Question

Two manufacturers, Take-A-Paws (Paws) and Raise-The-Woof (Woof), each make dog collars and dog leashes, and they each operate 10 hours a day. Paws has 10 workers and Woof has 20 workers. In a given hour, Paws can produce 3 collars or 4 leashes, whereas Woof can produce 7 collars or 5 leashes. Part 1. Indicate whether the following statements are true (T) or false (F) and explain why: A. Since Woof has the absolute advantage in collars, Woof should produce only collars. B. Paws has the absolute advantage in leashes Part 2. The two companies decide to join each other in production and are open to trading with the rest of the world. The world price of a leash in terms of collars is x. Suppose that Paws produces only leashes: check all of the price ranges where all x within that range are feasible (in terms of collars per leash) and explain why:

Answer 1

In a given hour, Paws can produce 3 collars or 4 leashes whereas, Woof can produce 7 collars or 5 leashes.

Paws has 10 workers whereas, Woof has 20 workers. Now, working for 10 hours a day, Paws can produce 30 collars or 40 leashes whereas, Woof can produce 140 collars or 100 leashes.

1) Here, as Woof can produce more of both the goods, Woof has absolute advantage in the production of both goods over Paws. Thus, the given statement is incorrect.

Again, opportunity cost of producing collars in Paws = units of leashes sacrificed/units of collars produced = 40/30 = 1.33

and opportunity cost of producing leashes in Paws = units of collars sacrificed/units of leashes produced = 30/40 = 0.75

Similarly, opportunity cost of producing collars in Woof = units of leashes sacrificed/units of collars produced = 100/140 = 0.7

and opportunity cost of producing leashes in Paws = units of collars sacrificed/units of leashes produced = 140/100 = 1.4

A) As opportunity cost of producing collars is lower for Woof, Woof has comparative advantage in the production of collars. Since, Woof has comparative advantage in production of collars, Woof will produce collars only.

B) As opportunity cost of producing leashes is lower for Paw, Paw has comparative advantage in the production of leashes. Since, Paw has comparative advantage in production of leashes, Paw will produce leashes only.

2) When opened to trade, the world price of leash in terms of collars is x.

Woof's price of leashes in terms of collars is 0.75 collars per leash (i.e, opportunity cost of producing leash for Woof) and Paw's price of leashes in terms of collars is 1.4 collars per leash (i.e, opportunity cost of producing leash for Paw).

Then, the feasible range for x is : 0.75 collars per leash < x < 1.4 collars per leash.

Above and below this range trade will not be possible.