Question

What will be the indirect utility function, expenditure function and hicksian demand function for U=min {x,y}+z ?

Answer 1

Here in the question utility function is given as below

U=min{x,y}+z, so we take $x=p_1,y=p_2$

then its Marshallian demand function will be

$x_1= \frac{m}{p_1+2p_1^{0.5}p_2^{0.5}}$

now we can find its indirect utility function as

U(x,y,z,m)= $\frac{m}{p_1+4p_1^{0.5}p_2^{0.5}+4p_2}$

now its expenditure function will be

e= $\frac{e(p_1,p_2,u)}{p_1+4p_1^{0.5}p_2^{0.5}+4p_2}$

and

hisksian demand function

$h_1=(p_1,p_2,u)= u(1+2p_1^{-0.5}p_2^{0.5})$