Dear everyone

If a production function is homothetic, we can prove that its TRS is constant, so elastisity of subsititution=dln(tX1/tX2)/TRS(t)=dln(X1/X2)/TRS, so its elastisity of subsititution must be constant, so we can say this production function is a CES function, and can be written as

y=(X1^1/p + X2^1/p)^1/p

And we know this function is homogeneous of degree 1.

However, we know a homothetic function is not necessarily be homogeneous of degree 1.

Then, what is the matter here?

Thanks