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 (m) to some people. Assume a closed economy (no change in population) and all of the residents work. With some additional assumptions,l the distribution of residents in terms of their residence and workplace location can be described as follows: 'w (P where rm is equal to the fraction of people living in residence r and workplace location m (i.e., Tl'rm X N is equal to the number of people living in r and working in m); B1. > 0 corresponds to a numerical value of residential amenities in residence 1\"; mm is the wage earned from working in workplace location m; qr is the home price in r; drm is the distance between r and m (drm : 1 if r : m; work and live in the same location; very short distance of commuting); erm is a random error term with mean equal to zero. Assume 9b > 1, o: 6 (0,1), 6 > 0. Note that 2;, 2;, arm : 1. 1. Based on Equation (1), compute the expression for the elasticity of commuting (i.e., the probability of commuting from r to m) with respect to distance between 7' and am. You can do this by computing: 6 _ arm X drm 01' _ aln'rm \"id adrm rm 3 ll] drm Hint: You should get 5. 2. Based on Equation (1), derive an expression for the number of people living in residence 1\" (denote it as LRT) as a function of amenities, distances, home prices, wages, and errors. You can do this by summing 'R'rm over m, then multiplying the summation by N. That is, J LR, : (2 mm) x N m=1