PPFs: drawing, calculating opportunity costs, and allowing for technical change.

This post goes through another question, that starts with drawing a PPF, and continues onto discussing opportunity costs, and allowing for a change in the PPF due to a technical change.

Question: Imagine that a country can produce just two things: goods and services. Assume that over a given period it could produce any of the following combinations:

Units of Goods	Units of Services
0	80
10	79
20	77
30	74
40	70
50	65
60	58
70	48
80	35
90	19
100	0

a) Draw the country’s production possibility curve?
b) Assuming that the country is currently producing 40 units of goods and 70 units of services, what is the opportunity cost of producing another 10 units of goods?
c) Explain how the figures illustrate the principle of increasing opportunity cost?
d) Now assume that the technical progress leads to a 10% increase in the output of goods for any given amount of resources. Draw the new production possibility curve. How has the opportunity cost of producing extra units of services altered?

When drawing the PPF, we simply take the different combinations of goods and services and plot them on a graph, which will look similar to that below:

 Keep in mind that this graph isn’t to scale, but the intercepts are valid, at both 0,80 and 100,0 (the first and last point shown on the table above).  In order to make this graph to scale, you could go through each observation and place the point by hand (using a hand drawn graph with a ruler is probably your best bet).   Watch the video below, for information on how to draw a PPF:

Now on to the opportunity cost question.  When we decide to produce another ten units of goods, we have to give up producing some services.  If we look at the table above, we can see that to move from 40 units of goods to 50 units of goods, we will have to move from 70 units of services to 65 units of services.  Because we are now producing 5 less units of service, that is our opportunity cost.  So the answer to this question is 5 units of service is the opportunity cost.

The table and PPF also demonstrate the idea of increasing opportunity costs.  If we consider the first change (from 0 units of goods to 10 units of goods) we have to give up 1 unit of service.  However, when we change from 10 to 20 units of goods, we have to give up 2 units of service.  As we keep getting more and more units of goods, we have to give up an increasing number of units of service until we get to the last tradeoff from 90 units of goods to 100 units of goods where we have to give up a whopping 19 units of service.  You can see that at first we only had to give up 1 unit of service for 10 units of goods, but towards the end we had to give up 19 units of service for the same 10 units of goods.  This shows us that we have increasing opportunity costs.

Finally, if technical progress leads to a 10% increase in output of goods then we will see the PPF move right a little.  Since the technical progress didn’t affect services, we still intersect on the Y axis at 80, but now the possible amount of goods being produced increases to 110.  We can also re-write the table above adding 10% to the value of each number in the goods column.  This change means that the opportunity cost of producing services anywhere along the curve has gone down (because the slope has changed, it is now more steep).   Also, the change in each increment for units of goods will be 11, instead of 10.  So when we calculate the opportunity for each change in units of service, we will be dividing by 11 instead of 10 (the new change in units of goods) so that the opportunity cost of units of service will go down for each given increment.