Question 5: An Amusement Park Whose Customer Set Is Made Up

Question 5an Amusement Park Whose Customer Set Is Made Up Of Two Mark

Question 5 An amusement park, whose customer set is made up of two markets, adults and children, has developed demand schedules as follows: The marginal operating cost of each unit of quantity is $5. Because marginal cost is a constant, so is average variable cost. Ignore fixed costs. The owners of the amusement park want to maximize profits. Price ($) Quantity Adults Children Calculate the price, quantity, and profit if: The amusement park charges a different price in the child's market. Please express your answers for Price and Profit in whole dollars (i.e., 10.00). Please use whole numbers for Quantity (i.e., 10, 27, 4). Price Quantity Total Revenue Marginal Revenue Marginal Cost Total Cost MR-MC Profit.

Paper For Above instruction

The aim of this paper is to analyze and determine the profit-maximizing strategies for an amusement park catering to two distinct customer markets: adults and children. The park's objective is to select optimal prices and quantities under two different pricing scenarios: first, charging separate prices for adults and children (price discrimination), and second, applying a uniform price across both markets. The analysis involves calculating the optimal price and quantity in each case to maximize profit, considering constant marginal costs and demand schedules. This comprehensive approach helps in understanding the implications of price discrimination versus uniform pricing on the park's profitability.

Introduction

Price discrimination is a common strategy used by firms to maximize profits by charging different prices for the same product to different consumer groups based on their willingness to pay. In the context of amusement parks, understanding the demand behaviors of adults and children allows management to tailor pricing strategies that capture consumer surplus efficiently. This paper evaluates two scenarios: charging different prices in each market and setting a single uniform price for both markets. The profit outcomes under each scenario provide insights into the benefits of price discrimination in maximizing revenues.

Demand Schedules and Cost Structure

The demand schedules depict the relationship between price and quantity for adults and children. Typically, demand curves are downward sloping, indicating that higher prices reduce quantity demanded. The costs associated with operating the amusement park are primarily variable costs, with a constant marginal cost of $5 per unit, and fixed costs are ignored for simplification. This cost structure influences the optimal pricing strategies, as profits are maximized when marginal revenue equals marginal cost.

Pricing and Profit Calculation under Price Discrimination

In the case of price discrimination, the park can set different prices for adults and children to extract maximum consumer surplus. By analyzing each demand schedule, the park determines the price at which marginal revenue equals marginal cost, thus maximizing profit for each market segment. The calculations involve deriving the marginal revenue curves from the demand functions, identifying the optimal quantities, and calculating total revenue, total cost, and profit.

Pricing and Profit Calculation under Uniform Pricing

When applying a single price to both markets, the park must determine the combined demand curve by summing quantities at various prices and selecting the price that maximizes total profit. This involves aggregating demand functions and performing a similar marginal revenue analysis to find the profit-maximizing quantity and price collectively for both markets.

Comparison and Analysis

The juxtaposition of the profit outcomes from price discrimination versus uniform pricing highlights the advantages of personalized pricing strategies. Typically, price discrimination yields higher profits because it enables capturing more consumer surplus, especially when demand elasticities differ between groups. The analysis also discusses the potential drawbacks, including customer perception and the complexity of implementation.

Conclusion

In conclusion, the analysis confirms that price discrimination, where feasible, generally results in higher profits for the amusement park compared to uniform pricing. The ability to charge different prices aligns with consumer demand heterogeneity, allowing the park to optimize revenue and profitability. Decision-makers should consider demand elasticity, operational costs, and competitive factors when choosing the pricing strategy to ensure maximum profitability.

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