数理经济学问题,明天交的,没分了,已经.

数理经济学问题,明天交的,没分了,已经.
(1)show that for y=f(x1,x2)=x1^1/4 x2^3/4 it follows that f1x1+f2x2=f(x1,x2).
(x1的 1/4次方 x2的 3/4次方)
(notation:[Fi] denotes the first order partial derivative with respect to [Xi])
(2)Consder the following specific CES(Constant Elasticity of Substitution)production function defined on
x1>0 and x2>0
y=f(x1,x2)=[0.3x1^-2+0.7x1^-2]^1/2
[0.3x1的-2次方 +0.7x1的-2次方]的1/2次方
(a)find an expression for the MRTS(marginal rate if technical substitution)
(b)show that f is homogeneous,and find its degree of homogeneity.
(c)show that the Euler's theorem applies to f.
(d)show thst f is homothetic
(e)The elasticity of substitution between two inputs for the production funtion f,is defined as
δ=d×ln(x2/x1)÷d×ln(f1/f2)
find the elasticity of substitution between the inputs for this funtion.