Final answer:
The correct relationship among cost functions is that the marginal cost of the fifth unit of output is the difference between the total cost of five units and the total cost of four units.
Step-by-step explanation:
The relationship among different cost functions involves understanding how costs change with the level of output. The correct answer to the question provided is 'd) the marginal cost of the fifth unit of output equals the total cost of five units minus the total cost of four units.' This statement accurately describes the marginal cost, which is the additional cost of producing one more unit of output.
To further clarify, marginal cost is calculated as the change in total cost that arises when the quantity produced changes by one unit. In other words, it is the cost of producing one additional unit of a good. Therefore, if you want to know the marginal cost of the fifth unit, you subtract the total cost of producing four units from the total cost of producing five units.
Other statements, such as the one regarding average variable cost, do involve a calculation based on the total variable cost; however, the average variable cost of seven units equals the total variable cost of seven units divided by seven, not multiplied by seven. Therefore, the relationship between average variable cost and total variable cost is incorrectly represented in option 'c'.