Weber Location Model

1. Under which conditions is the optimal location in the Weberian triangle a location on one of the lines connecting two of the corners of the triangle? Clearly explain your answer.

1. Moses Model
2. What is the fundamental difference between the classical (Weber) location model and the Moses-model? Focus in your answer on the fundamental difference between the production technologies.
3. What is the implication of this difference for the optimal location and the optimal decision on the input mix for the firm?

1. Location Choice

There is a new tech company “Humbl”, with a single consumer market in town A. Humbl uses two inputs, these are obtained from respectively the cities B and C, which are 600 kilometers apart. The distance between A and B, and between A and C is 500 kilometers.

Humbl can sell its output in A at a price of \$100 per unit. In order to produce one unit of output, they need two units of inputs from B and three units of input from C. The cost of one unit of input from B is \$5. For a unit input from C the cost is \$10.

The costs for the transportation of the finished product from the site of production to A are zero. The transport of one unit of input from B costs \$2 per 100 kilometers, and the transportation costs for one unit of C \$3 per 100 kilometers.

1. Give a graphical representation of the situation described above by drawing the Weberian triangle as accurately as possible.
2. A situation where the (variable) cost of transporting finished products are zero (or negligible), is exceptional. Give an example of a product of which the variable costs of transportation to the consumer market are negligible.
3. Give a mathematical description of the production function of “Humbl”. What makes this production function so special?
4. Determine the optimum location for “Humbl” and determine the transport costs and profits in the optimal location. Provide a graphical illustration.

1. Location Choice

Consider four cities A, B, C and D located as follows:

Suppose the residents of these cities consume widgets, with consumption in each city equaling 100 widgets. The firm that produces widgets must decide how to arrange its production. It could set up four factories, one in each city, with each factory producing 100 widgets. In this case the firm incurs no cost for shipping its output. Or the firm could locate its factory in the centrally located city (D). The single factory must then produce 400 widgets, 300 of which are shipped to cities A, B, and C. The shipping cost per widget is \$2. A final assumption is that widget production exhibits economies of scale, with the cost per widget in a factory falling as output rises.

1. Suppose the cost per widget varies with output as follows: cost is \$4 if factory output is 100 widgets; cost is \$1 if factory output is 400 widgets. In this situation, find the lowest cost arrangement of production for the firm.
2. Repeat a. if the cost per widget varies with output as follows: cost is \$4 if factory output is 100 widgets; cost is \$3 if factory output is 400 widgets.
3. Explain intuitively any difference in answers to a. and b.
4. Suppose production costs are those given in a., and let shipping cost per widget be given by t. Although t=2 in a., what value of t would make the two arrangements for production equivalent in terms of cost?

1. Agglomeration
2. In your own words:
1. What are the three major sources of agglomeration economies, and how do the operate?
2. Explain the three main types of agglomeration effects. What difficulties exist in identifying those different classifications?
3. Which examples of industrial clusters in your region (Where you are now, or where you are most familiar with) best reflect each of the different types of industrial clusters?