Utility Part 1

Today’s post is about Utility. This will probably be the theme for the next couple of posts because it is a pretty important part of consumer preference economics.

Utility is a bit of a complicated topic. It used to be that when utility was a reference to a person’s overall well-being. It was a numeric measure of a person’s happiness. The problem with this is that it is very difficult to translate happiness into a number depending on choices. As such for the purposes of this brand of economics utility will used only as a way to describe preferences.

For economists all that matters is whether one bundle has a higher utility than another, how much higher really doesn’t matter. A utility function is a way of assigning a number to every possible consumption bundle such that more-preferred bundles get assigned larger numbers than less-preferred bundles. The only property of a utility assignment that is important is how it orders the bundles of goods. Because of the emphasis on ordering bundles of goods, this kind of utility is referred to as ordinal utility.

There are many examples of utility functions. A utility function looks like the following u(x₁, x₂). Depending on what type of goods there are different utility functions exist. For example with perfect substitutes. If we go back to the example of red and blue pencils we can see how this works. In this example all that mattered to the consumer is the number of pencils not whether they were red or blue. In this case the utility function looks like the following u(x₁, x₂) = x₁ + x ₂. To see that this works we can ask two questions. Is this utility function constant along the indifference curve and does it assign a higher label to a more-preferred bundle. The answer to both questions is yes, so we have a utility function.

If the consumer is willing to substitute good 1 for good 2 at a different rate, say 2 to 1 then we end up with a different utility function. It would look like this u(x₁, x₂) = x₁ + 2x₂. This means that the consumer values good 2 twice as much as good 1. The general form for a utility function with perfect substitutes is u(x₁, x₂) = ax₁ + bx₂ where a and b are some positive numbers that measure the value of goods 1 and 2 to the consumer.

Another type of utility function is for perfect complements. This is the case with left and right shoes. When these are the two goods the only thing that the consumer cares about is how many complete pairs of shoes they have. In this case the number of pairs of shoes that they have is the minimum of the number of right shoes you have x₁, and the number of left shoes you have, x₂. Thus the utility function of perfect complements takes the form u(x₁, x₂) = min{x₁, x₂}. If we look at shoes it is pretty easy to see that this holds. If we have 5 right shoes and 5 left shoes than the function would be u(x₁, x₂) = min{5,5} and so the utility would be five. If we increase the number of left shoes the utility should stay the same and we can test this. If we now have 5 right shoes and 7 left shoes our utility function would be u(x₁, x₂) = min{5,7} which equals 5. We can see here than that the function works.

The same way that we were able to change the one to one ratio of perfect substitutes also works here. As such the general formula for perfect complements is u(x₁, x₂) = min{ax₁, bx₂}. Where a and b are positive numbers that indicate the proportions in which goods are consumed.

This is a brief look at utility and some different types of utility functions. There is more to talk about however and so I will be posting more on this later in the week.

Marginal Rate of Substitution

Todays post is on the marginal rate of substitution. This is out of the third chapter of the textbook and is an important component of the indifference curve. The marginal rate of substitution is the slope of an indifference curve.

The name for the MRS comes from the fact that the MRS measures the rate at which the consumer is just willing to substitute one good for the other. If we take some small amount of good 1, Δx₁, away from the consumer. Then we give the consumer Δx₂, an amount that is just sufficient to put him back on his indifference curve, so that he is just as well off after this substitution of x₂ for x₁ as he was before. We think of the ratio Δx₂/Δx₁ as being the rate at which the consumer is willing to substitute good 2 for good 1.

One slightly confusing thing about the MRS is that it is typically a negative number. We’ve already seen that monotonic preferences imply that indifference curves must have a negative slopes. Since the MRS is the numerical measure of the slope of an indifference curve, it will naturally be a negative number.

The marginal rate of substitution measures an interesting aspect of the consumer’s behavior. Suppose that the consumer has well behaved preferences, that is, preferences that are monotonic and convex, and that he is currently consumer some bundle (x₁, x₂). We now offer him a trade: he can exchange good 1 for 2, or good 2 for 1, in any amount at a “rate of exchange” of E.

That is, if the consumer gives up Δx₁ units of good 1, he can get EΔx₁ units of good 2 in exchange. Or, conversely, if he gives up Δx₂ units of good 2, he can get Δx₂/E units of good 1. Geometrically we are offering the consumer an opportunity to move to any point along a line with slope –E that passes through (x₁, x₂), as depicted below.

We can now ask what the rate of exchange would have to be in order for the consumer to want to stay put at (x₁, x₂). To answer this question, we simply note that any time the exchange line crosses the indifference curve, there will be some points on the line that are preferred to (x₁, x₂) – that lie above the indifference curve. Thus if there is to be no movement from (x₁, x₂), the exchange line must be tangent to the indifference curve. That is, the slope of the exchange line, -E must be the slope of the indifference curve at (x₁, x₂). At any other rate of exchange, the exchange line would cut the indifference curve and thus allow the consumer to move to a more preferred point.

Thus the slope of the indifference curve, the MRS, measures the rate at which the consumer is just on the margin of trading or not trading. At any rate of exchange other than the MRS, the consumer would want to trade one good for the other. But if the rate of exchange equals the MRS, the consumer wants to stay put.

The MRS can also sometimes be useful in describing the shape of the indifference curve when we look at its behavior. For example, the perfect substitutes indifference curves are characterized by the fact that the MRS is constant at -1. The neutrals case is characterized by the fact that the MRS is everywhere infinite. The preferences for perfect complements are characterized by the fact that the MRS is either zero or infinity, and nothing in between.

This is a bit about the marginal rate of substitution. It is a very important concept that will be talked about in the future as well.

EconTalk on Aid, Migration and Poverty

Today I listened to a very interesting EconTalk with Michael Clemens from the centre for global development. It was an incredibly interesting conversation that focused on foreign aid and its impact on poverty as well as a lot of other global factors.

One of the most interesting things that I found out from this talk was that when you compare foreign aid and money sent back home by immigrants, the money sent back home privately comes up to about four times that of foreign aid. Clemens has said that while there is a positive benefit from foreign aid it is a very small benefit. A larger benefit comes from immigration.

They also talked a fair bit about the impact that immigration can have on the receiving countries and both the pros and cons of it. Overall this is a very interesting talk on global development and I highly recommend it. The EconTalk can be found here http://www.econtalk.org/archives/2013/07/clemens_on_aid.html

Habits

Today’s post will be quite a bit different from normal. I received a book as a present a while ago called “The Power of Habit” by Charles Duhigg. I have started reading the book as a way to try to analyze my own habits and see what I can do about changing them. Part of the idea of this blog for the summer was to learn better study habits. While this went okay at the beginning I have had a harder and harder time sticking with what I should be doing.

In an effort to change some of my habits I have started reading this book. Duhigg describes habits as having three parts, a cue that initiates the habit, a routine that is what we do, and a reward that is what we get. In learning to change your habits you need to be able to identify these three things about your habits.

Duhigg tells a lot of stories in his book about people who have changed their habits and about just how powerful habits can be. He even relates them to advertising in business and gives examples as to how habits and cravings are used there.

While I am looking to change several of my habits the book recommends starting with just one. He gives the example of a woman who stops smoking and in doing so changes her entire life. This is an example of a keystone habit that can make a big difference.

For myself probably the biggest habit that I have is of procrastination. It is something that affects my entire life, from not getting enough exercise to not getting my schoolwork done. This is something that I really want to work on changing and I think I will try to follow here as I read through the book, the small steps that I am taking towards doing that.

Economic Measures

I decided to do something a little bit different today. After having a conversation about different measures of a counties well-being I decided to do a bit of a discussion of some of them here. These are by no means all of the measures that exist out there merely a sample.

The first to talk about is the one that is most often used, that of GDP. The GDP of a country is the gross domestic product. This is the sum total of everything that is produced inside a country in monetary terms. Closely related to this is the GNP or the gross national product. The GNP is the sum of all of the citizens of a countries production, even if they are not in the country. This is what makes it differ from the GDP.

While both of these are reasonable economic measures of a countries well-being there are several problems that they both share. One of the first problems is that they do not include a lot of work that actually happens in the economy, any black market exchanges and any non-monetary exchanges are not counted. This includes stuff such as house work. Another problem with both of these measures is that while they are reasonable measures of economic well-being of a country they are not a good measure of the well-being of its people. While GDP-per-capita and individuals well-being is positively correlated it does not tell the whole story. GDP also does not say anything about the environmental impact that economic policies can have. Finally it also does not give a good indication of the inequality that there is in a country. While there are many more reasons than just these that there are problems with GDP these are some of the main ones.

Another popular measure used is the Human Development Index. This measure published by the United Nations Development Program is a combination of health, education and income for the population of a country. It has been revised and is now a fairly good measure of the well-being of the people in a country. It can also be adjusted for inequality which helps. Some of the problems with HDI is that it does not give any indication as to the environmental status of a country, it is purely concerned with the well-being of the population. The only time this would come into effect is if it started to affect one of the three indices.

A measure that has been developed to more accurately view the environmental aspect of economic development is call Green Gross Domestic Product or Green GDP. Green GDP is an attempt to factor in the environmental consequences of economic growth into conventional GDP. It monetizes the loss of biodiversity and accounts for costs caused by climate change. While this is a reasonable measure for economic growth factoring the environment, it in itself, is not a good measure for the overall well-being of the population of a country.

This a just a taste of the measures that are out there to look at. There are many more, and the reality is that we need to look at multiple measure to accurately determine the well-being of a country as a whole.

Econ Talk Michael Lind on Libertarianism

Today I listened to an Econtalk. I am still not feeling one hundred percent so until I am I will be posting every day but it might be shorter than usual.

Today’s Econtalk was a discussion on libertarianism. Libertarianism is a political and economic idea that liberty is the highest ideal. They usually support free market ideas and limited government intervention. The conversation was on how there seem to be no countries that have ever had a true libertarian society and how it can be difficult to support it given that it has not really been put into practice.

The second part of the econ talk was about how the basic ideas that are taught in beginner economics courses can make for bad policies. When just these beginning ideas are used instead of the more accurate but more complicated ideas this can have a bad effect on economic policy. Michael Lind wrote a blog about it that can be found here. http://www.salon.com/2013/07/08/how_%E2%80%9Cecon_101%E2%80%9D_is_killing_america/ It is very interesting and I highly recommend reading it.

Consumer Preferences Part 2

Today’s post is on the second part of people’s preferences. This is a continuation of the post the day before yesterday. Yesterday’s post was missed because I was sick but hopefully I am feeling better now and will continue for the rest of the posts this week.

To start off with we will work on perfect complements. Perfect complements are goods that are consumed together in fixed portions. A good example of this is right and left shoes. People like shoes but they always wear left and right shoes together. Having only one shoes instead of both does the consumer no good. The indifference curve for perfect complements looks like this.

If we take a bundle of shoes say (2, 2) the consumer will gain a certain amount of utility from that bundle. Now if we add one more shoe so the bundle is (3, 2) the consumer will be indifferent because they will be no better off than they were before. In fact if the bundle gets changes to (10, 2) or (2, 10) the consumer will still be no better off. The only way they are made better off is when both goods increase at the same rate.

The important thing about perfect complements is that the consumer prefers to consume the goods in fixed proportions, not necessarily that the proportion is one to one.

A bad is a commodity that the consumer doesn’t like. An example of this would be if a person like some toppings on a pizza but didn’t like others, such as pepperoni and anchovies. The consumer may like pepperoni but not anchovies, however there may be some amount of pepperoni that would compensate the consumer for having to consume a given amount of anchovies.

First we pick a bundle (x₁, x₂) consisting of some pepperoni and anchovies. If we give the consumer more anchovies, we have to give the consumer more pepperoni to compensate them. Thus the consumer has an indifference curve that slopes up and to the right as in the following.

There are also neutral goods.  A neutral good is a good that the consumer doesn’t care about one way or the other. If we take our previous example of the anchovies and pepperoni we can change it so that instead of the anchovies being a bad, instead the consumer is now just neutral towards them. In this case the indifference curve will just be vertical lines. Increasing the amount of anchovies will not take away from the enjoyment of the consumer but neither will it add to it.

There is also satiation for consumers. This is where there is some overall best bundle for the consumer and the closer they get to that best bundle the better off they are in terms of their own preferences. We assume that the consumer has some most preferred bundle of goods (x-bar₁, x-bar₂), and the further away from the bundle the worse off they are. X-bar is usually written as an x with a line over it, I was unable to find a symbol that works here so I will just write it out as x-bar. In this case we say that (x-bar₁, x-bar₂) is a satiation point and the indifference curve looks like the following.

In this case, the indifference curves have a negative slope when the consumer has too little or too much of both goods and a positive slope when he too much of one good.

There is also the case of discrete goods. For most goods we consume, we think of measuring goods in units where fractional amounts make sense. Over the period of a month you will consumer so many litres of water for example. Sometimes though we want to examine preferences over goods that naturally come in discrete units.

A good example of this is a consumer’s demand for cars. While we could define the demand for cars in terms of the time spent using a car, this would give us a continuous variable. For a lot of people though it is the actually number of cars demanded that is of interest.

We can use our preference model that we have used previously to describe the behaviour of consumers in this situation the same as we do for anything else. Just like in other circumstances we can use x₁ and x₂. x₁  in this situation would be the discrete good and x₂ will be money, or everything else. The indifference curve for this would look like the following, with the other graph showing the bundles that are weakly preferred.

Usually unless the consumer is consuming only a very small amount of a good, it will be more useful to think about most goods as if they are continuous. As we have looked at several different types of preferences, however it is most useful to focus on a few general shapes of indifference curves. We make some assumptions about these, and with these assumption we call them well-behaved indifference curves.  The assumptions are as follows:

1. We assume monotonicity of preferences. This is basically that we assume more is better. Specifically we are talking about goods and not bads. As we discussed in satiation, there is probably a point where this does not hold, however we will assume that what we are examining are situations before that point is reached.
2. We assume that averages are preferred to extremes.

Using these two assumptions most indifference curves will look like the following.

This are some of the basic ideas behind consumer preferences, there is more to come and reality is definitely more complicated than we would like, but this gives us some basic tools to analyze consumer preferences. A key thing to remember is that preferences are generally thought of as over a time period, so our desire for something over a day, a week, or a year. As such this makes them behave differently than if we were just looking at them at a specific time.

Consumer Preferences Part 1

The post today is on chapter three of the textbook which is all about preferences. The idea of consumer preferences is what economists mean when they talk about people acting in their own self-interest. In the last chapter we talked about how consumers look for the best thing that they can afford. Talking about what consumers are able to afford was what the last chapter was about and this chapter is about what we consider to be the “best thing”.

When we talk about consumer choice we need to talk about consumption bundles. Consumption bundles are a complete list of goods and services that are involved in the choice problem we are investigating. When we say that it is a complete list that is what we mean. We need to make sure that we are including all of the appropriate goods in the definition of the consumption bundle. It is also important when we are discussing consumption bundles to not only look at a complete list but to also consider when, where, and under what circumstances they would become available.

These things are important and it can sometimes be better to think of the same good in different circumstances as a different good. An example of this is an umbrella when it is raining will be valued more than when it is not. In this case it might be more useful to actually think of them as two separate goods.

We are still able to use our two good model however for this when looking at simple choice problems simply by looking at one good as what is relevant in the choice and the other good as everything else.

When we look at two consumption bundles we assume that the consumer can rank them as to their desirability. So if a consumer has a choice between two bundles (x₁, x₂) and (y₁, y₂) they would be able to say whether they preferred one bundle to another or whether they are indifferent.

We use the symbol > to mean that one bundle is strictly preferred to another, so that (x₁, x₂) > (y₁, y₂) should be interpreted as saying that the consumer strictly prefers (x₁, x₂) to (y₁, y₂), in the sense that they would definitely want the x-bundle rather than the y-bundle.  If the consumer is indifferent between two bundles we use the notation =. The symbols are a little bit different if we were writing them out but for the purposes of the blog this is the best I can do. If a consumer weakly prefers one consumption bundle to another then we use the symbol ≥. So in short

> means strictly preferred

= means indifferent

≥ means weakly preferred.

These are also not independent concept but these are all related. For example if we know that a consumers preferences for two bundles are the following. (x₁, x₂) ≥ (y₁, y₂) and (y₁, y₂) ≥ (x₁, x₂) then we know that (x₁, x₂) = (y₁, y₂).

Economists usually make some assumptions about the consistency of consumers’ preferences. For example it seems unreasonable to have a situation where (x₁, x₂) > (y₁, y₂) and at the same time (y₁, y₂) > (x₁, x₂). This would be saying that the consumer strictly prefers the x-bundle to the y-bundle, and that the consumer strictly prefers the y-bundle to the x-bundle. We end up making some assumptions about how preference relations can work. Some of the assumptions about preferences are so fundamental that we can refer to them as axioms of consumer theory. The textbook lists three of these axioms.

1. Complete. We assume that any two bundles can be compared. That is given any x-bundle and any y-bundle, we assume that (x₁, x₂) ≥ (y₁, y₂), or (y₁, y₂) ≥ (x₁, x₂), or both, in which case the consumer is indifferent between the two bundles.
2. Reflexive. We assume that any bundle is at least as good as itself. (x₁, x₂) ≥ (x₁, x₂).
3. Transitive. If (x₁, x₂) ≥ (y₁, y₂) and (y₁, y₂) ≥ (z₁, z₂), then we assume that (x₁, x₂) ≥ (z₁, z₂). In other words, if the consumer thinks that X is at least as good as Y and that Y is at least as good as Z, then the consumer thinks that X is at least as good as Z.

When we want to represent a consumers preference choices graphically we draw an indifference curve. An indifference curve is exactly what it sounds like. If we take a list of bundles for which the consumer is indifferent about and draw a line through them. This is the indifference curve. All of the bundles above it are called the weakly preferred set.

We are able to draw an indifference curve through any consumption bundle we want. This is because the indifference curve through a consumption bundle consists of all bundles of goods that leave the consumer indifferent to the given bundle.

One of the important part of indifference curves is that they cannot cross. More specifically, indifference curves representing distinct levels of preference cannot cross. Like the figure below.

The reason for this has to do with something that we mentioned before about consistency. If we take the three bundles in the graph, X, Y and Z we now want to compare them. X lies on one indifference curve, Y on another and Z at the intersection. As Z is on both indifference curves we know that X = Z and Y = Z, by the property of transitivity that means that X = Y. However since they are distinct indifference curves we can see that X (or Y) should be strictly preferred to Y (or X). These two things contradict each other. There are several different types of preferences that people can have.

One type of preference is if two goods are perfect substitutes. This means that the consumer is willing to substitute one good for the other at a constant rate. The simplest case being when a consumer is willing to substitute a good at a one to one ratio. An example of this would be blue and red pencils.

If the consumer has no preference over colour then the red pencils and blue pencils are perfect substitutes. If we have a bundle of pencils which is (10, 10) or ten red and ten blue pencils than any other bundle that has 20 pencils in it the consumer will be indifferent about. When we draw it graphically it will look like this.

The important fact about perfect substitutes in that the indifference curves have a constant slope. There are several other types of consumer goods with different preferences and I will be moving on to them tomorrow. I apologize for the lack of updates the last couple of days. I am starting to find myself struggling with concentrating on this. However I am trying to move through it and just post as much as I can. See you tomorrow.

Budget Constraints

This post will be on chapter 2 of the textbook which talks about budget constraints. I would like to apologize for the lack of post yesterday. This week has been very difficult for me to keep motivated and work on my studying. Today I woke up though and I just said to myself that I would go for a walk, clear my head and work. I am not trying to make up for lost time this week, I am just going to pick up where I left off and continue working.

To sum up the economic theory of the consumer is very simple. Economists assume that consumers choose the best bundle of goods they can afford. This deals with some vague terminology that we have to define more carefully in order to study it. First off is what is meant by what a consumer can afford. The next chapter in the textbook talks about what is meant by best.
So now we want to examine what we mean by what a consumer can afford. This has to do with the concept of the budget constraint. People consumer all sorts of things and this can be very difficult to study. When we look at some set of goods that a consumer can choose from we want to do some things to make it a little easier to study. The main thing that economists do is simplify what a consumer can choose from down to two goods. When we only deal with two goods we are then able to display the consumer’s preferences graphically.
While there can be some problems with the two good assumption it works fairly well. The reason for this is that you can make the assumption that one good is a particular item and the second good can represent everything else. As such with two goods you are able to represent fairly accurately what choices a consumer might have in regards to a good. One of the tricks to do this is to say that good 2 is just money. This sets the price of good 2 to 1 and it is able to represent what you could spend on everything else.
We indicate the consumer’s consumption bundle by (x1, x2). This is simply numbers that tell us how much the consumer is choosing to consume of good 1, x1, and how much the consumer is choosing to consumer of good 2, x2. By adding in the prices of each of the goods, (p1, p2) and the amount of money the consumer has to spend, income (m). We can then write the budget constraint of the consumer as:

p1x1 + p2x2 ≤ m.

p1x1 is equal to the amount of money the consumer is spending on good 1.

p2x2 is equal to the amount of money the consumer is spending on good 2.

The budget constraint of the consumer requires that the amount of money spent on the two goods to be no more than the total amount the consumer has to spend. The consumer’s affordable consumption bundles are those that don’t cost any more than m. We call this set of affordable consumption bundles at prices (p1, p2), and income m, the budget set of the consumer.
When p1x1 + p2x2 = m we call it the budget line. These are the bundles of goods that just exhaust the consumer’s income.

If we want to rearrange the formula for the line to make it look more like the standard line for an equation in formation y = mx + b we can do that as well and it will look like this.
x2 = m/p2 – (p1/p2)x1.
In this form, m/p2 represents the vertical intercept and –p1/p2 represents the slope of the budget line. The formula tells us how many units of good 2 the consumer needs to consumer in order to just satisfy the budget constraint if they are consuming x1 units of good 1.
The slope of the budget line has a nice economic interpretation. It measures the rate at which the market is willing to substitute good 1 for good 2, alternatively you can also say that it measures the opportunity cost of consuming good 1.
Changes in the price of goods as well as changes in income all change the budget line. If we start with income it is fairly easy to see how income affects the budget line. If we look back at our equation we can see that income (m) affects the intercept but not the slope of the line. This means that a change in income will result in a parallel shift in the budget line.

Changes in price act a little bit differently though. If we increase the price of good 1 (p1) while holding the price of good 2 (p2) and income (m) constant then if we look at the equation we can see that it will not shift the vertical intercept but that it will change the slope.

If we change the price of both goods it gets slightly more complicated. If we increase the price of both goods by, let’s say, double. Than the slope will not change at all but both of the intercepts will change. If we look at our original budget line of p1x1 + p2x2 = m and multiply both prices by a constant t so that it becomes tp1x1 + tp2x2 = m, we can see that we could rewrite the equation as p1x1 + p2x2 = m/t. So multiply both prices by the same amount is the same as dividing the income by the same amount. So a change in both prices will change the budget line depending on how much the change in each price is compared to each other.
When we look at the budget line we can see that it is made up of two prices and one income. We can do some mathematical tricks though and peg one of the variables to some fixed value, and adjust the other variables to describe exactly the same budget set. Thus we can take the equation
p1x1 + p2x2 = m
with a bit of movement it is the exact same as
(p1/p2)x1 + x2 = m/p2
Or
(p1/m)x1 + (p2/m)x2 = 1
These all represent the same budget line but what we are doing is, in the first equation pegging p2 to 1 and in the second equation doing the same for income (m).
When we do this we refer to the price as the numeraire price. The numeraire price is the price relative to which we are measuring the other price and income.
There are other things besides changes in income and price that can affect a consumer’s budget set. Economic policy often this by taxes or subsidies.
There are a couple of different types of taxes and how the tax is implemented affects how it interacts with a consumer’s budget set. For example if there is a quantity tax this means that the consumer has to pay a certain amount for each unit of the good they purchase. From the consumer’s viewpoint this is basically just an increase in price. So a quantity tax of t dollars per unit of good 1 simply changes the price of good 1 from p1 to p1 + t. This will cause the budget line to get steeper.
Another kind of tax is a value tax. This is a tax on the value, or price, of a good rather than the quantity purchased. This would be what sales taxes are. Value taxes are also known as ad valorem taxes and they changed the price of the good as well. In the case of an ad valorem tax of τ on the price of good 1, the price of the good will change from p1 to (1 + τ)p1. τ is the Greek letter tau.
A subsidy is just the opposite of a tax and it operates in the same way just doing everything the opposite.
Another kind of tax or subsidy that the government can use is a lump-sum tax or subsidy. While quantity and ad valorem taxes tilt the budget line one way or the other, a lump-sum tax or subsidy shifts the budget line out or in.
Taxes and subsidies are not the only affect that the government can have on a consumer’s budget line. A government can also ration goods. This means that the level of consumption for some good is fixed to be no larger than some amount. Suppose for example that good 1 were rationed so that no more than x1* could be consumed by a given consumer. Then the budget set of the consumer would look like this.

Sometimes taxes, subsidies and rationing are all combined. For example perhaps over a certain level of consumption a good is taxed but under that it isn’t. In that case then the consumer’s budget set will look like the following.

A good example of these in real life is the food stamp program in the U.S. Using the information in the textbook I will outline the example they give.
Before 1979, households who met certain eligibility requirements were allowed to purchase food stamps, which could then be used to purchase food at retail outlets. In January 1975 for example, a family of four could receive a maximum monthly allotment of $153 in food coupons by participating in the program. The price of these coupons depended on the household income.
The pre-1979 Food Stamp program was an ad valorem subsidy on food. The rate at which the food was subsidized depended on the household income. The budget line of it would look like this.

After 1979 the Food Stamp program was modified. Instead of required that household purchase food stamps, they are now just given to qualified households. Suppose that now a household receives a grant of $200 of food stamps a month. This means that regardless of how much it is spending on other goods the budget line will shift to the right by $200. The slope of the budget line will not change. That will look like this.

This has been a brief look at budget sets of consumers, that is, looking at what is affordable for people. Tomorrow will be looking at what consumers want to consumer and how we figure that out.

Update July 9th

Today I was not feeling well, so I focused mainly on a couple of Econtalks. The first one can be found here http://www.econtalk.org/archives/2013/07/morris_fiorina.html. It was a very interesting talk on the state of the U.S. political parties and how they have changed and why. As well as looking at how the U.S. people have not changed as much as the parties have. The second talk can be found here http://www.econtalk.org/archives/2013/05/epstein_on_the_1.html. It is on the U.S. constitution and how it has affected the U.S.