The production function for which the MRTS does not decrease as the firm substitutes labor for capital along the isoquant is 1. Q(K, L) = K^0.5 L^0.5. This is because the Cobb-Douglas production function exhibits constant MRTS.
How to explain
The other production functions have the following properties:
Q(K, L) = 5K + 5L - This is a Leontief production function with fixed proportions of inputs, resulting in an undefined MRTS.
Q(K, L) = LK + K - This is a non-homothetic production function with a decreasing MRTS.
L = 5K - This is not a production function in the traditional sense; it's a constraint on input usage, preventing substitution along an isoquant.
The COMPLETE QUESTION
Identify the production function for which the Marginal Rate of Technical Substitution (MRTS) does not decrease as the firm substitutes labor for capital along the isoquant.
Production Functions:
Q(K, L) = K^0.5 L^0.5
Q(K, L) = 5K + 5L
Q(K, L) = LK + K
L = 5K