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

Explanation / Answer

In fencing in a 1 square mile area, each of 4 sides is 1 mile long, so it would cost 4*10,000 = $40,000 dollars to fence in this area To fence 4 separate properties of the same size, this would be 4 * $40,000 = $160,000 dollars. If instead the 4 square mile area were fenced in as a single unit, each of four sides would only be 2 miles long. Each side would then cost 2 * 10,000 = $20,000. Since there are 4 sides, the total cost of fencing in this area would be 4 * $20,000 = $80,000. As such, it would be cheaper to fence in the single four square-mile property than four, one square-mile properties

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