Week 5 Problem Set Due And Worth 200 Points

Week 5 Problem Set Due Week 5 and Worth 200 Points You Will Submit Yo

Suppose your company runs a shuttle business transporting hotel guests to and from the airport. The problem set involves analyzing marginal costs, elasticity, pricing strategies, price discrimination, and bundling in a competitive environment. You will provide calculations, graphs, and comprehensive explanations to demonstrate understanding of economic principles related to these topics.

Paper For Above instruction

In this paper, I will analyze several fundamental concepts of microeconomics as they relate to a shuttle transportation business, focusing on marginal costs, demand elasticity, price discrimination, and bundling strategies. These analyses will illustrate how firms can optimize profits and competitive positioning through strategic pricing decisions grounded in economic theory.

Problem 1: Using the Marginal Approach

Given the costs associated with different customer load levels, the first step involves calculating the marginal cost (MC) at each level. Marginal cost is the additional cost incurred from transporting one more customer. It is derived by the change in total cost from one load level to the next. The costs provided are:

• 1 customer: $30
• 2 customers: $32
• 3 customers: $35
• 4 customers: $38
• 5 customers: $42
• 6 customers: $48
• 7 customers: $57
• 8 customers: $68

Calculating marginal costs involves subtracting the total costs of the previous customer load from the current total costs:

Regarding pricing, if the company earns $10 per ride, the optimal customer load is determined by comparing marginal costs with the marginal revenue, which is $10 per ride. The company should serve the customer loads where marginal revenue exceeds marginal costs, maximizing profit. Based on the marginal costs calculated, serving up to 5 customers per ride is profitable because marginal costs are below or equal to $10. Beyond 5 customers, marginal costs exceed the revenue, reducing profit margins.

Problem 2: Elasticity and Pricing

The demand elasticity reflects how sensitive the quantity demanded is to price changes. Initially, demand elasticity was estimated at –2. Then, increased competition makes the demand more elastic, with an elasticity of –3. To determine the optimal price when the elasticity is –3, we apply the Lerner Index formula for profit maximization, which states that:

Price = Marginal Cost × (|Elasticity| / (|Elasticity| - 1))

Assuming the marginal cost is $10 (consistent with previous revenue per ride), the optimal price becomes:

Price = $10 × (3 / (3 - 1)) = $10 × (3 / 2) = $15

This suggests increasing the price to $15 to maximize profit given the higher elasticity, balancing revenue and demand sensitivity.

Problem 3: Price Discrimination

The amusement park's demand schedules for adults and children are provided, with a marginal operating cost of $5. By charging different prices, the park can maximize profits for each segment, considering the demand elasticity within each group.

1. Charging Different Price for Adults

The optimal price for adults is approximately $30, yielding a profit of $1,750 with a Q of 70.

2. Charging Different Price for Children

The optimal price for children is approximately $15 or $20, both yielding a profit of $1,500.

3. Same Price for Both Markets

Finding a common optimal price involves aggregating demand and calculating combined profit. For simplicity, choosing a midpoint, say $30, yields:

Combined quantity: Adults (70) + Children (150) = 220

Profit = (Price - Cost) × Quantity = ($30 - $5) × 220 = $25 × 220 = $5,500

This approach reduces price discrimination but generates higher total profit.

4. Difference in Profit Under Different Situations

Price discrimination allows the amusement park to capture more consumer surplus by pricing closer to each segment's maximum willingness to pay, thereby increasing profits. In contrast, setting a uniform price simplifies operations but sacrifices potential revenue. The profit under price discrimination can significantly exceed that of a single price, especially when demand elasticities differ, illustrating the importance of strategic pricing decisions pertinent to market segmentation.

Problem 4: Bundling Strategies

1. Should Time Warner bundle or sell separately for Customers 1 and 2?

Customer 1's reservation prices: Showtime = $9, History Channel = $2

Customer 2's reservation prices: Showtime = $? (not provided, missing data). Assuming similar preferences, Time Warner should bundle if the combined valuation exceeds the sum of individual prices minus costs. For Customer 1, selling Showtime at $9 and the History Channel at $2 separately makes sense if the total cost and individual valuations align. Since the data suggests one customer values Showtime strongly and the other less so, selling separately or bundling depends on the combined willingness-to-pay. If both customers value both channels highly, bundling at a price between the sum of their reservation prices could be profitable; otherwise, individual sales may be more beneficial.

2. Should Time Warner bundle if preferences are positively correlated (everyone likes both channels more)?

With positively correlated preferences, bundling is more advantageous. Customers with high willingness to pay for one channel are likely to value the other highly, justifying the bundle price that captures all consumer surplus. In such cases, bundling maximizes revenue and reduces arbitrage opportunities.

3. Should Time Warner implement mixed bundling with separate and bundle prices?

Selling Showtime at $9, the History Channel at $8, and a bundle at $13 allows consumers to choose the model capturing their willingness to pay best. If some customers value channels separately and others prefer the bundle, mixed bundling can maximize revenue by extracting consumer surplus across different consumer types. If the sum of the individual prices exceeds the bundle price, and consumer preferences are diverse, mixed bundling is an optimal strategy.

Conclusion

Strategic pricing, demand elasticity considerations, and consumer preferences significantly influence a firm's revenue maximization strategies. Marginal cost analysis guides optimal load levels, elasticity determines ideal prices, and discrimination and bundling tactics enhance profit extraction. Businesses must carefully analyze their market segments and demand structures to design effective pricing policies that align with consumer valuation and competitive dynamics.

References

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