Utility Maximization

And finance Allah Shmoop What is utility maximization All right

Those three tennis courts the four swimming pools and the

porcelain fountain imported from Milan You own them all Not

to mention a G six with a hot tub and

your own basketball team So think of your resource is

as being well infinite Mohr less so Utility maximization wouldn't

come up much in your life That is You're not

too worried about using your pencil after you sharpen it

so that it's only two inches long before you throw

it out you just toss it rather than use another

inch Well utility maximization has to do with decisions consumers

make as they spend Their limited resource is all right

now you're this guy You get a modest paycheck You

have to figure out how to divide it up to

survive You've got rent food utilities entertainment and all the

other stuff you need Thio live So the basic question

with regard to utility maximization for you Well how do

consumers budget they're spending in order to get the most

out of it In other words how do they maximize

utility Or how do you do this Utility maximization has

to do with value Or rather how you allocate precious

resource is AII Cash So it produces the most value

to you the consumer Or set another way How do

consumers get the most satisfaction from spending their hard earned

dollars Well question How many gold plated toilets is Jeff

Bezos founder of Amazon Limited to buy Answer He isn't

limited by budget He is however limited by the happiness

Each additional gold plated toilet gets him Well the guy

has couple hundred billion dollars That's with a B in

Amazon stock wealth so he doesn't spend a nanosecond worrying

about resource allocation He just buys whatever he wants No

no no Mr Yacht broker I'll take two of them

well but a normal person would probably not take both

the pink and the green Buffy and Muffy yachts In

fact they wouldn't even be able to afford one yacht

of shame Normal people have constrained budgets and before they

spend their dough they predicted given level of satisfaction they

quote achieve unquote from hitting that by now button What

they have to spend is essentially a kind of mathematical

constraint on there Happiness or utility or ability to make

their life better What they have to spend is a

constraint on their budget They need to make tradeoffs among

the items they need to buy based on the happiness

each additional unit of whatever gets them So now back

to the average Joe liberal arts major your big tradeoff

choices might be more about buying ramen noodles in bulk

or getting the soft toilet paper hint by the ramen

You can always borrow toilet paper from the Burger King

bathroom or you know there's a newspaper laying around somewhere

This dynamic is called a budget constraint beautifully graphically illustrated

here for your viewing pleasure Yeah Check this out And

here's a graph of Jeff Bezos Budget constraint Yeah not

much constraint you know financially yet Well utility maximization is

all about these budget choices The goal of utility maximization

is to get the most value from the money you

have available to spend As an example We're making tradeoffs

between toilet paper and Rahman Here we have a budget

that shows our trade offs of the two Well here's

an indifference curve which measures the happiness we get from

each and where the slope of the indifference curve is

tangent to the budget constraint That's where we have the

maximum utility IAEA happiness within our budget constraint Getting all

this all right Now let's talk about another trade off

You have fifty boxes your last fifty bucks and it

has to last you nine days until your next liberal

arts style paycheck comes Costco the discount retailer has super

bulk boxes of Rahman on sale in a cost for

one month worth of noodles Well fifty bucks which is

grey but for the fact that you will be evicted

in an hour And the cost to remain in your

hovel into the freeway for nine more days happens to

be exactly fifty dollars Well that's the amount You pay

the head bum to tell the other bums not to

beat you senseless at night and steal your liver while

you're sleeping on the freeway there So you have a

trade off here You can either eat or you Khun

B Sheltered but you can't do both So in theory

there should be a tradeoff you could make where fell

Maybe you share a cardboard box with another bum for

twenty five dollars for nine days and spend the remaining

twenty five dollars on the well two weeks worth of

noodles that will get you through until you can collect

your next paycheck As you rue the day you know

that you did that whole liberal arts major thing Well

because economists are economists they have a bunch of mathematical

formulas to optimize the budget allocation of your precious dollars

The basic notion behind this math revolves around the idea

that consumers will allocate their money so that they get

the most marginal utility for each dollar they spend Right

Last dollar it's going to go in the best place

to them Okay Last concept for understanding utility maximization here

for marginal utility is the amount of extra use you

get out of buying mohr of something like you need

some rahmon to keep you alive But you don't need

like forty pounds of it to keep you alive For

just nine days A storage locker full of Rahman will

not do much good for you It would just sit

around doing nothing right What One pair of pants is

good for keeping your legs warm and making sure you

don't get it You know arrested you know been there

done that But a thousand para pants Well just wasteful

There's not much marginal utility being gained from that thousand

pair of you know khaki Dockers So utility maximization involves

trying to get the most value Out of limited resource

is such that the N plus one unit then begins

to decline dramatically in value art Example Like if you

need two thousand calories a day to basically maintain your

current weight and one packet of Rahm and his five

hundred calories Well then if you need to survive nine

days while you'll want four packets a day for nine

days or thirty six packets to just keep you alive

until your next paycheck after nine days At that point

you hope you can afford to make a change in

your life and lifestyle But for now you realize that

you would probably die or at least suffer greatly If

you went with no Roman for all nine days and

just tried to survive on water you would gain great

utility from having at least one packet today for nine

days But you'd realize that you have lost so much

weight in living on five hundred calories a day That

the storage locker of a thousand docker pants would have

almost no hands that fit you anymore Yeah you would

continue to gain meaningful marginal value from that second and

third packets of Rahman a day getting you to a

fifteen hundred calories a day Such that Well you might

only lose a few pounds over the course of those

nine days until you got that golden paycheck That'd be

just fine And after for four packet today well the

value of those Rahman noodles begins to decline massively or

set another way there Marginal utility than approaches Zero Well

this set of calculations mirrors the marginal utility value model

with the goal of getting the most marginal utility out

of each dollar or the most rum and out of

the dollar which is actually quite a bit of Roman

and