Question

Which of the following explains the relationship among different cost functions? Select one: a. The marginal cost of the fifth unit of output equals the total fixed cost of five units minus the total fixed cost of four units. b. The total variable cost of seven units equals the average variable cost of seven units divided by seven c. The average total cost of seven units equals the average variable cost of the seven units minus the average fixed cost of seven units. d. The marginal cost of the fifth unit of output equals the total variable cost of five units minus the total variable cost of four units.
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Answer 1

(d) The marginal cost of the fifth unit of output equals the
  total variable cost of the five units minus the total
   variable cost of the four units.

This can be explained below :-

Now, let's see why the other options are wrong and option (d) is right.
- Firstly, let's take option (a)

It is wrong because marginal cost has nothing to do with fixed cost since marginal means addition and there is no change is fixed cost. So marginal cost of fifth unit of output can never be equal to total fixed cost of five units minus total fixed cost of four units.
So, option (a) is wrong.

-Secondly, let's take option (b)

It is wrong because total variable cost equals average variable cost multiplied by units of good.
So, total variable cost of seven units can never equal average variable cost of seven units multiplied by seven.
So, option (b) is also wrong.

-Thirdly, let's take option (c)

It is wrong because average total cost equals average variable cost plus average fixed cost.
So, average total cost of seven units can never equal average variable cost of seven units minus average fixed cost of seven units.
So, option (c) is also wrong.

-Now the last option i.e. option (d) is right

This is because marginal cost means addition to total variable cost and it can be only calculated by subtracting total variable cost of a unit of output say 4 units from total variable cost of a unit of output say 5 units i.e. TVC of 5 units - TVC of 4 units (while calculating marginal cost of 5th unit)

So, option (d) is correct.