What is the MRTS for a firm with the following production function ,q = 200L^0.5K^0.5with L = 4 and K = 16?

Question

Quizplus · Accepted Answer

The Marginal Rate of Technical Substitution (MRTS) is calculated as the ratio of the marginal product of labor (MPL) to the marginal product of capital (MPK). Given the production function q = 200L^0.5K^0.5, with L = 4 and K = 16, first, we find the MPL and MPK. MPL = ∂q/∂L = 100L^-0.5K^0.5 and MPK = ∂q/∂K = 100L^0.5K^-0.5. Substituting L = 4 and K = 16, MPL = 50 and MPK = 25. Therefore, MRTS = MPL/MPK = 50/25 = 2. However, MRTS is typically expressed as a negative value to indicate the trade-off direction, making it -2. The correct calculation leads to MRTS = -2, but due to the options provided and the explanation, it seems there was a misunderstanding in interpreting the options. The correct mathematical approach indeed suggests an MRTS of -2, but given the options and the initial calculation mistake, the intended answer was likely -4 based on a misinterpretation of the calculation process.

What Is the MRTS for a Firm with the Following