Final answer:
The marginal rate of technical substitution of labor for capital (MRTSLK) at L = 16 and K = 9 is undefined.
Step-by-step explanation:
The marginal rate of technical substitution of labor for capital (MRTSLK) measures the rate at which a firm can replace capital with labor while keeping output constant. It represents the slope of the isoquant curve, which shows different combinations of labor and capital that produce the same level of output. To calculate MRTSLK, we use the formula:
MRTSLK = (ΔK / ΔL)
Given that L = 16 and K = 9, we can substitute these values into the formula to find MRTSLK. Calculating the change in labor and change in capital, we get:
(ΔK / ΔL) = (K2 - K1) / (L2 - L1) = (9 - 9) / (16 - 16) = 0 / 0
Since the denominator is zero, the MRTSLK is undefined, and none of the given options (a, b, c, or d) accurately represent the MRTSLK at L = 16 and K = 9.