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Consider the plight of two equally skilled economists, Ann and Bill. Ann lives in Ohio, where she pays a monthly rent of $1000 for a 1000 square foot apartment. Bill lives in Oakland in an 800 square foot apartment that is otherwise identical to Ann's but which costs him $2000 per month. Assume that the only other good that Ann and Bill consume is food, which costs $10 per unit in Ohio and only $5 per unit in Oakland.
a) Suppose that Ann and Bill both have ordinal utility functions U(h, z) = α log(h) + (1 - α) log(z), with 0 ≤ α < 1, where h is housing services (measured in square feet occupied per month) and z is food. Derive Ann and Bill's Marshallian Demands for housing and food. Give an interpretation of the parameter α ; how does it affect choices between housing services and food?
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