Michelle and James each live alone in an isolated region. They each have the sam
ID: 1229178 • Letter: M
Question
Michelle and James each live alone in an isolated region. They each have the same resources available, and they grow potatoes and raise chickens. If Michelle devotes all her resources to growing potatoes, she can raise 200 pounds of potatoes per year. If she devotes all her resources to raising chickens, she can raise 50 chickens per year. (If she apportions some resources to each, then she can produce any linear combination of chickens and potatoes that lies between those extreme points. If James devotes all his resources to growing potatoes, he can raise 80 pounds of potatoes per year. If he devotes all his resources to raising chickens, he can raise 40 chickens per year. (If he apportions some resources to each, then he can produce any linear combination of chickens and potatoes that lies between those extreme points.)Michelle
200 = potatoes (1potato = 1/4 Chicken) - comparative advantage
50 = Chickens
James
80 = potatoes
40 = Chickens (1 potato = 2 Chickens) - comparative advantage
•Suppose that they are thinking of each specializing completely in the area in which they have a comparative advantage, and then trading at a rate of 2.5 pounds of potatoes for 1 chicken, would they each be better off? Explain.
Explanation / Answer
Michelle can either produce 50 chickens or 200 potatoes, so that's a ratio of one chicken to four potatoes. In other words, if she is currently producing at some intermediate combination, if she produces one more chicken, she loses four potatoes. Thus the opportunity cost of producing chickens (or more accurately, one chicken) is 4 potatoes. Likewise, if she produces four more potatoes, she loses a chicken, so the opportunity cost of producing potatoes (or more accurately, one more potato) is 0.25 chickens. James can either produce 40 chickens or 80 potatoes, so the ratio is 1:2. If he is currently producing at an intermediate position, one more chicken means he loses two potatoes. Likewise, one more pound of potatoes means he loses 0.5 chickens. Those are both his opportunity costs. Michelle has an absolute advantage in both activies, because she is capable of producing more than James in both industries using the same amount of resources. However, James has a comparative advantage in producing chickens, because producing one more chicken is only a loss of two potatoes, instead of the loss of four that Michelle suffers. Similarly, she has a comparative advantage in producing potatoes because she only loses 0.25 chickens as opposed to James' 0.5 chickens. So if James specializes in chickens, and Michelle specializes in potatoes, James will produce 40 chickens and Michelle will produce 200 pounds of potatoes. Let's say they trade 80 pounds of potatoes, so therefore 80/2.5=32 chickens, according to the exchange rate. James will end up with 8 chickens (40-32) and 80 potatoes, and Michelle will end up with 32 chickens and 120 pounds of potatoes. James is clearly better off, since we know that if he only produces potatoes, he will only make 80 pounds, and now he has that AND 8 chickens. Michelle now has 120 lbs of potatoes and 32 chickens. If made an equation from the data 200 potatoes and 50 chickens that we were given in the problem, we'd see that if she produces p number of potatoes, she will produce -0.25p+50 chickens. So if we plug in 120 into the equation, we get -0.25(120)+50 = 20 chickens. But now she has 32, so she's better off, too. Thus, they are both better off. As for extending the problem to businesses or a society, I would say that it proves that trade increases economic efficiency. By specializing, both nations can end up with production combinations that would have been unattainable otherwise, even if one nation has an absolute advantage in everything it produces.