Question

1. The steel factory makes steel from iron ore and coal. Both iron and coal mines are near city A, while the demand for steel is in city B, which is 100 kilometers away. The factory makes 1 ton of steel from 1 ton of coal and 2 tonnes of iron ore. Shipping is costly and exhibits increasing returns to scale. Shipping 1 ton of goods (either raw materials or final products) incurs a terminal cost of $100 (the fixed cost incurred as long as one needs to ship something, no matter how far it is shipped) and $10 per kilometer a. Is the production of steel weight-losing or weight-gaining? (5 pts) b. Determine where the factory will be located in order to save as much as possible in shipping cost? Suppose that if the factory is built in city A, it has immediate access to coal and iron ore, no shipping cost involving raw materials is required. if the factor is built in city B, it has immediate access to the market, no shipping cost involving the final product is required. (10 pts) c. Now suppose that the coal mine near city A is depleted. Now coal is shipped to city B, which is also a major port city, from overseas. Suppose now if the factory is located in city B, it has imme diate access to coal, no shipping cost is incurred. Determine where the facotry will be located in this new situation. (5 pts)

Answer 1

Answer:

A)

It is weight loosing process, i.e. the weight of shipped out material is lesser than the weight of shipped in material. As 3 tons of raw material shipped (2 iron ore and 1 coal) produces 1 ton of steel to be shipped.
B)

It should be located in City A. As the product transported for 1 ton of steel is 3tons (Input) for city A and is 1 ton for City B(Output).
So if located in B, the transportation cost will be for 3 ton. Where as it is for 1 ton only in case of locating in city A.
The reason we are not exploring the possibility of locating in between is that: we have a fixed cost, so rather than having that fixed cost incurred at both the city, it is cost effective to incur it at one city by locating facility in other city.
C)

Now the transportation required for 1 ton of steel is 2 ton (input ore) for city A and 2 ton (1 ton coal and 1 ton steel output).
So using similar approach as used in B) , we can have facility in any of the city.
Hence In this case facility can be located in any city A or B