Problem 15 - Basic Statistics for Business and Economics with Student

Question

The Bookstall, Inc., is a specialty bookstore concentrating on used books sold via the Internet. Paperbacks are \(\$ 1.00\) each, and hardcover books are \(\$ 3.50 .\) Of the 50 books sold last Tuesday morning, 40 were paperback and the rest were hardcover. What was the weighted mean price of a book?

Step-by-Step Solution

Answer

The weighted mean price of a book is \(\$1.50\).

Step 1: Identify the Data Points

We know the prices of paperback and hardcover books. Paperbacks are priced at \(\\(1.00\) each while hardcovers cost \(\\)3.50\) each. There were 40 paperbacks and \(50 - 40 = 10\) hardcovers sold.

Step 2: Calculate Total Revenue for Each Type

Calculate the total revenue from paperback books by multiplying their quantity by the price. For paperbacks: \[ 40 \times \\(1.00 = \\)40.00 \]For hardcovers, multiply the number by the price: \[ 10 \times \\(3.50 = \\)35.00 \]

Step 3: Calculate Total Revenue

Add the revenue from both paperbacks and hardcovers to find the total revenue: \[ \\(40.00 + \\)35.00 = \$75.00 \]

Step 4: Compute the Weighted Mean Price

The weighted mean price of a book is found by dividing the total revenue by the total number of books sold. Thus, the weighted mean price is \[ \frac{\\(75.00}{50} = \\)1.50 \]

Key Concepts

Bookstore Economics

Running a successful bookstore, whether physical or online, involves understanding economics to make informed pricing and stocking decisions. Bookstore economics covers concepts like supply and demand, cost management, and sale strategies. For a specialty bookstore like The Bookstall, Inc., focusing on used books allows them to cater to a niche market.
This approach impacts their buying decisions and inventory management.

• Supply and Demand: By offering used books, the store can purchase books at a lower cost and offer competitive prices, in this case selling paperbacks at $1.00 and hardcovers at $3.50.
• Cost Management: Lower purchasing costs of used books allow for potentially higher profit margins even at lower sale prices. This is critical for maintaining profitability.
• Sales Strategies: Offering a diverse inventory at attractive prices helps draw in a wider customer base and increase sales volume. This strategy can result in higher total revenues, as seen with The Bookstall's sale of 50 books in a single morning.

Understanding these economics fundamentals can help a bookstore better align its pricing strategies with consumer expectations and market trends.

Used Books Pricing

The pricing of used books is a unique task that blends several important considerations. Unlike new books, used books are priced based on factors like condition, rarity, and demand. In the scenario with The Bookstall, pricing is simplified for efficiency and ease of consumer decision-making.
Here are some key elements in used books pricing:

• Condition: Better-preserved books often command higher prices compared to those showing wear and tear.
• Rarity: Rare or out-of-print books can be priced higher due to limited availability.
• Simplicity: Simplicity in pricing helps streamline operations. For instance, uniform pricing such as $1.00 for paperbacks and $3.50 for hardcovers can simplify transactions.

By considering these elements, bookstores can effectively price used books to maximize appeal and profitability while still turning over inventory efficiently.

Revenue Calculation

Accurately calculating revenue is essential to understanding the financial health of a business like The Bookstall. In this context, revenue calculation involves determining the total sales made during a particular period and analyzing profitability. Let's explore how this applies to the exercise in question:

• Sales Data: For The Bookstall, 40 paperbacks and 10 hardcovers were sold, resulting in revenues of $40.00 and $35.00 respectively.
• Total Revenue: By adding sales from both types, we get a total revenue of $75.00 for the sales period.
• Weighted Mean Price: This is calculated by dividing the total revenue by the total number of books sold. Here, it's $75.00 divided by 50 books, resulting in a weighted mean price of $1.50 per book.

Understanding revenue calculation helps The Bookstall to set financial goals, budget effectively, and assess the success of their pricing strategies in terms of market response and profitability.