Anna and Bob are the only residents of a small town. The town currently funds its fire department solely from the individual contributions of these two residents. Each of the two residents has a utility function over private goods a and total number of firemen M, of the form: u(x, M) = 2 ln x + In M. The total provision of firemen hired, M, is the sum of the number hired by each of the two persons: M = Mª + M².Ann and Bob both have income of 200 each, 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 con be man-years). Suppose that the government recruits additional N firemen and taxes Ann and Bob equally to cover the cost. Therefore, the total number of firemen is Mª + MB + N,where MA, M² are appropriate individually-optimal contributions of A an B (i.e., the agents behave optimally, conditional on the policy), and each agent is taxed N /2. How many additional firemen should the government hire in order to guarantee that in equilibrium the total number of firemen is optimal?

The town of Wollulung has two residents: Bach (B) and Mozart (M). The town currently funds its free outdoor concert series solely from the individual contributions of these residents. Each of the two residents has a utility function over private goods (X) and total concerts (C), of the form: U = 3 × log(X) + 2× log(C) The total number of concerts given, C, is the sum of the number paid for by each of the two persons: С %3D Св + См Bach and Mozart both have income of 60, and the price of both the private good and a concert is 1. Thus, they are limited to providing between 0 and 60 concerts. a) How many concerts are given if the government does not intervene?

Suppose the Super Bowl is this week, and Raphael is in need of a television to watch the big game. As a college student, Raphael knows that he can either buy his flat-screen television at the local electronics store, or he can shop online for a better deal but have to wait four days for the television to arrive. The following problem uses the economic concept of rate of time preference to help determine which decision is better for Raphael. Throughout the question, assume that Raphael pays for the good the day he buys it, so his wealth is affected in the initial time period no matter where he buys the good. Also, assume the shipping cost and cost to travel to the store are incorporated into their respective given prices. Finally, assume the goods are identical, and there's no cost to gaining information about prices-in other words, he knows the best price online and in the store without having to search. Suppose Raphael receives a utility of 35.11 utils once he actually receives his…

Find the marginal rate of substitution for Household A.