D = 100 - 0.2P_D, Q_S = 25 + 0.1(P_S)

Post-tax, supply price becomes P_S + T. The new market equilibrium must satisfy:

Q_D(P_D) = Q_S(P_S + T) = 150

From demand: 150 = 100 - 0.2P_D → P_D = (100 - 150)/0.2 = -$250

From supply: 150 = 25 + 0.1(P_S + T) → P_S + T = (150 - 25)/0.1 = 1250

Because in equilibrium, P_D = P_S + T, we can set:

-$250 = P_S + T

But P_S is equivalent to P_D in equilibrium, so T = 1250 - (-250) = 1500 dollars, matching the quota rent. However, this enormous tax would be impractical, indicating that the perfect substitution of quota with tax to exactly achieve the same reduction is complex and can lead to administrative difficulties.

Graphically, the tax shifts the supply curve upward by T, reducing quantity demanded to Q=150, aligning with the quota's effect. The tax incidence would be shared between consumers and producers depending on the elasticities, but typically, consumers bear a larger share when demand is more inelastic.

Tax Revenue and Tax Incidence

The total tax revenue equals the tax rate times the quantity sold:

Tax revenue = T Q_sold = 1500 150 = $225,000

Since the tax is paid partly by consumers and producers, the incidence analysis involves examining the change in prices paid by consumers and received by producers:

Pre-tax, consumers paid P* = $250, producers received $250. Post-tax, consumers pay P_C and producers receive P_P' such that:

P_C - P_P' = T = $1500

Elasticity considerations suggest that consumers with inelastic demand shoulder a heavier burden. The graphical representation depicts the wedge between consumer and producer prices equal to the tax, with the steeper the demand curve, the larger the incidence on consumers.

Positive Effects of Policy Interventions

Implementing quotas or taxes aims to prevent overharvesting, ensuring sustainable lobster populations. Such mechanisms can regulate the industry, prevent resource depletion, and generate public revenue. Quotas allocate property rights efficiently, aligning private incentives with conservation goals, while taxes internalize environmental externalities. Both policies incentivize harvesters to reduce effort, promote sustainability, and potentially support conservation investments.

Effect of Taxes on Various Markets

Case 1: Textbooks

The imposition of an excise tax increases the price paid by students from $50 to $55, while publishers' revenue per book drops from the initial value to $30, indicating a tax burden shared. The elasticity of demand suggests that consumers bear a substantial part of the tax burden, especially if demand is inelastic. Tax revenue is the tax rate ($5) times the quantity sold post-tax (600,000), totaling $3 million. The high tax burden can deter purchases, leading to inefficiency and missed educational opportunities.

Case 2: Airplane Tickets

Before the tax, tickets sell at $500; after, the consumer price is $550, and airlines receive $450, meaning airlines absorb part of the tax. The tax revenue equates to the difference in price times quantity: ($550 - $500) * 1.5 million = $75 million. The elasticity differences suggest consumers bear part of the tax burden, though airlines also absorb some, reducing overall market efficiency and possibly decreasing travel accessibility.

Case 3: Toothbrushes

Pre-tax, sales are 2 million units at $2.00 each; post-tax, consumers pay $2.50, and producers receive $0.75, significantly reducing profit margins. The tax rate per toothbrush is ($2.50 - $0.75) = $1.75; total revenue is $1.75 * 800,000 = $1.4 million. The demand's elasticity influences burden sharing, with consumers likely bearing most due to inelastic demand for essential hygiene products. Such taxes can cause inefficiency, reduced consumption, and potential health impacts if alternatives are unavailable or costly.

Conclusion

These scenarios exemplify how tax policies affect market prices, quantities, and welfare. A crucial insight is the distribution of tax burdens determined by relative elasticities, which influence economic efficiency and fairness. Governments should consider these factors when designing interventions to balance revenue generation, resource sustainability, and social welfare.

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