For the production function given,
the marginal product of labour will be,
δLδQ=0−1×30×L1−1+0=−30
and the marginal product of capital will be,
δKδQ=2×2×K2−1−0+0=4×K
now, for finding the marginal rate for technical substitution(MRTS)
we use,
Q=2K2−30L+300
or,
K=(2Q+30L−300)1/2
on differentiating with respect to L, we obtain
MRTS(K,L) =δLδK=1/2×15×(2Q+30L−300)−1/2
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