Question 6. Let u(a,b,c) = min[(ap + b)1/8, c]. 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). a) Homogeneous of degree 1 b) Homothetic c) Quasi-linear d) Additively separable e) Weakly separable (Hint: u is weakly separable. You need to show this.] Suppose now that an agent with this utility function faces the usual budget constraint paa + pob + pec=m. f) Using the 2-step maximisation process for weakly separable utility (or otherwise), find the Marshallian demand. Question 6. Let u(a,b,c) = min[(ap + b)1/8, c]. 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). a) Homogeneous of degree 1 b) Homothetic c) Quasi-linear d) Additively separable e) Weakly separable (Hint: u is weakly separable. You need to show this.] Suppose now that an agent with this utility function faces the usual budget constraint paa + pob + pec=m. f) Using the 2-step maximisation process for weakly separable utility (or otherwise), find the Marshallian demand