(3) Locations of Transfer-Oriented Firms Assume the distance between the resourc
ID: 1138489 • Letter: #
Question
(3) Locations of Transfer-Oriented Firms Assume the distance between the resource (R) and the market (M) is 10 miles. A firm's procurement cost is given by PC-x2, where x is the distance from the resource measured in miles. The firm's distribution cost is given by DC 100-0.5x2. Again, x is the distance from the resource. (a) What is the Total Freight Cost at each milestone (i.e, x-1, 2,3, ...). Where should the firm locate? (b) How does your answer to all parts under (a) change if the marginal procurement cost were equal to zero?Explanation / Answer
Answer:
given data is
Total freight cost (TC) = PC + DC = 20 + 9x + (10 - x)3
(a)
(i) x = 10
TC = 20 + (9 x 10) + (10 - 10)3 = 20 + 90 = 110
(ii) x = 5
TC = 20 + (9 x 5) + (10 - 5)3 = 20 + 90 + 125 = 235
(iii) x = 0
TC = 20 + (9 x 0) + (10 - 0)3 = 20 + 0 + 1,000 = 1,020
Since TC is lowest when x = 10, this is the ideal distance of location.
(b)
DC = 20 + (10 - x)3
TC = 20 + 9x + 20 + (10 - x)3 = 40 + 9x + (10 - x)3
(i) x = 10
TC = 40 + (9 x 10) + (10 - 10)3 = 40 + 90 = 40
(ii) x = 5
TC = 40 + (9 x 5) + (10 - 5)3 = 40 + 90 + 125 = 255
(iii) x = 0
TC = 40 + (9 x 0) + (10 - 0)3 = 40 + 0 + 1,000 = 1,040
Since TC is lowest when x = 10, this is the ideal distance of location.
The result is unchanged because the fixed cost incraeses the total cost equally for all 3 options.
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