Question

there are economies of scale in ranching, especially with regard to fenching land. Suppose that barbed-wire fencing costs $18,000 per mile to set up.

Answer 1

If fencing cost $10,000 per mile, then to fence a single property in a shape of a perfect square with 1 mile sides, it would cost $10,000 per side, for a total of $40,000 for the entire property. Then, to fence four identical properties will cost four times $40,000, or $160,000. So, in fencing four identical one square-mile properties, or a total area of four square-miles, the total cost will be $160,000. Now, suppose there is another perfect-square property with 2 mile sides. The total square-mileage of this property is 4 square-miles which is exactly the same area as the four properties with 1 mile sides put together. The cost to fence this 2 mile per side property is then $20,000 per side ($10,000 per mile x 2 miles), and since the property has four sides, so, the total cost will be

Thus, to fence a single four-square-mile property, it will cost $80,000. It is then more costly to fence four one-square-mile properties than it is to fence one four-square-mile property, which shows that there are economies of scale in fencing.