Introduction: In economics the property of the slope of a tangent line to a level curve is used in different settings. In consumer behavior this property is known as the marginal rate of substitution and it is denoted by MRS(x,y), while in producer behavior it is known as the marginal rate of technical substitution and is denoted by MRTS(L,K).
Definition: For a utility function U(x,y) of a consumer the quotient U′x(x,y)U′y(x,y) at the point (x,y) is called the marginal rate of substitution and is denoted by MRS(x,y):
MRS(x,y)=U′x(x,y)U′y(x,y).
For a production function F(L,K) of a producer the quotient F′L(L,K)F′K(L,K) is called the marginal rate of technical substitution and is denoted by MRTS(L,K):
MRTS(L,K)=F′L(L,K)F′K(L,K)
or, in terms of the marginal physical product of the input factors,
MRTS(L,K)=MPPL(L,K)MPPK(L,K).
Definition: For a utility function U(x,y) of a consumer the quotient U′x(x,y)U′y(x,y) at the point (x,y) is called the marginal rate of substitution and is denoted by MRS(x,y):
MRS(x,y)=U′x(x,y)U′y(x,y).
For a production function F(L,K) of a producer the quotient F′L(L,K)F′K(L,K) is called the marginal rate of technical substitution and is denoted by MRTS(L,K):
MRTS(L,K)=F′L(L,K)F′K(L,K)
or, in terms of the marginal physical product of the input factors,
MRTS(L,K)=MPPL(L,K)MPPK(L,K).