Exercice 3.2

If f(X1X) is homogeneous of degree 1 implies by Euler Theorem that:

f=f1*x1+f2*x2

If we divide by x1, then

AP1=MP1+f2*X2/X1

Rearranging, (AP1-MP1)=f2*X2/X1 (1)

If we assume, X2 and X1 > 0, then if AP1 is increasing, implies that

DAP1/dx1= (MP1-AP1)*1/x1>0

And because x1>0 implies that MP1>AP1

Therefore, in (1), f2<0, and f2 is the MP2

QED