6. (9 points) A multi-sector model Consider a version of the manufacturing bid-rent curve, but with two sectors. Let 21 and 22 be the distance that firms in sector 1 and sector 2 locate away from the city center. Firms face freight, labor, land costs, and a fixed intermediate goods cost ( 1 = 5). To simplify the algebra, lets also assume that firms in each sector use only one unit of land (and thus the land cost, LC(xi) = P(xi) for i = 1,2. The labor costs for each firm (as a function of distance to center) is given by: = L(x1) = 25 A1 * x1 L(x2) = 35 A2 * 22 The freight costs for each firm as a function of distance is given by F(x1) = = (B1 +3) * 21 F(x2) = (B2 + 3) * 22 (a) (1 point) Write out the profit function for a firm in each sector. You should provide two equations. Do not assume that revenue is equal in each sector. (b) (2 points) Use your answer from part A to derive the bid-rent curves for manufacturing firms in each sector. (c) (2 points) For each sector, find the point at which the WTP for land is zero (this won't be a number, but a function of the model's parameters). (d) (1 point) Interpret your answer from part C. How does the distance you calculated for sector one change with Aj? Provide economic intuition for your answers. 6. (9 points) A multi-sector model Consider a version of the manufacturing bid-rent curve, but with two sectors. Let 21 and 22 be the distance that firms in sector 1 and sector 2 locate away from the city center. Firms face freight, labor, land costs, and a fixed intermediate goods cost ( 1 = 5). To simplify the algebra, lets also assume that firms in each sector use only one unit of land (and thus the land cost, LC(xi) = P(xi) for i = 1,2. The labor costs for each firm (as a function of distance to center) is given by: = L(x1) = 25 A1 * x1 L(x2) = 35 A2 * 22 The freight costs for each firm as a function of distance is given by F(x1) = = (B1 +3) * 21 F(x2) = (B2 + 3) * 22 (a) (1 point) Write out the profit function for a firm in each sector. You should provide two equations. Do not assume that revenue is equal in each sector. (b) (2 points) Use your answer from part A to derive the bid-rent curves for manufacturing firms in each sector. (c) (2 points) For each sector, find the point at which the WTP for land is zero (this won't be a number, but a function of the model's parameters). (d) (1 point) Interpret your answer from part C. How does the distance you calculated for sector one change with Aj? Provide economic intuition for your answers