Which of the following statements is (are) TRUE?

I. If labor and capital are perfect substitutes in production, the isoquant is a downward-sloping line.
II. If a company needs to use inputs in fixed proportion such that the capital to labor ratio is always 2, the firm's isoquants are L-shaped.
III. If the production function is given by Q = min(14, 7), the firm can produce, at minimum, 21 units of output.

Question

Which of the following statements is (are) TRUE?

I. If labor and capital are perfect substitutes in production, the isoquant is a downward-sloping line. 
II. If a company needs to use inputs in fixed proportion such that the capital to labor ratio is always 2, the firm's isoquants are L-shaped.
III. If the production function is given by Q = min(14, 7), the firm can produce, at minimum, 21 units of output.

BlackTom AI · Accepted Answer

Re-stating the question and options for clarity:
Question: Which of the following statements is (are) TRUE?

I. If labor and capital are perfect substitutes in production, the isoquant is a downward-sloping line.
II. If a company needs to use inputs in fixed proportion such that the capital to labor ratio is always 2, the firm's isoquants are L-shaped.
III. If the production function is given by Q = min(14, 7), the firm can produce, at minimum, 21 units of output.

Options:
A) I and II
B) III
C) I
D) I, II, and III

Now, we analyze each option carefully:

Option A (I and II):
- For I: When inputs are perfect substitutes, a linear production possibility set emerges, and isoquants are straight lines with a constant negative slope, i.e., downward-sloping. This matches the typical representation of perfect substitutes where one input can fully replace the other in producing output. Therefore, this statement is true.
- For II: A fixed-proportion (Leontief) production technology imposes that inputs must be used in fixed ratios, producing L-shaped isoquants with a right-angle kink at the required input mix. If the capital-to-labor ratio is always 2, the isoquants indeed take an L-shape rather than a smooth curve. This statement is also true.
Thus, both I and II are consistent with standard microeconomic theory.

Option B (III):
- The function Q = min(14, 7) evaluates to the minimum of the two constants 14 and 7, which is 7. This means the production function yields a constant output of 7 units, regardless of input amounts, not 21 units. The claim that the firm can produce at minimum 21 units is incorrect.
Therefore, this option is false.

Option C (I):
- As discussed under I, isoquants for perfect substitutes are downward-sloping straight lines. This makes the statement true. However, since Option A also contains II as true and the question asks for all true statements, selecting only I would omit a correct companion statement. In a multiple-choice setting that requires identifying all true statements, this option is incomplete.

Option D (I, II, and III):
- Since III is false (see above), this all-encompassing option cannot be correct.

Summarized reasoning about each choice:
- I: True, matches the standard depiction of isoquants under perfect substitutes as downward-sloping lines.
- II: True, aligns with Leontief/fixed-proportion logic yielding L-shaped isoquants when the input mix is fixed.
- III: False, because Q = min(14, 7) evaluates to 7, not 21, so the stated output capability is incorrect.
- Consequently, the combination that reflects the true statements without including the false one is the pair I and II.

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