Questions: Production Technology and Isoquant Analysis

Question 1

At a given point on an isoquant, MPL = 12 and MPK = 4. If the firm adds one more unit of labor, approximately how many units of capital can it remove while keeping output constant?

• A. 4 (equal to MPK)
• B. 3 (equal to MPL/MPK)
• C. 12 (equal to MPL)
• D. 1/3 (equal to MPK/MPL)

Answer: (B)

MRTS = MPL/MPK = 12/4 = 3. Adding one unit of labor raises output by MPL = 12; to restore output, you remove enough capital to reduce output by 12. Each unit of capital removed reduces output by MPK = 4, so you remove 12/4 = 3 units. The MRTS measures the rate of substitution between inputs at the margin, not just one marginal product in isolation.

Question 2

A bakery requires exactly 2 workers per oven — adding ovens without workers, or workers without ovens, produces no additional bread. What do this bakery's isoquants look like?

• A. Smooth, convex curves that become flatter as labor increases (Cobb-Douglas shape)
• B. Straight lines with constant negative slope (perfect substitutes)
• C. Right-angle (L-shaped) curves with kinks at the fixed-ratio combinations
• D. Upward-sloping lines reflecting positive MRTS

Answer: (C)

Fixed-proportion (Leontief) production — where inputs must be combined in a fixed ratio and extras add nothing — produces right-angle isoquants. The kink occurs at the optimal ratio (2 workers : 1 oven). Adding workers beyond the kink adds no output because there are no ovens to pair them with, and vice versa. This is the defining geometric signature of perfect complementarity in production.

Question 3

As a firm moves along a convex isoquant from left to right (adding more labor, removing capital), the MRTS increases.

• T. True
• F. False

Answer: False

Along a typical convex isoquant, the MRTS *decreases* as you substitute more labor for capital — this is the diminishing MRTS. As labor becomes more abundant relative to capital, each additional unit of labor contributes less output (diminishing MPL), while each unit of capital foregone costs more output (as capital grows scarce, MPK rises). Since MRTS = MPL/MPK, the numerator falls and denominator rises, flattening the isoquant as you move right.

Question 4

An isoquant and an indifference curve are conceptually identical — both show combinations of inputs that yield equal satisfaction for the decision-maker.

• T. True
• F. False

Answer: False

While isoquants and indifference curves share the same geometric form, they represent fundamentally different things. An indifference curve captures subjective *preference* — a consumer's willingness to trade one good for another. An isoquant captures objective *technology* — the physical possibilities determined by engineering or biology, not by anyone's preferences. A firm's isoquants cannot be changed by attitudes; they are constrained by the laws of production.

Question 5

Explain why the MRTS diminishes along a typical convex isoquant as you move from left to right. What does this pattern reveal about production with multiple inputs?

Model answer: As you move right along the isoquant (substituting labor for capital), two things happen: (1) labor becomes more abundant, so its marginal product falls due to diminishing returns; and (2) capital becomes scarcer, so its marginal product rises. Since MRTS = MPL/MPK, the numerator falls and the denominator rises, making MRTS decline. This reveals that inputs are imperfect substitutes in most production processes: the more extreme your allocation toward one input, the costlier each further unit of substitution becomes.

The diminishing MRTS is the production analog of diminishing MRS in consumer theory. Both capture a fundamental reality of trade-offs: the more extreme your allocation, the less efficient each additional substitution becomes. This is also why isoquants bow inward (are convex to the origin) rather than bowing outward.