There are economies of scale in ranching, especially with regard to fencing land
ID: 2494902 • Letter: T
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. a. 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? $. b. How much would it cost to fence exactly four such properties, which together would contain four square miles of area? $.c. 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. $.d. Which is more costly-fencing in the four, one-square-mile properties or the single four-square-mile property?Explanation / Answer
a)
Perimeter of the fencing land = 4×side = 4×1 = 4 miles
Cost of fencing = $10,000 per mile
Thus, total cost of fencing the given land = 4×$10,000 = $40,000
b)
Cost of fencing 4 such properties = 4×$40,000 = $1,60,000
c)
New perimeter of the fencing land = 4×side = 4×2 = 8 miles
Cost of fencing = $10,000 per mile
Thus, new total cost of fencing the given land = 8×$10,000 = $80,000
d)
It is more costly to fence the 4 properties together.
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