Indifference Analysis

Back to a more educational point of view now following the last post I wrote. Today will be a look back, potentially in more detail, at the concept of indifference analysis. I'll try and start at the very basics and work my way through the subject - if you feel I've left anything out do not hesitate to let me know in a comment and I'll try and go over it for you. This post is long, I won't hide that fact. Make full use of the search bar to the left of this to make sure this contains what you're looking for. Even better still, use Ctrl + F and search for keywords. That could save you some time!

Indifference analysis is a basic concept in economics which looks at consumers preferences for two goods. It is an "exactly what it says on the tin" topic - we are looking at combinations of these two goods that the consumer would feel indifferent about. The definition of 'Indifferent' from dictionary.com, by the way, is "having no bias, prejudice, or preference; impartial; disinterested." So, rephrasing it into Layman's terms: we are looking at combinations of these two goods that the consumer would feel equally as happy, content, etc with. This will become evident later on in the analysis.

The very first step in the analysis will be to construct an indifference curve. This is done below.

Here we have an indifference curve. This is modelling different combinations of Good A and Good B that the consumer would feel indifferent about. Anywhere along this curve the consumer will be feeling the same level of satisfaction. Indifference curve slope downwards - that is a general rule. Why? I hear you ask. Well, it's due to the diminishing marginal rate of substitution. This piece of jargon essentially means the rate at which we would swap Good A(Y) for Good B(X) while remaining equally as satisfied. It looks as follows:

                                               
If we used some figures as an example, let's say that the consumer is indifferent between 25 of Good A and 5 of Good B and is also indifferent between 20 of Good A and 6 of Good B. Right. So, the top of the equation would be (20 - 25) and the bottom of the equation would be (6 - 5). That leaves us with -5 as the answer. So, between the points (25,5) and (20,6) on a diagram the slope would be -5. We can focus in on the negative sign here, this shows why the curve is always downwards sloping. We have to give up some of Good A to get more of Good B. Keeping up? Good.

An indifference curve alone tells us very little, an indifference map on the other hand tells us a lot more. An indifference map is a series of indifference curves showing which combinations of two goods give different levels of satisfaction.

If you think of the map as a mountain, starting from the bottom left corner and working diagonally to the right and up - the higher up the mountain we go the more satisfied the consumer. At any point on I4 the consumer is more satisfied than at any point on I2 for example. The question that creeps up a lot regarding indifference curves is "Could they ever cross?" In short, the answer is no. This can be proved via contradiction.

Consider the three points here: a, b and c. From the analysis we've just done we can say that a is indifferent to b. We can also say that a is indifferent to c. So, b 'should' be indifferent to c. But b has more of Good A for the same amount of Good B than c does, and therefore point b would be preferred. b and c aren't indifferent, and therefore indifference curves cannot cross. Bosh!

Now, for a consumer to make a decision about what to consume we need more information than just the indifference curves. We need information on prices and incomes. This is where the budget line enters. I fear I'm stating the obvious here, but I'll have to continue: the budget line is how much of the two goods the consumer can afford. So, it'll have the following formula, which reads 'Price of Good A times the quantity of Good A plus the price of Good B times the quantity of Good B equals the consumers income:

If Good A was £2,  Good B was £1 and the consumer's income was £30 then we'd have an equation to work out: 2A + B = 30. Now we have our equation we can plot the budget line on a graph.

It is literally as simple as that for the budget line. All we need is the price of the two goods and the consumer's income and we can work out the quantities of each good they can purchase. While on the topic of the budget line I think I'll mention what happens to the line when prices and incomes change. If just one price changes then the budget line will swing in or out, pivoting around a point. For example, if the price of Good B fell, then we'd see the line swing out to the right, pivoting around the point on the Y axis. It would swing out because a fall in price of Good B means we can afford more of them. A rise in price causes a swing in. A change in the total budget or consumer's income means a shift in the whole budget line parallel to the current one. A rise in the budget shifts the curve out to the right, a fall in the budget shifts it in to the left. If both incomes and prices rise by the same percentage, or fall by the same percentage for that matter, we see no change in the budget line.

Moving swiftly on, we're ready to combine the indifference map and the budget line. This can give us the consumer's optimal consumption point. Utility or satisfaction for the consumer is maximised at the point of tangency between the budget constraint and the indifference map, as is highlighted in the graph below.

The slope of the indifference curve is the marginal rate of substitution and the slope of the budget constraint is (minus) the relative price of Good A and Good B. Therefore, where these meet, the consumer chooses optimally when MRS = Price of Good B / Price of Good A.

Another piece of jargon you may need to learn is the 'Price-Consumption curve'. This is a curve derived from the changing price of one of the goods. From this curve we can create a demand curve for that good. Clever stuff.

Now, to derive the demand curve from it. We make one alteration to the diagram above, we make the Y axis 'Expenditure on all other goods' instead of just Good A. Then, we follow the points of tangent down and onto a new diagram. On the Y axis of the below diagram we list the prices, which come from dividing the Budget by the quantity of Good B when expenditure on all other goods is 0. Match these prices up to the lines we've just drawn down and Bob's your uncle - a demand line. In words it sounds confusing, take a look at the diagram below and then re-read this until sense is made.

I hope that makes sense - reread and study the diagram.

Another 'special' curve we need to be aware of is the Income-Consumption curve. This tracks the effect a change in income has on our optimum choices of the two goods. The slope of this curve tells us about the desirability of Good A and Good B as incomes rise. In general, the curve will look something like this:

There is a special case where the shape of this curve bends the other way. This is when one of the goods is an inferior good - I trust we all know what that means. A higher budget will mean less is demanded and therefore the income consumption curve will bend back on itself.

Bravo to those of you that have made it this far and hello to those that skipped straight to this section. Neither of you will be judged... honest. Finally, we are going to look at the Engel Curve. An Engel Curve shows how the demand for a good changes as income changes. We use the Income-Consumption curve and track it down onto a new diagram below.

If incomes increase and this leads to a demand increase for the good then we are looking at a normal good. If demand decreases it is an inferior good. The final, more peculiar outcome, is in the case of a giffen good. Giffen good prices rise when demand rises, odd - but they do exist.

By gosh, I think we might be finished. I said 'potentially' more in depth at the beginning - I think that word can be scrapped. If you're still unsure of anything Indifference Analysis related then drop me a comment and I'll be happy to try and help you out if I can. Thank you for reading, have a good day!

Sam.

Principles of Economics: The Budget Line (Microeconomics)

This post will make the next logical step on from indifference analysis by introducing the concept of the budget line. The budget line shows us the combinations of two goods that can be purchased with a given income to spend on them at their set prices. You guessed it, a graph is coming! The easiest way to show a budget line is for me to construct a diagram. Here is it, this is a budget line for good X and good Y assuming good X costs £2 and good Y costs £1 and the budget available is £30.

The area above the line isn't feasible to achieve given the prices of the two goods and the budget available. If incomes were to increase, say to £40 or the prices of both goods were to fall by the same percentage we would see the budget line shift as is shown in this next diagram. The rule is, changes in income or equal changes in price will cause the budget line to shift parallel to the original curve. Here's the new curve with an increased budget of £40:

The slope of the line here represents the relative price of the two goods. So in the example above it was 30/15 = 2 for the first line and 40/20 = 2 for the second line. The rule of thumb for that is Price of Y / Price of X. Prices can also change independently of each other, as we well know. If one price changes and the other doesn't, this causes a pivot on the diagram. If good X changed from £2 to £1 we'd see a pivot around the initial point on the Y axis. This next diagram will show that:

The pivot here is quite clear, as the price of good X decreases it means more can be consumed while the consumption of good Y remains constant. 

Next, we'll move on to a more complex concept - the optimum consumption point! This is where we combine the budget line from above and the indifference curves from the blog post I did a few days back. By definition, the optimum consumption point will be where the budget line touches the highest indifference curve on an indifference map. As with most concepts, this is also much easier to understand when represented on a diagram:

Here you can see that the budget line touches, or is tangential, to the indifference curve L2, which is the highest one it touches. Therefore we can say that the optimum consumption point for these two goods would be X1 of good X and Y1 of good Y. We know the slope of the budget line is Px / Py and we know from the previous blog post that the indifference curve slope at any point is MuX / MuY. Therefore, the optimum consumption point is the point where (Px / Py) = (MuX / MuY)!

A change in income will cause a change to the diagram. The budget line will either shift out or in depending on whether incomes rose or incomes fell. This new budget line would cross and indifference curve at a different point, if you joined the new optimum consumption point and the old one you'd have created a new line that we call the income-consumption curve in economics. As with a change in price of one of the goods, the budget line will pivot and a new optimum consumption point will be formed. Connect the original point and the new point and this line you've created is called the price-consumption curve. 

Now for the exciting bit! Actually deriving a consumers demand curve for a good!  

Ok, there is a demand curve derived for good X using the indifference curves and budget lines. Look at it, take it in, see if you can see what's going on. It's difficult, I know. Here's my explanation attempt: On the top diagram we have used good X along the bottom and money for all other purposes on the Y axis. We have a set budget and at varying prices of X this budget line is pivoting. Each of these new pivoted budget lines crosses indifference curves at different points to form a price-consumption curve. The points of intersection of each budget line translate down to as the quantities demanded of good X. Now, to work out the prices for the second diagram. Lets look at the first budget line for this. It crosses L1, we can see that. At that point it has translated down to the bottom diagram as Q1. The price here is the same as the slope of the curve.. so assuming we have a budget of £30 I'd say the budget line hits the X axis at roughly 17. So, 30/17 = 1.76, which is the roughly where the point is on the second diagram. If we did the same for the other two budget lines we'd receive prices of 1.2 and 0.94. These are those two other price points you can see on the diagram. Then as with any other demand curve, join the dots to actually complete the demand curve for good X. PHEW!

That's it, finally. It may be difficult to grasp in parts, if it is then comment with where you are finding it difficult and I'll give you a helping hand. I'll get back to you within a few hours normally, so keep checking back! Thanks for reading again guys, have a good day.

Sam.