The steel factory makes steel from iron ore and coal. Both iron and coal mines a

Question

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 immediate access to coal, no shipping cost is incurred. Determine where the facotry will be located in this new situation. (5 pts)

Explanation / Answer

A. As we can see, to produce 1 ton of steel we need 2 tons of iron ore and 1 ton of coal. Here quantity required of raw material is more than finished product. Hence, we can say that production of steel is weight losing

B. Usuall, it case of weight loosing products, factories are built in cities closer to raw material as raw material is heavier than finished product and raw material shipping cost will be more than cost of distribution of steel. Let us do the calculations to know the final answer

Cost in Scenario 1 (Factory in City A)

Cost in Scenario 2 (Factory in City B)

Hence , we can safely say that we should make factory in city A to save on raw material shipping cost.

C. If in the new situation, factory is located in city B we are saving on both raw material shipping cost as well as final product shipping cost. Hence, it is profitable to open factory in city B in this scenario.

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