Final answer:
The statement that each additional unit of input to a production function yields the same amount of output is false. Production functions vary by product and firm, and due to concepts such as diminishing marginal returns, additional units of input may yield less output over time.
Step-by-step explanation:
The main answer to whether adding one more unit of input to a production function will yield the same amount of output as all other units of input is false. Production functions define the relationship between inputs and outputs for a firm, indicating how much output can be produced with varying amounts of input. These functions are specific to each product and firm, meaning that different inputs might have heterogeneous effects on output. Moreover, inputs are categorized as either fixed or variable. A fixed input, such as capital, does not change in the short term and sets a boundary for the maximum output capacity. As more units of a variable input, like labor, are added, the additional amount of output that they produce can vary due to factors such as diminishing marginal returns.In the context provided, it sounds like the firms are operating in a strategic environment where their output decisions depend on the behavior of the other firm. However, this does not change the fundamental principle of production functions where the output resulting from an additional unit of input—also known as the marginal product—may decrease after a certain point of input usage. This concept is critical in understanding the cost of producing output and informs the firm's production decisions.