In order to answer this question, what you need to do is to find three ordered pairs for each country. By finding these three points, you will be able to draw a production possibilities frontier.
It does not really matter what label you put on each axis. One axis has to be labelled “Kiwis” and the other has to be labelled “Bauxite,” but it doesn’t matter which is which.
To find our three points, we need to use the equations given for each country. For New Zealand, we will start by seeing how much bauxite will be produced when the country produces no kiwis. So, we set K equal to 0 and solve for B.
0 = 1000 – 50B
1000 = 50B
B = 20.
So we know that New Zealand can produce 20 units of bauxite when it produces 0 units of kiwis. This will be one of the intercepts for New Zealand’s PPF (depending on which axis you put kiwis on).
Now we look to see how many kiwis New Zealand can produce if it produces no bauxite. So we set B = 0 and solve for K.
K = 1000 – 0
K = 1000
So we know that New Zealand can make 1000 units kiwis if it makes 0 units bauxite. We now have the two end points for the PPF.
Let us find one more point. We will look at how much bauxite New Zealand can produce if it produces 500 kiwis.
500 = 1000 – 50B
500 = 50B
10 = B.
So we know that New Zealand can produce 500 units kiwis if it makes 10 units of bauxite. Now we have three points and can draw a curve through them to find New Zealand’s PPF.
Now we do the same things for Australia. We will find three points and you can graph them. Be sure that you keep all the points in the same order. They can be either (bauxite, kiwi) or (kiwi,bauxite), but you must be sure they are all in the same order.
If Australia produces no kiwis:
0 = 700 – 20B
700 = 20B
B = 35
So Australia can produce 35 units of bauxite when it produces 0 units of kiwis.
If Australia produces 0 units of bauxite:
K = 700 – 0
K = 700
So Australia can produce 700 units of kiwis if it produces 0 units of bauxite.
Finally, let us see how much bauxite Australia can produce if it produces 400 kiwis:
400 = 700 – 20B
300 = 20B
B = 15
So Australia can produce 15 units of bauxite if it produces 400 units of kiwis.
Again, put all three numbers for Australia in the same order that you put the numbers for New Zealand. They can be (K,B) or (B,K) as long as they are all in the same order. Make one graph using the three ordered pairs for New Zealand and another using the three ordered pairs for Australia.