Assume that the price of consumption is 1 and the price of a given public good i

Question

Assume that the price of consumption is 1 and the price of a given public good is 1 as well. Furthermore, assume that there are two consumers with identical preferences represented with UA(CA,F) = 20log(CA) + 20log(F) and UB(CB,F) = 20log(CB) + 20log(F), where F = FA+FB denotes the total amount of public good in this economy. Morever, assume that income of each consumer is equal to 240. In addition, assume that consumer B chooses on her own 80 units public good, i.e., FB=80, and 160 units of consumption good. What is FA in this case? (a) 120 (b) 80 (c) None of the above

Explanation / Answer

Consider the given problem, here there are 2 consumers each have same level of income (240) and same preference. So, if consumer-B decided to spend “160” on the consumption and “80” on the public good, => FB=80.

Now, let’s assume that “A” want to spend totally on the consumption of good and not on public good. Which implied FA=0, => the utility of A is, “20*log(240) + 20*log(80), since even if FA=0, F=FB=80. So, UA=85.66.

As, we can the utility function of “A” is given by “UA = 20*log(CA) + 20*log(F). Since, both of them is “log” function and the coefficient are also same, => both of the goods are equally efficient to increase utility, => and price of both are also same, => the utility will be maximum if CA=F, now FB=80. So, if FA=80 and CA=160, => F=FA+FB=160.

=> the utility of A is, “20*log(160) + 20*log(160) = 88.16 > 85.66.

=> here FA=80. => (b).

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