Answer:
a. The production process shows that the more the quantity produced, the less the average cost of production. It proves that there are advantages arising from economies of scale.
AC with Q = 150 = $10 ($1,500/150) and
AC with Q = 750 = $2 ($1,500/750)
b. The optimal arrangement is (centralized production) to produce the 750 routers at city C and ship to the 4 other cities.
c. AC with Q = 150 = $10 (14000/(150+1250) and
AC with Q = 750 = $7 (14000/(750+1250)
d. The cost-minimizing arrangement of production in this case is decentralized production.
e. The average cost of producing 150 units at the various cities has remained unchanged while the average cost of producing the 750 units at city C has increased from $2 to $7.
f. Suppose now production costs are those given in part (a) but let shipping cost per router be given by t (in the preceding discussion, we had t = 6, now we assume we don’t know the cost of shipping).
The value of t that would make the two arrangements for production (centralized versus separate factories) equivalent in terms of cost is:
t = $10 per router
Therefore, centralized production cost will be equal to $7,500 ($1,500 + ($10 * 600), and decentralized production cost will remain at $7,500 (750 * $10).
Explanation:
a) Data and Calculations:
Cities with consumers of wi-fi routers = A, B, C, D and E
Demand for routers by each city = 150
Total number of routers required = 750 (150 * 5)
b) Suppose the average cost of producing a router is AC (Q) = 1500/Q, where Q is the number of routers produced in a factory:
Therefore AC with Q = 150 = $10 ($1,500/150) and
AC with Q = 750 = $2 ($1,500/750)
Cost of Production of routers in city C:
cost of producing 750 routers at $2 per router = $1,500
Shipping cost of 600 routers to 4 cities at $6 per router = $3,600
Total cost of producing at city C = $5,100 ($1,500 + $3,600)
Total cost of producing 750 routers at 5 cities = $7,500 ($1,500/150 * 750)
c) Suppose the average cost of producing a router is AC = 14000/(Q+1250):
Therefore, AC with Q = 150 = $10 (14000/(150+1250) and
AC with Q = 750 = $7 (14000/(750+1250)
Cost of Production of routers in city C:
cost of producing 750 routers at $7 per router = $5,250
Shipping cost of 600 routers to 4 cities at $6 per router = $3,600
Total cost of producing at city C = $8,850 ($5,250 + $3,600)
Total cost of producing 750 routers at 5 cities = $7,500 ($1,500/150 * 750)
d) $7,500 = $1,500 + tQ
where Q = 600 (150 * 4)
Therefore, $7,500 - $1,500 = t600
simplifying
t600 = $6,000
t = $6,000/600 = $10
