We consider the production function P(L,K)=KL4K+L and determine the marginal rate of technical substitution at (L,K)=(2,3).
P′L(L,K)=K(4K+L)−KL(4K+L)2 and P′K(L,K)=L(4K+L)−4KL(4K+L)2. Therefore, MRTS(L,K)=P′L(L,K)P′K(L,K)=4K2L2.
Consequently, MRTS(2,3)=4⋅3222=9.
This implies that if labor at (L,K)=(2,3) increases by one-tenth of a unit, ΔL=110, and the input of capital decreases simultaneously by 910 units, then the output will approximately not change.
P′L(L,K)=K(4K+L)−KL(4K+L)2 and P′K(L,K)=L(4K+L)−4KL(4K+L)2. Therefore, MRTS(L,K)=P′L(L,K)P′K(L,K)=4K2L2.
Consequently, MRTS(2,3)=4⋅3222=9.
This implies that if labor at (L,K)=(2,3) increases by one-tenth of a unit, ΔL=110, and the input of capital decreases simultaneously by 910 units, then the output will approximately not change.