Question

If a farmer adds 1 pound of fertilizer per acre, the value of the resulting crops rises from \(\$ 80\) to \(\$ 100\) per acre. According to marginal analysis, the farmer should add fertilizer if it costs less than a. \(\$ 12.50\) per pound. b. \(\$ 20\) per pound. c. \(\$ 80\) per pound. d. \(\$ 100\) per pound.

Short answer

The marginal value of the added fertilizer is \(\$20\) per pound, calculated as the difference in crop value per acre after adding 1 pound of fertilizer (\(\$100 - \$80\)). Therefore, according to marginal analysis, the farmer should add fertilizer if it costs less than \(\$20\) per pound. The correct answer is b. \(\$20\) per pound.

Step-by-step solution

Identify the given values

The value of the crops rises from \(\$80\) to \(\$100\) per acre when 1 pound of fertilizer is added. So, we have the following information: - Initial value of crops per acre = \(\$80\) - Final value of crops per acre after adding 1 pound of fertilizer = \(\$100\) - Amount of added fertilizer = 1 pound

Calculate the marginal value of the added fertilizer

To find the marginal value, we need to find the difference in the value of the crops after adding the fertilizer: Marginal value = Final value - Initial value Then divide by the amount of fertilizer added: Marginal value = \(\frac{(\$100 - \$80)}{1 \text{ pound}}\) Marginal value = \(\frac{\$20}{1 \text{ pound}}\) Marginal value = \(\$20 \text{ per pound}\)

Compare the marginal value to the given cost options

Now, we can compare the marginal value of \(\$20\) per pound to the given options: a. \(\$12.50\) per pound b. \(\$20\) per pound c. \(\$80\) per pound d. \(\$100\) per pound Since the marginal value is \(\$20\) per pound, the farmer should add fertilizer if it costs less than \(\$20\) per pound. Therefore, the correct answer is: b. \(\$20\) per pound.

Key concepts

Marginal Value

When analyzing economic decisions, the concept of marginal value is pivotal. In the simplest terms, marginal value refers to the additional benefit received from consuming or using one more unit of a good or service. Imagine you're deciding whether to add an ingredient to a product you're making. To assess the worth of this action, you'd calculate the extra revenue obtained from the improved product and compare it against the cost of the added ingredient.

In the case of our textbook exercise, the farmer assesses the marginal value of adding fertilizer by determining the increase in crop value per acre. To calculate marginal value, the increase in output value is measured against the input increase (in this case, the fertilizer). This assessment helps determine the profitability of utilizing an additional unit of input and aids in making an informed decision on whether to incur the additional cost.

Cost-Benefit Analysis

The cost-benefit analysis is a systematic approach to compare the strengths and weaknesses of alternatives, specifically evaluating whether the benefits outweigh the costs. For our farmer, it means examining if the benefits of adding one more pound of fertilizer justify the expense.

For practical implementation, list all the potential costs and benefits of the action. Costs may include financial outlays, time, labor, and other resources. Benefits are typically the increased revenues or savings that result from the decision. After assigning a monetary value to each element, the net result guides whether the action should be taken. For businesses and individuals, this process is essential for optimizing resource allocation and pursuing the most value-additive actions.

Decision Making in Economics

Every day, individuals and businesses face choices that have financial implications. These are often analyzed using basic principles of decision making in economics. The core idea is to weigh the additional benefits and costs of any action.

Decision-making with economic rationality involves selecting the option that maximizes the net benefit or minimizes the net cost. Real-world scenarios complicate decisions with multiple variables and uncertainties, so decision theories and models aid in simplifying these complexities into manageable components. Using tools like marginal analysis and cost-benefit analysis, decision-makers can methodically assess their options and pursue the most advantageous course of action.

Opportunity Cost

The concept of opportunity cost is fundamental in economics and is intertwined with the decision-making process. Opportunity cost represents the benefits one forgoes when choosing one option over alternative ones.

In the context of our fertilizer example, if the farmer decides to spend money on an additional pound of fertilizer, the opportunity cost is what that money could have been used for otherwise—maybe buying seeds or investing in farm equipment. It's not just financial costs that have to be considered, but also time, labor, and other resource allocations. Understanding opportunity cost is vital as it helps to ensure that resources are being used efficiently and that the benefits from the selected option are greater than the benefits of the next best alternative.