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Constructing Indifference Curves

Using Indifference Curves

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In the previous section "Indifference Curves - How Do I Use and Understand Them?" we learned that our job was to figure out who to hire and for how many hours in order to produce the number of hockey skates that we need. The productivity of each employee is given on the bottom of the page in the section Indifference Curve Data.

Let's suppose the sales department informs us that we need to assemble 90 hockey skates today. How can we do it?

Goal: Assemble 90 Skates

Looking at our indifference curve chart, there's a couple of ways we can get this done.

One way would be to hire Sammy for 1 hour of work. In Sammy's first hour of work we know that he can assemble 90 skates.

Another way would be to hire Chris for 3 hours of work. Since Chris can assemble 30 skates an hour, we need to hire him for 3 hours to meet our production quotas.

From a production point of view (though not necessarily a cost point of view), we do not care how we assemble the 90 skates. We just need the work done. Hence we are indifferent between hiring Sammy for 1 hour and hiring Chris for 3 hours.

We can show this relationship graphically . We have two decision variables here, the first being the number of hours we assign to Sammy, and the second the number of hours we assign to Chris. Thus let's put the number of hours we assign to Sammy on the Y-axis and the number of hours we assign to Chris on the X-axis.

The first point on our graph is the point where Chris works 0 hours and Sammy works one. To represent this we will make a point at (0,1).

Our second point on our graph is the point where Chris works 3 hours and Sammy works zero. To represent this we will make a point at (3,0).

There are also other possible combinations of hours that Chris and Sammy could work to assemble 90 hockey skates if we allow for fractions of hours. One such one would be where Chris works for an hour and a half, and Sammy works for half an hour. To represent all these possible combinations, we will draw a line from our points (0,1) and (3,0). When you have done this, your indifference curve should look like indifference curve 1.

This blue curve (line) that we have drawn represents all the possible combinations of working time that will allow us to assemble exactly 90 hockey skates. From a production perspective any possible point on this blue line is just as good as any other point, as they will all lead to 90 skates being assembled.

We can continue our analysis by considering another level of production. In Constructing Indifference Curves - Part 2 we do just that.

Indifference Curve Data

Hour Sammy's Chris's
Worked Production Production
1st 90 30
2nd 60 30
3rd 30 30
4th 15 30
5th 15 30
6th 10 30
7th 10 30
8th 10 30

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