quick question?

DR.ZOIDBERG

Hi everyone first time poster here but long time lurker, Im having a bit of a problem with a college economics question for my revision, I having a feeling the answer is very simple but for some reason I can not wrap my head around it at all, any help would be much
appreciated!

"Assume a two-country, two-good, two-factor of production world with the countries being the United States and the Rest of the World, the two goods being cars and wheat, and the two factors of production being capital and land. Further assume that the United States is capital-abundant and car production is capital-intensive. Suppose that in autarky the United States operates at a point on its production possibilities curve where it produces 50 units of wheat and 50 units of car. Once international trade opens, the international price of one unit of car is three units of wheat. In response to the opening of trade, the United States moves along its production possibilities curve to a new point where it produces 70 units of steel and 10 units of wheat. Is the United States better-off following the opening of trade? Provide a logical proof of your answer and illustrate it diagrammatically. "

irish_goat

Let's assume we're talking about dollars here and that the price of 1 unit of wheat is $1 and 1 unit of car is $3.(the question changes in the 2nd half to steel instead of cars but I'm assuming that must be a typo).

Initially the US is producing:
50 wheat = $50
50 cars = $150

Total = $200

When they readjust they produce:
10 wheat = $10
70 cars = $210

Total = $220

So they're $20 better off.
Draw it out on a graph and it should be clearer too.

DR.ZOIDBERG

thanks for the reply, would I be right in saying the best way to graph this would be to use a supply and demand curve?