A multi-sector modelConsider a version of the manufacturing bid-rent curve, but with two sectors. Letx1andx2be the distance that firms in sector 1 and sector 2 locate away from the city center. Firms face freight, labor, and land costs butno intermediate goodscost. 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) fori= 1,2. The labor costs for each firm (as a function of distance to center) is given by:

L(x1) = 20A1x1

L(x2) = 30A2x2

The freight costs for each firm as a function of distance is given by

F(x1)=(B1+3)x1

F(x2)=(B2+3)x2

A)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. (1 points)

B)Use your answer from part A to derive the bid-rent curves for manufacturing firms in each sector. (1 points)

C)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). (2 points)

D)Interpret your answer from part C. How does the distance you calculated for sector one change withA1? Provide economic intuition for your answers. (1 point)

E)

Now assume that A1=5,A2=6,B1=7andB2=4. Furthermore, you may now assume thatTR1=TR2= 40. Find the range of distances from the center each sector will be located. Hint: draw a graph of these lines. Remember: land is always allocated to the highest bidder. Don't worry about units and note that your answer may include fractions. (2 points)