All Terrain Thinking

A Compendium of things I think are Important

Economics: It's not just whats' in your wallet

Possibility Curves
A picture is worth a thousand words

If you believe there is any truth to the above phrase, then you should not be surprised to find economists have attempted to present their analysis of choice in visual form. The visual form is the possibility curve that describes graphically the options open to a decision maker.  This diagram could be used to describe the choice situations facing an individual, a firm, or an entire society. What you will see is the possibilities open to a decision maker depend upon two very important concepts - the level of available resources and the productivity / efficiency with which those resources can be employed to produce an output. 

I suggest you make the investment needed to understand these graphs since you are likely to see them again. The practice at interpreting and creating graphs will prove valuable as we go further into the course and these diagrams are quite useful in highlighting the similarities in a wide array of choice situations. We will also use the model to look at issues as diverse as war, international trade, the cost of an MBA program, and the cost of a good grade in Economics. 

As a warm-up exercise to see what we are talking about with this possibility curve model, let's return to RIU where we will now look at students' study choices and the administration's choice of the mix of class sizes.  We can begin by examining the situation facing Fred as he begins the semester. To make life easy, let's assume Fred is taking this Economics course and a History course and he must decide how to allocate his time. Time is the scarce resource he will need to allocate in an effort to produce grades, the output. You also know that his grade in each course depends upon the time he puts into study for the course and on the productivity / efficiency of his study time. What we would like to know are the choices open to Fred who is allocating the time.

To demonstrate the choices graphically, we will construct a 'grade' possibility curve for Fred. On the two axes we will measure the outputs, in this case they will be grades in the two courses.  On the vertical axis we will measure the grade Fred gets in economics and on the horizontal axis we will measure the grade Fred gets in history.  

As for the available resources, we will assume that Fred has 10 hours to study for Economics and History (we must be talking about only one day). You have reason to believe each hour spent studying History brings improves his History grade in the course by 6 points, and each hour spent on Economics improves his Economics grade by 5 points. Given these resources and productivities, we can fill in Fred's grade-possibility diagram that appears below.

The blue grade possibility line presents visually the choices open to Fred.  Any point inside the line is achievable, but all of the resources would not be used.  Fred would not be using the ten hours for studying if we found Fred getting grades that were inside of the possibility curve.  An example would be if Fred received a grade of 20 in both courses.  

Any point outside of the line would be impossible to attain given the existing resources.  Given the current situation, Fred could not get a grade of 50 in both courses.  The points on the line represent all of the possibilities open to Fred.  By choosing a specific allocation of the ten hours between HIS and Economics Fred would be on one of the point on the possibility curve.  For example, Fred could use all 10 hours studying Economics and get a 0 in History and a 50 in Economics (horizontal intercept), or he could use all of the time studying History and get a 0 in Economics and a 60 in History (vertical intercept). If Fred split the ten hours evenly between the two, the History grade would be 30 and the Economics grade would be 25.

So what advice do we give Fred who wants to do better? How can Fred improve his grades? If you return to the making of the graph, you may see the options open to Fred.  He can either increase the resources (time) devoted to study or increase the productivity of that study time. Let's look at what happens if Fred decides to devote 12 hours to studying. If Fred spends all 12 hours studying Economics then he can get a grade of 60, while 12 hours spent studying History would give him a grade of 72. As you can see from the outward shift in the grade possibility diagram below, Fred can now attain what was unattainable before.

But there are other ways to extend the possibilities. Fred could work to improve study habits, maybe no TV while studying or forming a study group to work with someone from the class. Let's look at the situation where Fred increases his productivity in Economics so each hour in Economics  now translates into 6 points. The new grade possibility curve appears below and once again Fred can attain what was once unattainable.

As you work through other examples, keep in mind the four features of the graph mentioned below are important and you should keep the list in mind as you create or interpret a possibility diagram. These features determine the nature of the story being conveyed by the graph.  The four important features of a possibility graph are:

• Slope: rate of exchange / production technology/productivity
• Curvature: substitutability of factors
• Height: resource availability - productivity
• Location: efficiency (static / dynamic)

Now you are ready to look at a few examples of where this analysis can be used. If you are interested in some additional warm-up, you might want to look at the situation of an individual entering an MBA program who must make choices regarding the allocation of time. You could also look into the choice between consumption and investment - a choice that individuals, firms, and nation's must deal with. With these warm-ups you will be ready for our discussion of the end of war.

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