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 most, 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 most, 21 units of 
output.

BlackTom AI · Accepted Answer

Let's evaluate each statement one by one, keeping in mind basic isoquant shapes and production function properties.
Option I: 'If labor and capital are perfect substitutes in production, the isoquant is a downward-sloping line.' When inputs are perfect substitutes, the isoquant is linear, i.e., a straight line, reflecting a constant trade-off between labor and capital. Such a line is indeed downward-sloping because increasing one input can be offset by decreasing the other to keep output constant. Therefore, this statement is true.
Option 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.' A fixed-proportions (Leontief) production function requires inputs in fixed ratios, yielding L-shaped isoquants that reflect no substitution between inputs once the ratio is fixed. If the capital-to-labor ratio must stay at 2, the marginal rate of technical substitution is not smooth anywhere except at the corner where both inputs are used in that fixed proportion. Hence this statement is true.
Option III: 'If the production function is given by Q = min(14, 7), the firm can produce, at most, 21 units of output.' The expression Q = min(14, 7) evaluates to the constant 7, since the minimum of 14 and 7 is 7. It does not depend on inputs at all in this form, so the maximum output is 7, not 21. This statement is false.
In summary, the true statements describe standard properties of linear isoquants under perfect substitutes (I) and Leontief fixed-proportion isoquants (II), while the numerical form in III does not support a 21-unit maximum. Therefore, the correct combination is I and II.

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