For each of the following, determine whether u satisfies this property. If it does, prove this. If not, prove it does not (either by providing a counterexample or otherwise). The utility function is u(a, b, c)= min[(a^m+b^m)^1/m , c]

a) Homogeneous of degree 1

b) Homothetic

c) Quasi-linear

d) Additively separable

e) Weakly separable

Suppose now that an agent with this utility function faces the usual budget constraint (p_a)a + (p_b)b + (p_c)C= Q

f) Using the 2-step maximisation process for weakly separable utility or find the Marshallian demand.