Question

Consider the following scenario. Xavier and Yannis can switch between producing baskets and produc-
ing birdhouses. Xavier uses 8 hours to produce 1 basket and 2 hours to produce 1 birdhouse. Yannis
uses 1.5 hours to produce 1 basket and 2 hours to produce 1 birdhouse. In 24 hours, Xavier can produce
3 baskets and 12 birdhouses, and Yannis can produce 16 baskets and 12 birdhouses. If they decided
to trade with one another, at which of the following prices would both Xavier and Yannis gain from
trade? Justify your answer

a. 30 baskets for 15 birdhouses
b. 30 baskets for 18 birdhouses
c. 30 baskets for 24 birdhouses

Answer 1

As per the question,

In 24 hours, Xavier can produce
3 baskets or 12 birdhouses, and Yannis can produce 16 baskets or 12 birdhouses.

So, We must find out who will specialize in producing what. As both are capable of producing 12 birdhouses while Yannis is producing 16 baskets while Xavier is producing only 3 baskets in 24 hours.

So we see clearly Yannis has an absolute advantage in producing baskets. While Xavier will produce birdhouses.

So, Now for exchange,

Xavier who is producing birdhouses would want Baskets in exchange from Yannis. So we can see for Xavier opportunity cost of producing 12 birdhouses is 3 baskets. So Opportunity cost of producing 1 birdhouse = 3/12 = 1/4 basket. So if he gets more than 1/4 basket in exchange for every 1 birdhouse he will gain from trade.

Now, For Yannis who is producing baskets would want birdhouses in exchange from Xavier. So we can see that for Yannis opportunity cost of producing 16 baskets is 12 birdhouses. So opportunity cost of 1 basket = 12/16 = 3/4 birdhouse. So if he gets more than 3/4 birdhouse in exchange for every 1 basket he will gain from trade.

So now let's see each option.

a. 30 baskets for 15 birdhouse :- For Xavier 15 birdhouse must give more than 15*(1/4) basket = 15/4 = 3.75 baskets. Since 30 is greater than 3.75, Xavier will gain from trade. Now for Yannis 30 baskets must give more than 30*(3/4) = 22.5 birdhouse. Since 15 is less than 22.5, Yannis will not gain from trade.

b. 30 baskets for 18 birdhouse :- For Xavier 18 birdhouse must give more than 18*(1/4) basket = 18/4 = 4.5 baskets. Since 30 is greater than 4.5, Xavier will gain from trade. Now for Yannis 30 baskets must give more than 30*(3/4) = 22.5 birdhouse. Since 18 is less than 22.5, Yannis will not gain from trade.

c. 30 baskets for 24 birdhouse :- For Xavier 24 birdhouse must give more than 24*(1/4) basket = 24/4 = 6 baskets. Since 30 is greater than 6, Xavier will gain from trade. Now for Yannis 30 baskets must give more than 30*(3/4) = 22.5 birdhouse. Since 24 is greater than 22.5, Yannis will also gain from trade.

So, From above we can see in option a and b only Xavier is gaining from trade while Yannis was not. Whereas in option c both Xavier and Yannis were gaining from trade.

• Hence, Option c. 30 baskets for 24 birdhouses is correct