Basic Microeconomics help!

Question

Australia and China both produce televisions and corn. In Australia, 1 hour of labour is required to produce a bushel of corn, while 8 hours are required to produce a television. In China, 2 hours of labour are required to produce a bushel of corn, while 5 hours are required to produce a television. China has 1000 labour hours, and Australia has 400 labour hours. To begin with, the two countries do NOT trade, and each of them devotes one half of its labour hours to the production of each good.

What is the opportunity cost of a television in Australia? Of a bushel of corn? What is the opportunity cost of a television in China? Of a bushel of corn?

Show how trade can benefit both countries. To do this, start by determining the consumption of each good in each country when they do NOT trade. Show that with trade, it will now be possible for each country to consume MORE of each good, if each country specializes in the good for which it has comparative advantage. Also, find the terms at which Australia and China would have to trade corn and televisions in order to achieve the combination of goods that you suggest.

From my calculations, they cant trade becuase australia doesnt produce enough corn to cover both aust and chinese sufficiency points, let alone produce extra corn for the countries to trade so they both consume extra corn?

Anyone with a little micoeconomics knowledge know where I'm going wrong here?!

Answer 1

Of course they can trade.

First off, Aust produces 200 corn and 25 tv before trade, and china 250 corn and 100 tvs. total = 450 corn and 125 tvs.

Aust has opor cost of 8 corn = 1 tv, china 2.5 corn = 1 tv.

With trade, if Aust produced all corn, it could produce 400 bushels, and if China did all TVs it could do 200. But we don't want less corn, so let's say China does 50 corn and they can still do 180 tvs, so we would have totals of 450 corn and 180 tvs, more total than w/o trade.

What is the exchange rate? 2.5 corn = 1 tv.