Hi could you please help me with this question? I also need the process in detail. Thank you.

The town of Economia has two residents: Ann and Bob. The town currently funds its fire department solely from the individual contributions of these residents. Each of the two residents has a utility function over private goods (X) and total firemen (M), of the form: U = 2 log(X) + log(M). The total provision of firemen hired, M, is the sum of the number hired by each of the two persons: M = MA + MB. Ann and Bob both have income of 200, and the price of both the private good and a fireman is 1. They are limited to providing between 0 and 200 firemen. For the purposes of this problem, you can treat the number of firemen as a continuous variable (it could be man-years).

(a) How many firemen are hired if the government does not intervene? How many are paid for by Ann? By Bob?

(b) What is the socially optimal number of firemen? If your answer differs from a), explain why.

(c) Suppose the government is not happy with the private equilibrium, and it decides to provide 20 more firemen. It taxes Ann and Bob equally to pay for the new hires. What is the new total number of firemen? How does your answer compare to part a? Have we achieved the social optimum? Why or why not?

(d) Suppose now that the government is still not happy, so it decides to provide 75 new firemen. It taxes Ann 50 to pay for them, and it taxes Bob 25. What is the new total number of firemen? How many are provided by Ann, and how many by Bob? How does this compare to the level of provision in c), and why?

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