Raymond B. answered 06/06/19
Math, microeconomics or criminal justice
In principle, the Production Possibilities Frontier could be straight, but generally it's bowed upward and to the right. That reflects diminishing marginal returns to an input and specialization of inputs. An example is a company or farmer who has land allocated to apples and oranges. He could put all his workforce, all his employees to work on the apple orchards and get 100 apples per hour, or he could put them all to work on the orange groves and get 100 oranges per hour. But the last worker in the apple orchard may be better at picking oranges than apples. IF the farmer put half his employees in the orchard and half in the grove, the output may be 75 apples and 75 oranges per hour. If the price of each is the same, such as $1, then splitting the work force means $150 per hour, while putting all the workers in one field gets only $100 per hour.
Plot those 3 points on a 2 dimensional graph, apples on the y or vertical axis, oranges on the x or horizontal axis. Then the 3 points are (0,100), (75,75) and (100,0) Try to draw a smooth curve through those points, and you get outward bowed curve. It's impossible to draw a straight line through those 3 points.
The PPF is the collection of all output combinations possible, that are efficient. Outside the PPF curve is impossible. Inside the PPF curve is inefficient or involves unemployed workers. The PPF curve can be for a single company or producer, or for the economy as a whole. Some workers or inputs are more productive at one production process, such as picking apples, than in another process such as picking oranges. That specialization best explains the curvature of the PPF. The orchard or grove may only accommodate a maximum number of workers, so you don't want all your work force in either one alone.
The PPF curve illustrates opportunity cost. If the American economy shifted its resources from domestic goods to military expenditures, this is sometimes done plotting "guns" on one axis and "butter" on the other, as two outputs. There is a trade off between the two. The more guns, the less butter, and vice versa. Adding more workers to the military industry at some point has diminishing marginal returns. Many workers are better as farmers or as soldiers or working building bombs. This specialization gives the PPF curve an outward bowed curve. It would have a straight line PPF only if every worker were equally productive making butter as making guns. The opportunity cost of shifting farmers into the military industry is the corresponding loss of farm products like butter.