The Residents Of Ectenia Love Eco

The Residents Of the Town Ectenia All Love Eco

The residents of the town Ectenia display a strong collective interest in economics, prompting the mayor to consider establishing an economics museum. The project involves a fixed cost of $2,400,000 and no variable costs per visitor. With a population of 100,000 residents, each sharing identical demand for museum visits modeled by the demand function QD = 10 - P, where P is the admission price.

This assignment covers several economic aspects: graphing costs, analyzing market structure, evaluating funding strategies, determining pricing, and assessing consumer surplus and welfare implications under different scenarios.

Paper For Above instruction

Introduction

The establishment of a museum in Ectenia offers a compelling case study in public economics, specifically regarding funding mechanisms, market structure, and consumer welfare. By analyzing the fixed and marginal costs, demand curves, and different funding proposals, we can understand the economic rationale behind public provision and pricing strategies. This analysis explores the museum’s cost structure, examines optimal pricing, and evaluates the impacts on residents' welfare under various scenarios, ultimately offering policy reflections rooted in economic theory.

Cost and Market Structure Analysis

The museum's fixed cost is $2,400,000; it has no variable costs, meaning the marginal cost (MC) per additional visitor is zero once the museum is open. The average total cost (ATC) is thus high initially, given by:

ATC = Fixed Cost / Quantity = $2,400,000 / Q.

The marginal cost curve (MC) in this case is zero at all quantities except at zero (where it is undefined), indicating a natural monopoly or a public good scenario where the museum can serve multiple visitors without increasing costs.

The demand function QD = 10 - P implies that at P = 0, QD = 10, decreasing to zero at P = 10. Graphically, the demand curve is downward sloping from Q=10 at P=0 to Q=0 at P=10. The average total cost (ATC) curve starts at $2,400,000 / 10 = $240,000 per visitor if only one visitor attends, decreasing as more visitors come in. The marginal cost (MC) is zero across all quantities because there are no variable costs.

Market Description

This setup resembles a natural monopoly or a public good, where the fixed costs dominate and marginal costs are minimal or zero. Since the museum can serve any number of visitors without additional costs, it fits a natural monopoly model, where single-provider efficiency is optimal. The demand curve suggests that the ideal price can be set at any point up to P=10, but social welfare considerations and cost recovery drive price decisions.

Funding Strategy Analysis

Part A: Museum Funded by a Lump-Sum Tax and Free Admission

If the mayor finances the museum through a lump-sum tax of $24 per resident, total revenue from tax is:

Total tax revenue = $24 × 100,000 = $2,400,000.

This exactly covers the fixed cost of the museum, allowing free admission. With free access, residents will visit when their marginal benefit exceeds zero, which is at the maximum demand when P = 0 (Q=10). The total visits are determined by consumer willingness; since the demand curve is QD = 10 — P, at P=0, Q = 10, so each resident visits 10 times if the benefit is maintained.

However, the actual number of visits per person depends on their valuation of the museum experience (their willingness-to-pay). Assuming visit frequency remains consistent, each resident visits approximately 10 times because P=0 maximizes utility. The individual benefit is the consumer surplus, which in the case of free admission is maximized, but the actual benefit per person is reduced by the tax burden.

Calculating Individual Benefit

Consumer surplus for each resident is given by the area of the triangle between demand and the price line, which is zero since admission is free, and the residents are willing to pay up to P=10 for each visit. But with free access, the entire demand of Q=10 per person is realized without additional cost, translating to significant welfare gain. The net benefit after considering the lump-sum tax is thus the consumer surplus minus the tax paid, which diminishes the net benefit.

Part B: Lowest Price without Incurring Losses

To prevent losses, the museum must charge at least a price that covers the average cost. Since ATC declines as Q increases, and total fixed costs are $2,400,000, the minimum price corresponds to the point where revenue just covers fixed costs.

Given MC=0, the lowest feasible price ensures no losses at a certain visitation level. Calculating for P=2, P=3, P=4, and P=5:

  • At P=2, Q=10−2=8; total revenue = 2×8=16; total costs = 2,400,000 / 8 = $300,000 per visitor, which is not feasible. But this indicates a need to find the quantity where revenue covers total costs. Since costs are fixed, a more precise approach involves equating revenue to total costs:

Instead, because the fixed costs are substantial, the minimum ticket price needs to be set where total revenue equals or exceeds fixed costs. Therefore, the minimum price is just above zero, but practically, it must cover the average fixed cost at some feasible visitation level. Given the demand function, the lowest price at which the museum can operate profitably is near zero, but to avoid losses, a positive price should be set approximately at P=10, where Q=0, which is not feasible.

Part C: Break-Even Price and Consumer Surplus

The break-even price aligns with the average total cost at the level of demand where total revenue equals total cost. Since total cost is $2,400,000 and demand is Q=10−P, the minimum price that covers fixed costs at a feasible demand level, for example where Q=10, the total revenue is P×Q. For P=1, Q=9, total revenue=9. For P=2, Q=8, revenue=16. These are negligible compared to fixed costs, indicating the need for substantial pricing or government subsidy.

The most reasonable approach is to set the price at P=$10, where demand drops to zero—thus, the feasible break-even occurs at a pressure closer to the point where total revenue = fixed costs. Calculating consumer surplus at the break-even price shows that residents will value the museum highly when admission is free but will have their surplus reduced as fees increase.

Part D: Welfare Comparison

When charging the break-even price, residents’ consumer surplus diminishes proportionally with the admission fee, with the higher prices aligning with lower visits. Compared to free admission, adopting an admission fee shifts some welfare benefits from consumers to the museum or government, reducing overall consumer welfare but ensuring financial sustainability.

Specifically, at the break-even price, each resident's consumer surplus is the area between their willingness-to-pay and the actual price, which decreases as the fee rises. This reduction is undesirable from a welfare standpoint but necessary for financial viability.

Part E: Real-World Considerations

Several practical factors might favor setting an admission fee despite the theoretical implications:

  • Funding sustainability: charging fees helps cover ongoing operational costs and maintenance.
  • Welfare effects: fees can regulate demand, preventing overcrowding and ensuring quality experiences.
  • Perceived value: paid entry can enhance perceived value and prestige.
  • Equity considerations: free entry may encourage overuse by those with limited resources, while fees can restrict access to financially disadvantaged groups.
  • Policy and political factors: public support for subsidizing cultural institutions often involves fee structures or alternative funding mechanisms.

Conclusion

The analysis illustrates that, given the fixed costs and demand structure, a free admission funded by a lump-sum tax maximizes residents' welfare, but requires significant government subsidy. Charging an admission fee can ensure financial sustainability but at the cost of reduced consumer surplus and potentially lower visitation. Ultimately, policymakers must balance fiscal sustainability with equitable access and social welfare considerations, integrating insights from cost analysis, demand elasticity, and societal goals.

References

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  • Tiebout, C. M. (1956). A Pure Theory of Local Expenditures. The Journal of Political Economy, 64(5), 416-424.
  • Weimer, D. L., & Vining, A. R. (2017). Policy Analysis: Concepts and Practice. Routledge.
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