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Question 5. Maximum Word limit: 100 words. A choice function C satisfies Prop- erty Alpha when: for all menus A and B, if A C B, r E A, and x E C(B), then TEC(A). Informally: A choice function satisfies Property Alpha if, whenever option a is chosen from a larger menu and available in a more limited menu, then x must also be chosen from the more limited menu. Suppose C is a choice function which satisfies WARP. Show that C' also satisfies Property Alpha. Question 6. Let u(a, b, c) = min[(a + be)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 Pad + Pob + Pec = m. f) Using the 2-step maximisation process for weakly separable utility (or otherwise), find the Marshallian demand