A set of classical production possibilities Y = F(K,L,M) is said to be homothetic if there exists a strictly increasing transformation o of the non-negative real line onto itself such that 0(F(K,L,M)) = f(K,L,M) is positive linear homogeneous in inputs.

What is a homothetic production function?

Homothetic functions are functions whose marginal technical rate of substitution (the slope of the isoquant, a curve drawn through the set of points in say labour-capital space at which the same quantity of output is produced for varying combinations of the inputs) is homogeneous of degree zero.

How do you know if a function is homothetic?

A function is homogenous of order k if f(tx,ty)=tkf(x,y). A function is homothetic if it is a monotonic transformation of a homogenous function (note that this second function does not need to be homogenous itself). This is homogenous, since f(tx,ty)=(tx)a(ty)b=ta+bxayb=ta+bf(x,y).