Market Intervention Due Date: February 5, 2013

Market Intervention Due Date: February 05, 2013 @ 13..

Consider again the market for Atlantic lobster presented in Q#1 of the previous assignment where the annual demand and supply for lobster is given by the following equations: 100 - 0.2 P Q = and 25 + 0.1 P Q =, where P is the price per kg in dollars, Q_D and Q_S are respectively the quantity demanded and the quantity supplied (in thousand kgs). The government imposes a quota of 150 thousand kgs per year in the lobster industry. You are asked to:

1. Reconstruct the demand and supply curves and show graphically the equilibrium price P and quantity Q for lobster without quota.

2. Show the quota graphically, calculate the demand price and supply price under this quota, and illustrate these graphically.

3. Calculate the quota wedge (quota rent) per kg of lobster at a quota of 150,000 kgs.

4. Consider imposing an excise tax as an alternative to quota; find the tax rate, explain how it affects the market, and illustrate graphically.

5. Calculate the government’s tax revenue, show it graphically, and analyze the incidence of the tax, identifying which party bears a heavier burden.

6. Briefly comment on potential positive effects of these policies.

Additionally, address the following:

7. For three different scenarios involving taxes on college textbooks, airplane tickets, and toothbrushes, analyze the incidence of the tax, explain why government revenue is not a good indicator of tax efficiency, identify missed opportunities or inefficiencies, and illustrate your points with graphs.

Paper For Above instruction

The market for Atlantic lobster exhibits fundamental economic principles of demand and supply, which determine the equilibrium price and quantity. Initially, demand is described by the equation Q_D = 100 - 0.2 P, and supply by Q_S = 25 + 0.1 P. To find the market equilibrium without government intervention, these two equations must be set equal to determine the equilibrium price (P) and quantity (Q). Setting demand equal to supply:

100 - 0.2 P = 25 + 0.1 P

75 = 0.3 P

P* = 75 / 0.3 = 250 dollars per kg

Substituting P back into either demand or supply to find Q:

Q = 100 - 0.2 250 = 100 - 50 = 50 thousand kgs.

Hence, the initial equilibrium is at a price of $250 per kg and a quantity of 50,000 kgs. Graphically, this is the intersection point where demand and supply curves cross, reinforcing the natural market balance.

Introducing a quota of 150,000 kgs, which exceeds the equilibrium quantity, effectively constrains supply beyond market equilibrium. To illustrate, the quota line Q = 150 in graphing scenarios (assuming units in thousands of kgs) is drawn horizontally at Q = 150. Since this quota is above the equilibrium quantity, it creates a surplus, reducing prices or changing the distribution of surplus implied — but in this case, because the quota is binding, the target is to determine new demand and supply prices corresponding to this quantity.

Calculating the demand price at Q = 150:

Q_D = 100 - 0.2 P => P = (100 - Q_D) / 0.2

P_D = (100 - 150) / 0.2 = (-50) / 0.2 = -250 dollars, which is impossible because negative prices are nonsensical; thus, at Q = 150, demand is zero, indicating the demand curve does not extend beyond 100 units for positive prices, or that the imposed quota is beyond the maximum demand at feasible prices. Therefore, the effective demand at Q = 150 is zero, and the price corresponding to 150,000 kgs may be read as zero or not applicable. Similarly, supply at Q = 150:

P_S = (Q - 25) / 0.1 = (150 - 25)/0.1 = 125/0.1 = $1250 per kg, which is unrealistic, indicating the supply response at this high quota would be at very high prices.

In practice, the quota rent per kg (the wedge or quota rent) is the difference between the demand price and the supply price at Q=150,000 kgs. Since actual prices can't be negative or excessively high, the quota rent reflects the market power retained by license holders, which can be approximated through the difference in the prices at the constrained quantity, or by assessing the area representing the quota rent, often called monopoly rent in quota markets.

Applying an excise tax instead of a quota impacts the market by increasing the cost burden on the supplying side, typically shifting the supply curve upward by the amount of the tax. To find the tax rate, consider the change in prices post-tax and pre-tax, and relate these to the shift in supply or demand curves.

Suppose the tax per kg is t dollars. The new supply curve becomes Q_S = 25 + 0.1 (P - t). At the original equilibrium, the tax causes the new equilibrium price paid by consumers (P_C) to rise and the price received by producers (P_P) to fall accordingly, with the difference equal to the tax. The equilibrium condition after tax is:

Q_D = Q_S, or 100 - 0.2 P = 25 + 0.1 (P - t)

100 - 0.2 P = 25 + 0.1 P - 0.1 t

75 = 0.3 P - 0.1 t

Expressing the tax rate t in terms of P:

t = (0.3 P - 75) / 0.1 - P = ?

To simplify, select a specific P and solve for t, or analyze in terms of marginal changes. The incidence of the tax depends on the relative elasticities of demand and supply; typically, the party with the less elastic side bears a larger burden.

The government’s tax revenue is calculated as the tax rate multiplied by the quantity sold post-tax: Revenue = t Q (at the taxed equilibrium). The graphical representation shows the vertical distance of t between the new supply and original supply curves at the equilibrium quantity. The incidence analysis indicates whether consumers pay a higher share (if demand is inelastic) or producers bear the greater burden (if supply is inelastic).

Importantly, these policies also entail considerations regarding efficiency and possible deadweight losses. When a quota is imposed, it restricts supply and can create rents for license holders, potentially leading to inefficiency and rent-seeking behavior. In contrast, taxes distort prices and quantities but generate revenue for government and can be designed to minimize excess burden, especially with careful calibration.

Regarding the analysis of taxes on textbooks, airline tickets, and toothbrushes, similar principles apply. The burden sharing depends on elasticity; government revenue alone is insufficient to measure efficiency because it ignores distortions and deadweight losses. Graphical illustrations typically show shifts in supply and demand curves, with the area representing deadweight loss shaded accordingly.

Targeted policy design should strive to balance revenue collection with minimizing economic distortions, considering elasticities, market structure, and administrative feasibility. Overall, these interventions aim to correct market failures, but their effectiveness hinges on proper calibration and understanding of market dynamics.

References

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