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### Course: Macroeconomics > Unit 7

Lesson 1: The consumption function# Consumption function with income dependent taxes

Thinking about a consumption function where taxes are also a function of income (which is more realistic than constant taxes). Created by Sal Khan.

## Want to join the conversation?

- Wouldn't the Base consumption (CSub0) has come out of the Total Income(Y)?

If Consumtion= Base + Disposable Income, Wouldn't we have to also substract, Taxes AND the Base consumption to get to disposable income?

I know this adds a little more complexity to the model, and may make it less clear, but it seems obvious to me that if I have a Base, or bare minimum consumption, it will have to come out of my salary. It won't just pop out of my pocket!

Consumtion = Base + MPC*Disposable Income

Consumtion = Base + MPC(Income - Taxes - Base)

Consumtion = Base + MPC(Income(1-tax rate) - Base) => C= Csub0 + csub1[Y(1-t)-Csub0]?

Also, wouldn't we have to make a "broken" curve if we consider that Csub0 has to come out of Y?? See my example below to make this clearer.

In my mind the first part of the curve would have a 45º(1-t) slope until Y(1-t)>Csub0

Example:

If need for base 100$ (Minimum for me to keep me alive) and only get and income of 60 with a tax rate of 20%, I will get 48$ that I will spend totally, because I need 100$ as base.

Once I get an income greater than 125$,which turns into 100$ after taxes, every extra dollar above 125$ will I THEN spend in my Marginal Propensity to Consume (MPC) minus the tax rate.

To me, a model that will reflect this would be:

When Y(1-t)< or = Csub0 -> C=Y(1-t)

When Y(1-t) > Csub0 -> C=Csub0 + Csub1[Y(1-t) - Csub0]

I might be wrong (Not unusual), so please anyone correct me and tell me if my asumptions (or algebra) are wrong. Sorry for my "Engrish"(7 votes)- Your first assumption is wrong, Base consumption doesn't come from Income, its the bare minimum you'd have to spend to survive when your Income is non-existent. You dont substract base consumption from aggregate income to get disposable income because:

Base consumption is the very minimum amount a person HAS to consume in order to survive. So when aggregate income is 0 (because that person is unemployed or receiving no income at the time for any reason) that person will have to get resources to buy food and water at least to survive, be it: dig into their savings, sell their stuff, ask for money,etc.

When a person DOES have an income, they don't continue to use base level funds to cover their consume costs (if you have a salary you don't spend your savings or ask for money for groceries, instead, you spend part of your salary on groceries while saving another part).

If your salary (aggregate income) is not enough to cover your consume costs then you'll dig into your base level funds PROPORTIONALLY to the amount your income does not cover. So if your income can only cover your consumption costs by 85% you'll use your base level funds to cover the remaining 15%, of course, this would mean your costs exceed your aggregate income and this lifestyle wouldn't be sustainable for a prolonged period of time.

Because of this, base level funds never intersect with income and they aren't included in the Disposable Income formula.(3 votes)

- I don't really get the last part can you plz explain again in more detail thank you very much.(3 votes)
- After deriving the expression of the consumption function including income taxes, one gets. C = MPC(1-t)Y + C0 where t is take rate, Y National Income and C0 the autonomous consumption.

Like Sal explains after about4:18, the term (1-t)Y is nothing but disposable income as (1-t)Y =

Y - Yt. Yt is the income tax and hence this is basically Y - Income Tax which gives the Disposable Income.

If disposable income is represented by the variable Yd = Y-Yt = (1-t)Y then subsituting this in the consumption function derived that was C = MPC(1-t)Y + C0 one gets

C= MPC(Yd)+C0 or C = MPC(Disposable Income) + Autonomous Consumption(3 votes)

- What happens to the consumption function when the country follows a progressive tax system? That is the percentage of income taxed increases as income increases.(2 votes)
- i don't think tax system being progressive will effect the consumption function because here we are talking about aggregate income and aggregate tax revenue, and the tax rate is simply the ratio between tax revenue and income. Progressive tax system will effect individual income.(1 vote)

- How do you explain autonomous consumption? How is someone able to consume without income? By stealing maybe?(1 vote)
- well, without income the people can sell their wealths.(3 votes)

- Is there any mathematical relationship between MPC and Tax Rates that the government makes use of to increase Aggregate Consumption: c1x(1 - t1) < c2x(1 - t2) ?(1 vote)
- But if that country were to charge a higher tax rate for companies that have outsourced jobs overseas, than that country could have minimized the monitory rate of circulation, and thus reduce on capital flight. However, that country would have had to compare the company’s source of profit. If a company’s profit is greater than 50% and the company has outsourced jobs overseas, than that company can be classified under a different tax bracket depending on record of US job creation V. outsourcing.(1 vote)
- The condition for this proposition dictates that if a domestic company outsource jobs while most of their profit is retained from the same domestic country any bad economic decision could have caused this company to suffer major losses which would have eventually weaken the monitory rate of circulation within that country, meaning that the country’s circulating currency will pass fewer hands before it leaves the country of origin, considering that there are multiple companies doing the same exact thing.(1 vote)
- A speculation is as follow: Scenario #1 if a company retained more than 50% of their profit from country “A” while their factories are outside of that country, than they should be charge a higher tax rate to compensate for the capital flight they’ve caused that country. Scenario #2 If jobs from a particular country are being outsourced, than by definition this country has loss in capital flight.(1 vote)
- Squeezy Oranges total cost of production is now 18%. And after investor’s earnings, total labor cost, taxes and insurance, the competitive leverage which now exist between these two companies are comparatively the same.(1 vote)
- labor cost for Orange Land company and 18% overall labor cost for Squeezy Oranges.

Suppose now Squeezy Oranges realizes that the company Orange Land begins to feeds off their consumers and investors. Obviously this would have resulted into a condition of Competitive Rivalry where one US Company tries to outsource another by taking advantage of the global economy to(1 vote)

## Video transcript

In the last video where we generalized the linear consumption function. I said that the tax, the
total amount of taxes, the aggregate taxes are constant, all of these were constants right here. You can merge them into a constant that ended up being our
independent variable intercept right over here. YouTube user nilsor1337
asks a very interesting and good question. "Aren't taxes in some way a
function of aggregate income? "In most modern economies "people pay a percentage of their income. "In general, the tax base
grows as aggregate income "or as GDP grows. "Is it appropriate to make this constant?" The simple answer is it
depends on how carefully you want to model it. In some cases you might just say, "Well, let's just assume
that this is a bulk tax. "We're just trying to
understand one aspect of it." You will see that in
some economics courses or some economics textbooks. The other way is you
could actually model it a little bit more realistic. You could say, "Hey, taxes really are "a function of aggregate income." We could say that T really
is going to be equal to some tax rate. I'll write that as a lower
case t times aggregate income. In a place like the U.S.,
this might be close to the 30% of aggregate income or 20%. Whatever it might be or aggregate income is what is going to go for taxes. If you do it this way, and you substitute back to this you could actually get an
expression for consumption in terms of aggregate income that takes into consideration
the idea that taxes are function of aggregate income. Just to do that algebraically, we can rewrite this expression up here. You have aggregate consumption =
my marginal propensity to consume times aggregate income +
autonomous consumption, the amount that would be
consumed no matter what. Minus the marginal propensity to consume, shows up again. Instead of writing T right over here, I'm going to write lower case t x Y, tax rate times aggregate income. Times the tax rate times aggregate income. I just took this, instead
of writing upper case T, I wrote lower case t
times aggregate income and they should be the same thing. But now we've expressed t as a
function of aggregate income. Now we can merge both of these, these are something
times aggregate income. We can combine those 2 terms. This one and this one write over here. If we factor our a
common factor of c1 x Y, we get, let me write it this way. Actually, let me just combine them first so that the algebra doesn't confuse you. We get C = c1 x Y. Marginal propensity to
consume times aggregate income and I'm going to write this one. Minus the marginal propensity
to consume times ... I'll switch the order here. Well, let me not switch the order, times the tax rate, not just the aggregate total tax value but the actual tax rate
times aggregate income. That's those 2 terms there and then we're just left with
the autonomous consumption. So, plus the autonomous consumption. Over here, we have a common factor. We can factor out the c1 and the Y, or essentially the marginal
propensity to consume and the aggregate income. This is just algebraic
manipulation right over here. We get aggregate consumption is equal to, let's see, we could write this c1(1 - t)Y. You can multiply this out to verify. If you multiply it all out then the 1st term is c1(1)Y
is this right over here and c1(-t)Y is this term right over here. Then you're left with your
autonomous consumption. This actually makes a lot of sense because when you write it like this, when you write it like this you could look at this
term right over here. What is this term right over here? Well, (1 - t)Y, if the tax rate is 30% then this 1 - 30% is going to be 70%. 70% x aggregate income, that's essentially what
people get in their pockets. This whole term right over here is essentially disposable income. Disposable income right over here. We could actually, if we wanted to write this
as some other variable we could just put that
variable right over there and say it's disposable income and then it actually becomes a very simple thing to graph. We could graph this 2 different ways. If we wanted to write a
function of aggregate income we would graph it like this. Now, when we express it this way, taxes as a function of aggregate income now our vertical intercept. This is aggregate consumption. Our vertical intercept is
this term right over here. That is C [not] and our slope is all of this business. The slope of our line
is going to be C1(1 - t) and this right over here, the independent variable
is aggregate income. Another option, we could
set some other variable to what we could say disposable income. Let me call it Y disposable = (1 - t)Y then we could write this. It's essentially equal to this
business right over there. Then we could rewrite the
consumption function as aggregate consumption =
marginal propensity to consume times disposable income + sum
level of autonomous consumption. plus sum level of autonomous consumption. This actually takes us back to the basics. This takes us back to our
very original situation here where we had some autonomous consumption plus our marginal propensity to consume times disposable income. If we wanted to plot it this way as a function of disposable income, not aggregate income then it would look like this. This is consumption, and now
this is an aggregate income, this is disposable income which is the same thing as (1 - t)Y. Now, still our vertical
intercept is C [not] and our line slope is the
marginal propensity to consume. This is C1 just like that. All of these are completely
valid consumption functions and I thank nilsor1337
for bringing up a topic that actually was a
cause of confusion for me because it really does depend. Because I thought the way, he or she, originally thought about the problem. Well, taxes are a function and a lot of econ books tend
to treat this as a constant. That is actually just
an assumption they make to often simplify the calculations. If they don't want to make that assumption you can still show that
it is a linear function, that aggregate consumption
is still a linear function of aggregate income.