Suppose a factory can produce a shirt for the equivalent cost of 2 loaves of bre
ID: 1189172 • Letter: S
Question
Suppose a factory can produce a shirt for the equivalent cost of 2 loaves of bread, and a household can produce a shirt for the equivalent cost of 8 loaves of bread. The factory is located in a rural area with a uniform population density. It costs the equivalent of 0.5 loaves of bread for a household to make a one-mile trip to or from the factory (of course they have to travel both directions!)
a. Assuming the consumer price of a shirt equals the factory's cost of production, what will be the radius of the factory's market area?
b. Now suppose the factory develops an innovation that allows it to produce a shirt for the equivalent of 1 loaf of bread. What is the new radius of the factory's market area?
Explanation / Answer
The consumer will purchase shirt from factory when its cost is less than the household cost of producing the shirt.
Household cost of producing a shirt = 8 Loaves of bread.
The radius should be such that it costs the consumer less than 8 loaves of bread to purchase from factory.
Cost to the consumer will be cost of the shirt + Travel time cost of 1 loaf of bread for one mile round trip from the household to the factory and back. (0.5 + 0.5).
The radius of the factory's market area should 5 miles, because it will cost the consumer 7 loaves of bread.
When the radius is 5 miles cost = 2 loaves for the shirt + 5 loaves for the travel time = 7 loaves of bread.
An addition of 1 mile to the radius will equal the household cost for producing a shirt, hence the consumer will prefer to produce the shirt at household rather than going to the factory and purchasing it.
If the factory manages to reduce the cost to equivalent of 1 loaves of bread, then it can increase the radius to 6 miles, as the cost will still be 7 loaves which is less than the household cost of producing shirt.
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