Question

According to data from the U.S. Department of \(\begin{array}{lll}\text { Agriculture's } & \text { National } & \text { Agricultural } & \text { Statistics }\end{array}\) Service, 124 million acres of land in the United States were used for wheat or corn farming in a recent year. Of those 124 million acres, farmers used 50 million acres to grow 2.158 billion bushels of wheat and 74 million acres to grow 11.807 billion bushels of corn. Suppose that U.S. wheat and corn farming is efficient in production. At that production point, the opportunity cost of producing 1 additional bushel of wheat is 1.7 fewer bushels of corn. However, because farmers have increasing opportunity costs, additional bushels of wheat have an opportunity cost greater than 1.7 bushels of corn. For each of the following production points, decide whether that production point is (i) feasible and efficient in production, (ii) feasible but not efficient in production, (iii) not feasible, or (iv) unclear as to whether or not it is feasible. a. Farmers use 40 million acres of land to produce 1.8 billion bushels of wheat, and they use 60 million acres of land to produce 9 billion bushels of corn. The remaining 24 million acres are left unused. b. From their original production point, farmers transfer 40 million acres of land from corn to wheat production. They now produce 3.158 billion bushels of wheat and 10.107 bushels of corn. c. Farmers reduce their production of wheat to 2 billion bushels and increase their production of corn to 12.044 billion bushels. Along the production possibility frontier, the opportunity cost of going from 11.807 billion bushels of corn to 12.044 billion bushels of corn is 0.666 bushel of wheat per bushel of corn.

Short answer

a) Farmers use 40 million acres to produce 1.8 billion bushels of wheat and 60 million acres to produce 9 billion bushels of corn. b) From the original production point, farmers transfer 40 million acres from corn to wheat, now producing 3.158 billion bushels of wheat and 10.107 bushels of corn. c) Farmers reduce their production of wheat to 2 billion bushels and increase their production of corn to 12.044 billion bushels. Answer: Unclear as to whether or not any of the given points is an efficient use of resources.

Step-by-step solution

Understand the given information

This problem tells us that in total, there are 124 million acres of land used for wheat or corn farming. Farmers used 50 million acres for 2.158 billion bushels wheat and 74 million acres for 11.807 billion bushels corn. The opportunity cost of producing 1 additional bushel of wheat is 1.7 fewer bushels of corn. Because of increasing opportunity costs, additional bushels of wheat have an opportunity cost greater than 1.7 bushels of corn.

Analyze production point (a)

In this scenario, farmers use 40 million acres to produce 1.8 billion bushels of wheat and 60 million acres to produce 9 billion bushels of corn. This leaves 24 million acres unused. Since the total acreage available for use is 124 million acres and only 100 million acres are being used, this point is feasible as there is still land available that hasn't been used. However, since they are not using all available land resources, it is not efficient in production. Answer: (ii) Feasible but not efficient in production.

Analyze production point (b)

From the original production point, farmers transfer 40 million acres from corn to wheat, which means they have now 90 million acres for wheat and 34 million acres for corn. They now produce 3.158 billion bushels of wheat and 10.107 bushels of corn. Since there is no information about total acreage being altered, and since the opportunity cost of producing 1 additional bushel of wheat is increasing, we cannot determine the feasibility of this point without more information. Answer: (iv) Unclear as to whether or not it is feasible.

Analyze production point (c)

In this situation, farmers reduce their production of wheat to 2 billion bushels and increase their production of corn to 12.044 billion bushels. Along the production possibility frontier, the opportunity cost of going from 11.807 billion bushels of corn to 12.044 billion bushels of corn is 0.666 bushel of wheat per bushel of corn. Here, we can see that the opportunity cost of producing an additional bushel of corn is less than the initial opportunity cost mentioned in the problem (1.7). Since the problem states that opportunity costs are increasing, this situation is not feasible. Answer: (iii) Not feasible.

Key concepts

Opportunity Cost

Opportunity cost is a fundamental concept in economics. It represents the benefits you miss out on when you choose one alternative over another. In the context of the production possibilities frontier (PPF), it helps measure the trade-offs involved in decisions about resource allocation.
Imagine we have limited resources, in this case, the 124 million acres of farmland, and must decide how much of this land to dedicate to growing either corn or wheat. The opportunity cost of shifting land from corn to wheat production can be expressed by the loss in corn production experienced.
For example, transitioning one additional bushel of wheat production results in sacrificing 1.7 bushels of corn. This figure demonstrates a scarcity constraint because resources for corn are reallocated to wheat production. The problem mentions increasing opportunity costs, which is typical as reallocating resources becomes more costly due to factors like land suitability variations for each crop.

Agricultural Efficiency

Agricultural efficiency concerns how effectively resources like land are used to maximize the production of goods, such as wheat and corn, with minimal waste. In an efficient system, production takes place on the production possibilities frontier, where all resources are maximized with no unused or wasted capacity.
In scenario (a), with 124 million acres available, only 100 million are utilized. This implies inefficiency because there's unused land, suggesting the farmers could potentially produce more wheat or corn without increasing resource input. Hence, while the production is feasible, it's not efficient.
Improving efficiency means adjusting resource use so that all land is actively contributing to crop output. To be efficient, farmers would need to ensure all 124 million acres are utilized, balancing resources between corn and wheat in a manner that maximizes total output without leaving any part of the land fallow unnecessarily.

Land Resource Allocation

Land resource allocation is crucial in determining the quantity of each crop to produce and ensuring the most productive use of land. It involves strategic decision-making based on current production needs, market demands, and the trade-off between different types of crops.
When farmers move 40 million acres from corn to wheat production (scenario b), end results may vary depending on the land's suitability and productivity for each crop. Without additional context, this reallocation's feasibility remains unclear. It highlights how shifting land alters the balance of opportunity cost and labor inputs, sometimes leading to uncertain production outcomes.
Maximizing land resource allocation isn't merely about using every piece of land but selecting the optimal crop for each plot, considering factors like soil quality and local climate conditions, thus increasing the overall agricultural yield and efficiency.