Budgets and consumption

Mr. Money Mustache

The FIRE movement and we actually value in life.

Source: https://www.mrmoneymustache.com

This lesson is about how microeconomists think about and model consumption.

Microeconomists will often make a simplifying assumption in their models that assumes that people are perfectly rational, even though we are well aware of the fact that in reality people often are not. Most microeconomists realize that many people will make purchases that in the end do not provide the utility or enjoyment that the purchaser initially thought they would get.

When I think about these types of questions, I often think about the blogger known as "Mr. Money Mustache (MMM)". MMM is one of the informal leaders of the FIRE movement: Financial Independence, Retire Early. Basically, a group advocating cutting spending and increasing income in your early working life, so that you can retire decades earlier.

Reading through the blog, you get not just financial advice, but also a well thought out philosophy about consumption, and what is important in life. Consumption is framed as a question of time-preference and priorities. Increased consumption now means spending more time at a job (which you may or may not enjoy). This type of thinking is very much in line with how microeconomists think. We will explore these ideas in the next few lessons.

The budget curve

To analyse consumption choices, we are going to simplify a bit and only consider the choice between two goods.

If we want to decide how much of each one of these goods we want, we need a little info.

We need

The prices of the two goods: $p_1$ and $p_2$.
Our income, or the total budget we have reserved for buying those two goods, which we call $m$

Then we are ready to set up a simple budget. Instead of referring to the abstract good 1 and good 2, let us call our goods apples (a) and bananas (b). $x$ represents the amount:

$$m > p_{a} x_{a} + p_{b} x_{b}$$

We can draw the budget in a figure with the following amounts

$$p_{a}=40$$
$$p_{b}=50$$

The maximum combination of apples and bananas that we can buy lies along the dark-blue line. That is what we call the budget curve. At each point along this curve, if we want more bananas, we need to give up some apples, and vice versa.

How many bananas would we need to give up if we wanted one more apple? That, of course, depends on the price. If a banana costs twice as much as an apple, then we only need to give up one banana to get two apples.

That's why the slope of the budget curve can be written as:

$$-p_{a} / p_{e}$$

We can call this slope the exchange ratio: How much of the one you have to give up in order to get one more of the other.

The end points of the budget curve are $m/p_b$ (on the banana axis) and $m/p_a$ (on the apple axis). Why?

What happens when we change the prices? For example, if the price of apples increases to 60? Try it.

Everything that lies under the budget curve (the light blue area) er all the combinations of apples and bananas that we are able to buy given our budget.

Problems

Assume that we have a budget of m=10.000. Apples cost 40 and bananas cost 50. Initially, we buy 150 apples and 80 bananas.

Are we on the budget curve or below it?

We are on the budget line since: $ 40*x_{a} + 50*x_{b}=10.000$
If we give up 40 bananas, how many apples can we buy with the extra money?

Hvis vi gir opp 40 bananas, hvor mange apples kan vi kjøpe med de ekstra pengene?

We give up 40 bananas that cost 50 each. That means we have an extra 2000 to spend. Apples cost 40, so we have 2000/40=50 apples that we can buy.

Visually, we can see it as moving up the budget curve:
What is the slope of the budget curve?

The slope can be interpreted as how much of the one good you have to give up in order to get more of the other
$$-p_{a}/p_{b} = -40/50 = -4/5$$
Let's say that the price of apples increases to 60, how does this change the budget curve? What is the new slope? How will this effect the consumption of apples and bananas?

The slope gets steeper: $-p_{a}/p_{b} = -60/50 = -6/5$ (you can see the effect by entering 60.)

We know that when the price of apples increases, the total amount we can buy decreases. We could, for example, have kept the same number of apples, and reduced our purchase of bananas. But we probably will reduce the number of apples we buy, since they have become relatively more expensive compared to bananas. More on that in lesson 3!

The effect of a change in income.

We start again with our budget curve where we initially have a budget (or income) of m=10,000. The price of apples and bananas are 40 and 50. What happens when we increase the budget by 50% to 15,000.

We see that:

We can buy 50% more of both apples and bananas
But the exchange ratio (slope) is unchanged.

When both income and prices change at the same time.

Now let's say that we increase both the income and the prices by 50%.

Initially, we have a budget of m=10,000, prices of apples and bananas of 40 and 50. If we increase all of these by 50%, we have 15.000, 60 and 75. See what happens:

Takeaway:

When prices and income change proportionally (all by 50% in the example), then we end up exactly at the same place we started.
We can buy exactly the same number of apples and bananas.
The exchange ratio (slope) between the two goods is unchanged.
If we think in terms of an entire economy where both incomes and prices of all goods are rising proportionally, then we call that inflation, which is often measured by an index of consumer good prices called CPI (Consumer Price Index).

Problems

Initially we have a budget of m=10,000, apples cost 40 and bananas cost 50. We buy 150 apples and 80 bananas.

We increase our budget by 2,000. If we wish to consume the same proportion of apples to oranges, how many of each can we buy?
We have increased our budget by 20%, therefor, we can increase the number of apples and bananas by 20%:
- $x_{a} = 150*1.2 =180$
- $x_{b}=80*1.2 = 96$
- We can double check that our budget holds: $180*40+96*50=12.000$
Now let's say that we increase both income and prices by 20% (to 12000, 48 and 60). If we wish to buy proportionally the same number of apples and bananas, how many can we buy now?

The exact same number. We can check:
$$48*150 + 60*80 = 12.000$$

Let us say that you are studying in the idyllisk university town of Trondheim, Norway. But you are considering moving to Oslo and study there instead. You have a income of 10,000 per month in loans and stipend, which you must buy three goods: rent for your flat, food and beer.

In Trondheim the prices are 5,000, 45 and 50

In Oslo the prices are 6,000, 45, and 60

In Trondheim you live with roommates for 5,000 a month, you eat 90 meals a month and you drink 19 beers per month.

Are you on the budget curve in Trondheim?

We now have 3 goods instead of 2, but the principle is the same. We calculate out:

5000*1 + 45*90 + 50*19 = 10.000

We use up our entire income, therefor we are on the budget curve.
If we were going to have the same consumption in Oslo, what would it cost?

We calculate

6000*1 + 45*90 + 19*60 = 11,190

It costs \(\frac{11,190}{10,000}) = 1.19 more to live in Oslo compared to Trondheim.

This is what is called Purchasing Power Parity between Trondheim and Oslo. If we want the same purchasing power in Oslo, we will need 1,19 times more income.
What would you cut in Oslo if you needed to stay within the same budget?

This of course is dependent on your own preferences, and we will work on modelling preferences in lesson 3. But we can begin to speculate...

We can perhaps assume that our housing choices are hard to change at short notice, so there we just continue to pay en ekstra 1,000. We then need to choose between food and beer in order save.

The price of food is unchanged, but the price of beer has become more expensive, and so the relative prices have changed. We might then drink less beer.

We might also think that our food budget will change less to a change in income compared to beer. In other words, food is less income-elastic. We would then expect our beer consumption to change more when we have less income.

But our income hasn't changed, has it? Well...

Since price(s) has increased, then what we can buy has decreased. What we will call our real income has decreased.

An increase in price then has two effects on consumption. It can change the relative price of goods, which we call the price effect. It can also decrease real income, which we call the income effect.