In: Economics
There are three bidders in town, office firms, office workers,
and agricultural firms. Their respective bid rent functions are
given by:
Office firm Ro=200-5x,
office workers Rw=180-x, and
agricultural firms Ra=164.
where R denotes the bid rent and x the distance from the city
center.
a) Where does each bidder locate? (calculate the respective
distances from the city center)
b) Now assume that the city imposes a fuel tax on offices and on
office workers resulting in an increase in their corresponding
marginal transportation cost by 1. How does this change your answer
to (a)?
c) Now assume that the entire revenue from the fuel tax is paid to
office workers (not to offices). The government sends out checks
resulting in an income growth of $2 for each worker. How does this
change the respective locations.
d) Now assume that, in addition to all effects mentioned under (b)
and (c ), climate change reduces profits (and bid rents) of
agricultural firms by 4. How does this change the respective
locations.
According to bid rent theory, the activity having the highest
bid rent is theoretically the activity that will occupy this
location.
A) Image
as the bidder occupies the location, points of intersection in
above are important
Ro and Rw : 200-5X=180 - X
X= 20/4 =5
Rw and Ro : 180 -X =164
X= 16
Office firms settle at X<5
Office workers settle at X<16, X>5
Agriculture firms settle at X >16
B) Marginal transport cost for office and office workers increase
by 1, i.e. for each unit distance , 1$ is the cost.
Updated rent functions : Ro = 200 - 5x - x = 200 - 6x
Rw = 180 - x -x = 180 - 2x
Again getting intersections :
Ro and Rw : x = 5
Rw and Ra : x = 8
Ra and Ro : x = 6
Office location x <= 5
Office workers location : 5 < x <= 8
Agriculture : x > 8
C) Income growth of 2$ for each worker
Rw = 180 - 2x + 2 = 182 - 2x
Other rent functions stay the same.
Getting intersections :
Ro and Rw : x = 4.5
Rw and Ra : x = 9
Ra and Ro : x = 6
Office location x <= 4.5
Office workers location : 5 < x <= 9
Agriculture : x > 9
D)
Now Ra is updated
Ra = 164 - 4 = 160
Getting intersections :
Ro and Rw : x = 4.5
Rw and Ra : x = 11
Ra and Ro : x = 20/3
Office location x <= 4.5
Office workers location : 5 < x <= 11
Agriculture : x > 11