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Homework 1 | Homework
2 | Homework 3 | Homework 4 | Homework
5
Exercise 1
In order to complete Exercise 1, you must be able
to plot straight lines on a graph. Find two points that satisfy the
rent
equation for each crop and draw a straight line through these points.
Do this by choosing a reasonable value for distance and solving the
equation for the corresponding value of economic rent. This pair of
values represents a point on the graph; it is a set of coordinates.
When
you solved the equation, you calculated the rent value at the distance
you chose. You need two points to draw the rent line for each of the
three crops. If you get a negative value for rent when you solve the
equation, choose a smaller value for distance. Make sure your two
points are far enough apart so that your line can be drawn accurately.
Question 2 asks you to use the rent lines you have created to draw a
map
of the crop zones. I want to make sure that you can translate from the
graphed results to the pattern of landuse that will appear on the
ground. A simple sketch map will suffice.
Before you attempt to answer questions 3 and 4, make sure you have drawn the three rent lines correctly. Then visualize what the rent lines for crops A and B would have to look like in order for the conditions described in questions 3 and 4 to be true. In other words, in order for crop A to be the only crop grown, what would its rent line look like? Use a set of coordinates from this "new" rent line to figure out what the transportation rate would have to be. Follow a similar procedure to solve question 4.
This solution is for one of the three versions of the homework. If your version is different, subsitute the numbers on your sheet in the appropriate places. The basic nature of the solutions is the same for all three versions.
Exercise 2
To complete Exercise 2, you must calculate the population potential and
the transportation potential for five hypothetical cities. Each
potential figure is the sum of five terms (numbers). In the case of
population potential, each of the five numbers is a fraction made up of
the population of each place divided by the distance between the city
for which the potential is being calculated and each other city. For
the
transportation potential, each figure is made up of the product of the
population and the distance. For the term that applies to the city
itself (that is, the city for which the potential is being calculated),
use a distance of 1.00 even though, in reality, the distance between a
place and itself is zero. (As you know, you cannot divide by zero.)
A simple case for three cities is given below.
The population potential of A = (pop of B)/(dist A to B) + (pop of C)/(dist A to C) + (pop of A)/1.00 = 300/50 + 250/35 + 350/1 = 363.14
The population potential of B = 350/50 + 250/27 + 300/1 = 316.26
The population potential of C = 350/35 + 300/27 + 250/1 = 271.11
The transportation potential of A = (300)(50) + (250)(35) + (350)(1)= 24,100
In this example, A has the highest population potential. To express
the potentials of B and C as a percent of A, simply divide the value of
B's potential by A's, that is, 316.26 /363.14 = .87 or 87 percent. To
find the value for C, divide C's potential by 363.14.
As in the case of #1, the solution is for one of several very
similar versions of this homework. Your version may be slightly
different, so be careful when comparing your results to the solution.
Exercise 3
Remember that the circles surrounding the two raw material sites and
the market are only location symbols. Do not begin with the circles
when
labeling the lines; start with the first partial circle radiating out
from each location.
As in the case of #1 and #2, the solution is for one of several very similar versions of this homework. Your version may be slightly different, so be careful when comparing your results to the solution.
Exercise 4
This exercise requires you to draw a few central place hexagons that
you will use to answer several questions. This process can be difficult
if you have never done it before. I will show you how to get started in
class. If you miss the in-class hints, you will find this exercise much
more difficult.
To answer the questions about the distances between places, I suggest that you use your diagram, measure, and convert to miles. Your answers do not have to be exact, but if your diagams are sloppy and inaccurate, it is possible that you will be unable to answer the distance questions correctly. The questions concerning the areas of the markets do not require any measurements. If you understand central place theory, you should be able to answer these questions easily.
To answer the questions about the market area sizes, remember that
the "k" number indicates the relative sizes of market areas as one
moves
up or down the urban hierarchy. In a k=3 system, the market area of a
central place is three times the size of the next smallest market area.
If, for example, the smallest market area is one square mile, the next
largest market area will be three square miles, and the next largest
will be nine square miles. If it is a k=4 network, the market areas
will be multiples by four.
As in the case of #1, #2, and #3, the solution is for one of several very similar versions of this homework. Your version may be slightly different, so be careful when comparing your results to the solution.
Solution to homework #4 page 1
Exercise 5
When completing the questions for this exercise, try to be accurate,
but do not worry about reading the graph exactly. Except in unusual
circumstances, graphs are not meant to provide precise numerical data.
As long as the numbers you use are close, you will not be penalized.
Remember that not all cells in the table should have entries.
Solution to homework #5