There are N number of people living and working in the economy, which is divided into J discrete neighbor- hoods {e.g., Neighborhood 1, Neighborhood 2,..., Neighborhood J } Each neighborhood can be a residence [1") to some people and a workplace location {-111} to some people. Assume a closed economy {no change in population} and that all of the residents work. With some additional assumptions,1 the distribution of residents in terms of their residence and workplace location can be described as follows: to e rm = Br (w) Erma {1} where rm is equal to the fraction of people living in residence 1" and workplace location 171 {i.e.,1r,.m X N is equal to the number of people living in 1" and working m m}: B :2- [1 corresponds to a nunlerical value of residential amenities 1n residence 1", mm is the wage earned from working In workplace location 711', 1;, is the home price in 1"; d,\" is the distance between 1" and m (Cl-rm = 1 if r = in: work and live in the same location; very short distance of commuting); cm is a random error term with mean equal to zero. Assume a": 2:2- 1, or E (U, 1:], {i 2-\" 0. Note that 211:, Ei=1 rm = 1, by construction. 1. Based on Equation [1}, compute the expression for the elasticity of commuting [i.e., the probability of commuting from 1" to m} with respect to distance between r and 11:. Provide your interpretation of the expression. You can do this by computing: arm drm (9 1\" Wm Dr adv-m x \"mm. = alndrm 911,111 = Hint: You should get n. 2. Based on Equation {1}, derive an expression for the number of people living in residence 1" {denote it as Lr} as a function of amenities, distances, home prices, wages, and errors You can do this by summing arm over we, then multiplyulg the summation by N. That 1s