Hi Chiro,

I see your point applied to the case of a single variable function.

For a multivariate function, I have followed either of two approaches (not sure if I am right in the conclusion about convexity in case 1.) :

- F(G,W,C,M) = G^a ·W^b· C^c· M^d is an homogeneous equation of degree a+b+c+d .

Therefore for a scalar number t:

F (tG,tW,tC,tM) = (t^(a+b+c+d))·(G^a)·(W^b)·(C^c)·(M^d)

If a+b+c+d>1, equation F presents

*increasing returns to scale* (this is the interpretation from an “economic” standpoint). Therefore, we can state that the function is convex.

The equation I have posted gives a+b+c+d =-2,5779+46,622-15,958+37,241 = 65,3271 > 1 shows increasing

*returns to scale*. Thus it is convex.

- In reality a more accurate determination of convexity and/or quasi convexity would be given by demonstrating that the hessian of function F is H(F) > 0. This alternative requires the obtention of all the second derivatives of F and the calculation of the determinant of a 4x4 matrix which means a long and tiresome algebraic development. Have not been able to complete such a huge job (at the moment).

Is it correct to conclude convexity following the reasoning in 1. concerning homogeneity of the function and increasing returns ?

Thanks