The optimal amount of insurance purchased determines the optimal consumption level in each state as indicated...

 

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The optimal amount of insurance purchased determines the optimal consumption level in each "state" as indicated before, and we have standard Walrasian demand functions c₁(p, m) and c₂(p, m), for the consumption of the two goods as usual, (where m = w₁ + pw2, but that is not important). Take as given that both c₁ and c₂ are normal goods for the consumer's preferences here. Demonstrate that the consumer may consume either less or more of good 1 as the price of insurance q decreases. [Note: yes, I am asking about the sign of a derivative of a function you don't know, so you cannot just take the derivative. No, you also don't need the implicit function theorem, this is an 'economics' question! Yet, the question has a short and simple answer of maybe 3 or 4 lines.] The optimal amount of insurance purchased determines the optimal consumption level in each "state" as indicated before, and we have standard Walrasian demand functions c₁(p, m) and c₂(p, m), for the consumption of the two goods as usual, (where m = w₁ + pw2, but that is not important). Take as given that both c₁ and c₂ are normal goods for the consumer's preferences here. Demonstrate that the consumer may consume either less or more of good 1 as the price of insurance q decreases. [Note: yes, I am asking about the sign of a derivative of a function you don't know, so you cannot just take the derivative. No, you also don't need the implicit function theorem, this is an 'economics' question! Yet, the question has a short and simple answer of maybe 3 or 4 lines.]

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Let c and c2 corresponds to good and bad state respectively Now ... View the full answer