Two regions A and B both produce firewood and baseball bats

Two regions, A and B, both produce firewood and baseball bats. These two products use just two inputs: wood and labor. To make a \"truckload\" of each of these products, the following amounts of each input are required. The cost of the inputs in the two regions is as follows: How much does it cost to make a truckload of firewood and a truckload of baseball bats in each of the two regions? If the market in each region requires five truckloads of baseball bats and five truckloads of firewood, how much would it cost each region to produce all its own requirements? Assume that both goods can be shipped between the two regions for $40 per truckload. Would the total cost of production and transportation of both goods in both regions be lower if Region A specialized in producing firewood and Region B specialized in producing baseball bats? (Assume five truckloads will be shipped). Compare the total cost for autarky and specialization. What would the total cost of production and transportation be for both regions if the shipping cost increased to $150 per truckload? What do these results tell us about the benefits of trade and the role of transportation cost?

Solution

a) The cost of 1 truckload of firewood in Region A is 12*15 + 18*7 = 180+126 = $ 306

               The cost of 1 truckload of firewood in Region B is 10*15+ 29*7 = 150+203 = $353

               The cost of 1 truckload of baseball bats in Region A is 12*125 + 18*3 = 1500+54 = $ 1554

               The cost of 1 truckload of baseball bats in Region B is 10*125+29*3 = 1250+87 = $1337

b) If the two regions A and B produce their own requirements of 5 truckloads of firewood and five truckloads of baseball bats on their own, then:

The cost of 5 truckloads of firewood and 5 truckloads of basketball bats in Region A = 5*306+5*1554 = 1530+7770= $ 9300

              The cost of 5 truckloads of firewood and 5 truckloads of basketball bats in Region B = 5*353+5*1337 =  

1765+6685= $ 8450

      

c) If the region A specializes in producing firewood and the region B specialises in producing baseball bats and if 5 truckloads of these two commodities are shipped between the regiona A and B, then:

The cost of 5 truckloads of firewood and 5 truckloads of basketball bats in Region A =5*306+ 5*1337+ 5*40 = 1530+6685 +200 = $ 7015

The cost of 5 truckloads of firewood and 5 truckloads of basketball bats in Region B =5*306+ 5*1337+ 5*40 = 1530+6685 +200 = $ 7015

d) If the shipping cost increases from $40 per truckload to $ 150 per truckload, then:

The cost of 5 truckloads of firewood and 5 truckloads of basketball bats in Region A = 7015+5*110 = $7565

The cost of 5 truckloads of firewood and 5 truckloads of basketball bats in Region B = 7015+5*110 = $7565

  

e) From the above data, it can be inferred that the cost of 5 truckloads each of Firewood and Baseball bats in both the Regions A and B goes down if these Regions restrict themselves to their own repective areas of specialization and import the other commodity from the other Region. This advantage will remain for Region A, till the cost of shipment of 5 truckloads of baseball bats from Region B touches 9300- 6815 = $ 2485 i.e. 2485/5 = $497 per truckload.

Similarly, the lower cost advantage will remain for Region B, till the cost of shipment of 5 truckloads of firewood from Region A touches 8450-6815= $1635 i.e $ 1635/5 = $ 327 per truckload.