According to data from the U.S. Department of $\begin{array}{llll}\text{ Agriculture’s }& \text{ National }& \text{ Agricultural }& \text{ Statistics }\end{array}$ 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.

Key Concepts: Production Possibility Frontier, Opportunity Cost, Efficiency, Feasibility Explanation: The question provides information on the production of wheat and corn in the United States, along with the opportunity costs of producing more wheat. The question then asks the student to determine the efficiency and feasibility of different production points. Step by Step Solution: Step 1. Draw a production possibility frontier (PPF) graph with wheat on the y-axis and corn on the x-axis, with the origin at (0,0) and the intercepts of the graph on the x and y-axes representing the maximum production of corn and wheat respectively. Step 2. Mark point A with coordinates (2.158,11.807) on the PPF graph representing the original production point for the given year. Step 3. For point (a), compute the opportunity cost of producing 1 additional bushel of wheat as (1/1.7) = 0.5882 bushel of corn and compare it with the opportunity cost along the PPF, which at point A is (11.807-2.158)/(2.158-0) = 5.4648 bushels of corn per bushel of wheat. Since 0.5882 < 5.4648, the production of 1.8 billion bushels of wheat and 9 billion bushels of corn with 40 million acres is feasible and efficient in production. Step 4. For point (b), mark point B on the PPF graph with coordinates (3.158,10.107) representing the new production point after transferring 40 million acres from corn to wheat production and compute the opportunity cost of producing 1 additional bushel of wheat at point B as (10.107-11.807)/(3.158-2.158) = -1.7 bushels of corn per bushel of wheat. Since the opportunity cost is negative, it is not possible to achieve this production point using the given resources, and hence it is not feasible. Step 5. For point (c), mark point C on the PPF graph with coordinates (2,12.044) representing the new production point. Since the opportunity cost of producing 1 additional bushel of corn is given as 0.666 bushels of wheat per bushel of corn, the opportunity cost of producing 0.237 (11.807-12.044) billion additional bushels of corn is 0.237*0.666 = 0.1574 billion bushels of wheat. Therefore, the slope of the tangent at point A is (11.807-12.044)/(2.158-0) = -5.4648, and the slope of the tangent at point C is (12.044-11.807)/(2-0.237) = 4.9615. Since the slope of the tangent at point C is less steep than at point A, point C represents a feasible but not efficient production point.