Question

In Exercises \(58-60\), use the following information. In \(1803,\) the Louisiana Purchase added \(8.28 \times 10^{5}\) square miles to the United States. The cost of this land was \(\$ 15\) million. In \(1853,\) the Gadsden Purchase added \(2.94 \times 10^{4}\) square miles, and the cost was \(\$ 10\) million. Writing Describe a factor that you think might explain the difference in the price per acre for these two purchases.

Short answer

Factors such as inflation, territory desirability (based on location and resources), political contexts and strategic importance could explain the difference in price per acre between the Louisiana Purchase and the Gadsden Purchase.

Step-by-step solution

Calculate the cost per square mile for Louisiana Purchase

Divide the total cost of the Louisiana Purchase by the total square miles. That is, \$15,000,000 divided by \(8.28 \times 10^{5}\) square miles.

Calculate the cost per square mile for Gadsden Purchase

This is done by the same process as step 1. Divide the total cost of the Gadsden Purchase by the total square miles. Therefore, it is \$10,000,000 divided by \(2.94 \times 10^{4}\) square miles.

Compare the cost per square mile of the two purchases

Compare the values obtained in Step 1 and Step 2, in order to see the difference in cost per square mile between the Louisiana Purchase and Gadsden Purchase.

Analyze difference

Consider factors such as inflation, location, resources, and political circumstances that might have contributed to differences in the cost per square mile between the two purchases.

Key concepts

Land Purchase Cost Analysis

When evaluating the cost of land acquisitions, it's crucial to consider the price per unit of area. This allows for a more accurate comparison, especially in historical contexts where the absolute numbers can be misleading.

In the case of the Louisiana Purchase, the cost analysis involves dividing the total purchase price of \(15 million by the 828,000 square miles acquired. The result is approximately \)18.12 per square mile. Similarly, for the Gadsden Purchase with its \(10 million cost for 29,400 square miles, the price is significantly higher, about \)340.14 per square mile.

This discrepancy in cost per square mile can be attributed to various factors, which we will explore further in the next sections.

Historical Land Transactions

Historical land transactions can be benchmark events that shape a nation's economic and territorial landscape. The Louisiana Purchase in 1803 and the Gadsden Purchase in 1853 are two monumental examples in U.S. history. Not only did these transactions significantly increase the nation's area, but they also demonstrated the economic principles of the times.

Analyzing these transactions involves understanding the historical context, including the geopolitical landscape, the reason behind the land's strategic importance, and the prevailing economic conditions. Inflation over time, technological progress, and international relations have profound impacts on land valuations.

Economic Factors in Land Valuation

Land valuation is a complex process influenced by many economic factors. In the context of the Louisiana and Gadsden Purchases, several elements could have affected the price per square mile:

• Inflation: The value of money changes over time, which could make direct price comparisons challenging without appropriate adjustments.
• Location and Quality: The geographical position and the quality of the land, including its fertility, resource availability, and topography, play critical roles in its valuation.
• Political Circumstances: The state of international relations and political stability can greatly impact investment and, consequently, land prices.
• Strategic Importance: Lands with strategic value, such as those offering trade advantages or military benefits, often command premium prices.

Therefore, a comprehensive cost comparison between historical land purchases needs to account for these diversified economic factors.

Exponential Notation in Area Measurement

Exponential notation, or scientific notation, is a concise way to express very large or very small numbers. It's particularly helpful in measuring large areas, such as in real estate transactions.

For example, the land area of the Louisiana Purchase was written as \(8.28 \times 10^{5}\) square miles. This notation represents the number 8.28 followed by 5 zeros, indicating the vast scale of land involved. The Gadsden Purchase is similarly noted as \(2.94 \times 10^{4}\) square miles.

Understanding this notation is key for accurately evaluating the magnitude of historical transactions and conducting cost analyses on such a grand scale. Moreover, applying exponential notation simplifies mathematical calculations, such as comparing the price per square mile of these large land purchases.