Market Intervention Due Date: February 5, 2013 At 13

Market Intervention Due Date: February 05, 2013 @ 13

Consider again the market for Atlantic lobster with demand and supply functions provided by the equations:

Demand: \(Q_D = 100 - 0.2P\)

Supply: \(Q_S = 25 + 0.1P\)

where \(P\) is the price per kg in dollars, \(Q_D\) and \(Q_S\) are the quantities demanded and supplied in thousands of kilograms respectively. The government imposes a quota of 150 thousand kgs annually, issuing licenses that allocate harvesting rights.

Paper For Above instruction

The market for Atlantic lobster serves as an insightful case study for understanding government interventions such as quotas and taxes. These measures aim to control supply, stabilize prices, or generate revenue but also come with economic implications that merit detailed analysis.

Market Equilibrium without Intervention

To determine the equilibrium price and quantity in the absence of governmental intervention, we set the demand and supply equations equal to each other:

\(100 - 0.2P = 25 + 0.1P\)

Rearranging for \(P\):

\(100 - 25 = 0.2P + 0.1P\)

\(75 = 0.3P\)

\(P^* = \frac{75}{0.3} = 250\) dollars per kg

Substituting \(P^ = 250\) into either the demand or supply function to find \(Q^\):

\(Q_D = 100 - 0.2 \times 250 = 100 - 50 = 50\) thousand kgs

Thus, the equilibrium price is $250 per kg, and the equilibrium quantity is 50,000 kgs.

Graphical depiction

Graphically, the demand curve slopes downward, and the supply curve slopes upward, intersecting at \(P^ = 250\), \(Q^ = 50\). The demand curve can be drawn from the intercepts: when \(Q_D=0\), \(P=500\), and when \(Q\) is large enough at lower prices. The supply curve intersects the price axis at \(P=-250\) (not economically meaningful but mathematically present). The intersection point determines the equilibrium in the absence of a quota.

Imposing a Quota of 150 Thousand Kgs

When the government sets a quota \(Q=150\) thousand kgs, it restricts supply to this level. Since equilibrium quantity without restrictions is only 50,000 kgs at a much lower price, the quota is effectively binding and reduces supply from the natural market equilibrium.

Graphically, this is shown by a vertical line at \(Q=150\), which intersects the demand and supply curves at different prices:

• Demand price \(P_D\) when \(Q=150\):

  \(Q_D=100 - 0.2P_D=150\)

  \(\Rightarrow 0.2P_D=100-150=-50\)

  \(\Rightarrow P_D=-250\) (negative, indicating that demand at 150kgs is not feasible without considering the price's compatibility with the demand function). But since demand cannot be negative, at 150kgs, demand is negligible.

• Supply price \(P_S\):

  \(Q_S=25 + 0.1P_S=150\)

  \(\Rightarrow 0.1P_S=125\)

  \(\Rightarrow P_S=1250\) dollars per kg, which signifies the price needed to supply 150kgs.

Thus, the demand will be at its maximum feasible level at the lower end of prices, while the supply is compelled to supply at the quota level at a higher price, creating a wedge that indicates a shortage and economic rent.

Quota Rent Calculation

The quota rent (or wedge) per kilogram equals the difference between the shadow prices on the supply and demand sides at the quota level. Since the quota limits supply to 150kgs, and the supply price at that quantity is \$1250, while the demand price at that quantity (if feasible) can be approximated at the point where demand and supply intersect at this quantity, the rent per kg is:

\(\text{Quota rent} = P_{S} - P_{D}\)

Finding \(P_D\) at \(Q=150\):

\(\ Q_D=100 - 0.2 P_D=150\Rightarrow 0.2 P_D=100-150=-50\Rightarrow P_D=-250\)

This negative demand price suggests demand becomes negligible at such high quantities, thus the actual market price at the quota is more determined by supply side, and the rent (or wedge) reflects the potential price difference at the quota level. Alternatively, the rent per kg is approximated by the difference between the supply price and the demand price at the same quantity.

Alternative: Excise Tax as Policy Tool

The government might instead impose an excise tax to achieve the same reduction in harvested lobster. An excise tax effectively shifts the supply curve upward by the tax amount, increasing the cost of supplying lobsters and reducing quantity supplied.

Determining the Excise Tax Rate

To enforce a harvest of 150,000 kgs, the tax must increase the effective price consumers pay or decrease the price producers receive so that the quantity reduces accordingly. We assume the tax shifts the supply curve vertically by an amount \(t\).

Considering the original equilibrium price and quantity, the new equilibrium after tax should be at the same quantity (150kgs), where supply equals demand at an increased price paid by consumers:

\(Q_D=Q_S\)

Demand function at \(Q=150\):

Rearranged:

\(Q=100 - 0.2 P\) => \(P_D = (100 - Q)/0.2\)

At \(Q=150\):

\(P_D= (100 - 150)/0.2 = (-50)/0.2 = -250\) (which indicates demand is practically zero at this quantity). Nonetheless, for an approximate tax rate, we study the difference between the prices at the original equilibrium and the targeted quota.

Original equilibrium price: \$250; at the quota level of 150kgs, the supply price was around \$1250 to meet the new demand, which is inconsistent with initial demand; thus, in practice, the tax rate would be set to raise the price to reduce supply to the quota level. Using calculus or more detailed modeling, the typical approach is the tax equals the difference in supply and demand prices at the new quantity, which can be estimated by examining the slopes and intercepts.

Tax Revenue and Incidence

The total tax revenue is calculated as:

\(\text{Tax revenue} = t \times Q_{Q}\)

where \(Q_{Q}\) is the quantity sold after the tax. The incidence on consumers and producers depends on the relative elasticities: the side with the less elastic response bears a heavier burden.

Graphically, the incidence is shown by shifts in the supply and demand curves. When a tax is imposed, the consumers typically pay more, represented as a higher price on the demand curve, while producers receive less after deducting tax, shown as a lower price on the supply side.

Conclusion on Policies' Effects

Both quota and tax policies aim to reduce lobster harvests, but their economic impacts vary. Quotas create a market rent or quota rent, distributing income between license holders, and may lead to inefficiencies due to rent-seeking behavior. Taxes, on the other hand, generate government revenue and can internalize externalities if present, but may also distort markets and reduce total output. Both interventions can have positive effects such as sustainable resource management; however, their design and implementation critically determine their efficiency and societal benefits.

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