There are economies of scale in ranching, especially with regard to fencing land

Question

There are economies of scale in ranching, especially with regard to fencing land. Suppose that barbed-wire fencing costs $10,000 per mile to set up.

How much would it cost to fence a single property whose area is one square mile if that property also happens to be perfectly square, with sides that are each one mile long?

$ for the single one-square-mile property

How much would it cost to fence exactly four such properties, which together would contain four square miles of area?

$ for four of the one-square-mile properties

Now, consider how much it would cost to fence in four square miles of ranch land if, instead, it comes as a single large square that is two miles long on each side.

$ for the single four-square-mile property

Which is more costly—fencing in the four one-square-mile properties or the single four-square-mile property?

Explanation / Answer

each side is one mile, each mile is $10,000, so 4 sides * 10,000 = $40,000 With four such properties, each side would be 2 miles. If we assume that the 4 plots are all touching in a square, we would add 2 sections each 2 miles long to divide each of the four properities for a total of 12 miles. at $10,000 a mile this would be $120,000. To fence in a four square mile area, there would only be 4 sides of 2 miles each to fence in, instead of the additional fence area to divide up the parcels. 4 sides, 2 miles each is a total of 8 miles of fence and at $10,000 a mile this would be a cost of $80,000 It is more costly to fence in the four one-square mile properties than a single four-square mile property

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