1. The law of diminishing returns implies that at some output level:

a) Marginal cost must fall
b) Average total cost must diminish
c) profit increases
d) Marginal cost must rise
e) Total cost must fall

2. The vertical distance between total cost curve and total variable cost curve is equal to:
a) Total fixed cost
b) Average Variable cost
c) Marginal Cost
d) Average variable cost
e) Average total cost

To answer these questions, we need to understand the concepts related to the law of diminishing returns and cost curves.

1. The law of diminishing returns states that as you increase the amount of one input factor while keeping other factors constant, the added marginal product of that input will eventually diminish. In other words, there comes a point where adding more of an input leads to smaller increases in output.

Based on this understanding, let's analyze the options:
a) Marginal cost must fall: The law of diminishing returns does not directly imply that marginal cost must fall. It only suggests diminishing marginal returns, not necessarily diminishing marginal cost.
b) Average total cost must diminish: The law of diminishing returns does not directly imply that average total cost must diminish either. It focuses on diminishing marginal returns, not average cost.
c) Profit increases: The law of diminishing returns is not directly related to profit. Profit depends on revenue and cost, but the law of diminishing returns mainly affects the relationship between input and output, not profit.
d) Marginal cost must rise: This is the correct answer. The law of diminishing returns implies that as output increases beyond a certain level, the additional inputs put into production lead to smaller increases in output. This causes the marginal cost to rise, as more is spent on inputs to produce each additional unit of output.
e) Total cost must fall: The law of diminishing returns does not directly imply that total cost must fall. It focuses on diminishing marginal returns, not total cost.

Therefore, the correct answer to question 1 is d) Marginal cost must rise.

2. The vertical distance between the total cost curve and the total variable cost curve represents the total fixed cost.

To understand this, let's differentiate between total cost (TC), total variable cost (TVC), and total fixed cost (TFC):
- Total cost (TC) is the sum of total variable cost (TVC) and total fixed cost (TFC): TC = TVC + TFC.
- Total variable cost (TVC) represents the cost of variable factors of production, such as labor or raw materials, which change with the level of output.
- Total fixed cost (TFC) represents the cost of fixed factors of production, such as rent or machinery, which do not change with the level of output.

Since the vertical distance between the total cost curve and the total variable cost curve represents the total fixed cost (TFC), the correct answer to question 2 is a) Total fixed cost.