Hey, afternoon everyone. Hope you all had a
good weekend. So, we're going to start
today on the supply side of economics.
And I'm not going to lie, I'm much more
interested personally in individual behaviour.
So, consumer theory, individual behaviour
is what I really love. Today's lecture is
going to be more a foundation for the next
couple of weeks, but I'll try and throw some
interesting stuff in there as well. so the
key thing to keep in mind is while we are shifting
from the individual to the firm a lot of
the same principles ideas and techniques
we talked about solving apply here as well
so a big thing is the idea that in terms of
like doing better we always want to think
on the margin rather than on the average
we optimize when the marginal benefit of an
action equals the marginal cost for the individual
it could be something like eating a slice
of pizza for the firm it's producing output
does the next output produce or adding an
extra bit of labor extra bit of capital
does that cost result in more benefit if so
we want to maximize the marginal benefit equals
marginal cost and as we saw in the consumer
optimization topic optimization occurs
when the slope of the indifference curve is
equal to the slope of the budget line we
have this tangential property where they're
just touching each other this is going to come
up again today in this lecture as well
okay so the production function this is a
mathematical function that defines the maximum
amount of output that a firm can produce
given a set of inputs so the quantity of output
is some sort of function this can take many
different forms we have some amount of
capital and some amount of labor you throw it
in and the function which is like the technology
specifies how much output will occur
based on those inputs. Labor is fairly
intuitive. It's obvious how many people
essentially and how many hours of labor
you have employed. And capital could be
anything from, you know, these crazy big machines
you get at these car factories to someone
running a lemonade stand that has like
something to squash the lemons with in a jug.
That's both capital. So your inputs of
capital and labour and the production
function will determine how much
output is produced. Okay, so the
managerial decision of what to do to
optimise differs in the short run
or the long run. And this is because
usually in the short run there is some
factor that is fixed and can't be changed.
So you might want to change something, but
you can't. So usually we say in the short
run capital is fixed. So to be able
to purchase and get a new machine
in, that takes months, sometimes
up to a year. Things are a lot
faster now, for sure, but you can't click
your fingers and change it. So if
you want to make a decision that is
implemented next week, you can't really do
that with capital. So in the short
run, in that short term, you can
only really change labour. You can
choose to hire 10 people easily
tomorrow if you want. In America, you can
easily fire 10 people tomorrow. much harder
to do in Australia due to labor protection
laws but in the short run you could
change your labor but not your capital
and in the long run so we usually say
the long run is six months or further
further in the future the manager has you know
full control over what they can optimize
both capital labor and other things as
well so to get us in the the mood of
being a firm and being a manager, we're
going to play a game. So you're all managers
of a fictional company that
creates two goods, green eggs and ham,
inspired by Dr. Seuss clearly. So
in the short run, when this game occurs,
capital is fixed, the labour isn't. So
you're going to have to make decisions regarding
labour, you don't have to worry about
capital. So there's going to be 10 rounds, and
each round you need to decide how much
labour to assign towards each of the two goods
green eggs and ham respectively and you
have a limited number of workers if you had
infinite workers this wouldn't be interesting
at all you got to decide how to allocate
them to the two goods green eggs and ham the
output of a process is measured in units
created so units of green eggs or units of
ham and this directly depends on how many
workers you assigned to work on creating each
good when you produce a good each unit of
that good will be sold for one dollars
above your cost of production so one dollars
profit so it doesn't matter if you create
one good of green eggs or one good of hemp
will get you one dollar profit and the aim
is to maximize your profit whoever has the
most profit will win and I obviously brought
prizes for the winner so fairly straightforward
you're going to do this individually
on your own. I don't mind if you chat to
the person next to you. It's kind of awkward
if it's silent in here, but we're going to
do this online. So if you can go to this
website, veeconlab.com, put in BL, this is an
LGR25 under the session name, enter your
name and away you go. You can do it on
your phone, on your laptop, and if you
don't have either, yeah, you can do
it with the person next to you if you
want. But that halves your chances of
winning, I guess. Does anyone have
any questions? So that's an L, not an I. It has the instructions
that you can read again, and you can
continue at your own pace, but it's
essentially what I said. Getting your head
inside the manager. Exploration and
experimentation that you can't even do. But there is a strategy. There is a strategy. So if you produce one
unit, it doesn't matter which one, because
this will be solved. Yeah, so that's
what you're doing. You don't know
how much at work. Yeah, so if you
put zero workers to either create an
example or produce zero units, the stars
mean you don't know. Okay. Yeah. So do you see
how we're going? Yeah? You get it out yet, or? No, you don't know. You don't know. When
you hire a worker, do you know how productive
they're going to be? Definitely a
lot of people. What could I do? What? Like, if you don't
produce this round, because I'm going to
go to the computer. It tells you how
many workers you have to assign
each round. Yeah. Yeah. You'll overthink it a little bit, yeah. Can we go in here
in this round? Good. Do you think you'll
have a chance to win? It's kind of hard
to see. Why are you doing this
on my computer? Yeah, yeah. Yeah,
definitely, if you're on a computer, you
have an advanced job for the phone
users, just because there's a lot of
stuff going on. So, the winner from
the previous class, for those who
have finished, the winner got $1,589 in
the previous class. But they have
double the amount of students in this
class as well. So, it's pretty good. Pretty good. Daniel, you done?
Yeah, I'm done. Solid. That's
good. That's good. Also, it's not a real company, so who
cares? Right. As long as it
helps you learn, that's what I'm
going to do. I'm going to give
you a couple more minutes, and if you
haven't finished, just keep going. We'll do
the prize in a second. I just got to push
on a little bit. How do we go? This is what we're
going to learn. So you can keep
going. If you want, take your
time. No rush. Get back to the
winner in a second. But I just want to
go back to what we're doing, and we have some
measures of productivity. How productive is a
firm? So the total product is the maximum
level of output that can be produced with a
given amount of inputs. This is what we
looked at before, the production function. On
the other hand, simple definition, the average
product is the measure of the output produced
per unit of input. So the average product
of labor is our total input divided by how
many units of labor we're putting into the
production and then vice versa but with quantity
so the amount of output divided by the
amount of capital we're allocating to the
production the important thing here the important
thing always is this idea of the marginal
product or the marginal revenue the marginal
cost and this is the change in total product
the output attributable to the last unit of
an input so what you kind of just did here
was thinking about the marginal product of
labor how does quantity change when the number
of laborers or units of labor changes that's
the important thing here also the marginal
product of capital is a change in the
quantity of output given some change in how much
capital you allocate so for example the
measure of productivity in action we have
five units of labor and 10 units of
capital we have this production function
q equals f of capital and five of
labor this equals 150. so we can compute
the average product of labor that's just
the output divided by how many units
of labor we use 150 divided by five
and that means on average we produce
30 units per worker and for capital we do
the same calculations here just capital
here we have 15 units produced for every
capital unit fairly straightforward this
is the interesting thing this is looking
at in in particular labor and we look
at the marginal product of labor the
total product of labor as well as the average
product of labor so as you can see the total
product of labor of the total product is
increasing for every worker we add all the
way up until j and then it actually decreases
so it's always positive up until j however from
a to e we have this increasing return so
this means while for every unit of labor
that we add total output increases at an
increasing rate at an increasing rate and once
we get to e and we go from a to j for every
unit of labor we add the output is still
increasing but now at a decreasing rate similar
to diminishing marginal utility for each extra
labor we add or unit of labor we add from
here we get more but less more than before
whereas it's the opposite here we get more than
before we get more and we also get more
than before as well i should say so as you
can see the marginal product of labor is
increasing the blue line up until e then decreasing
till 10 and then it goes negative at 11
negative at 11 and And you can see the average
product of labor is below the marginal
product of labor curve between A and here.
And once the marginal product of labor goes
below, dips below, then that's below the average
product of labor. And this is the exact same
thing, just in table form. So fixed capital,
capital is fixed here. We can vary the
amount of labor inputs. The change in labor is
one for all of them. This is the output.
so you can see the output is
increasing all the way up until here, and
then it decreases. Finally, the marginal
product of labor shows us that from
adding the first worker up until adding,
is this the fifth worker? It's increasing
at an increasing rate. We get 76
units of output from adding the first laborer,
then 172 from the second, 244 from
the third, etc, etc. Once we get to here,
every time we add a worker we get a positive
amount of output but it's less output than
the previous worker gave us and then this is
just the average here okay so who thinks I
got the highest profit in the game we just
played well what was your profit 1586
can you anyone be or equal 1586 yeah you
also got 1586 anyone beat that 1595 that's
incredible um okay no one's beating that
I guess what's your name sorry Ryan
congratulations no one's been in 1595 no one's
been 1595 so you get here you go ryan
congratulations so ryan you won not only this
class but out of the other 60 students can
you come and grab this in the in the other
class as well so you've got the highest
score out of like 100 students so far you
surely had a direct strategy to do this
correct what What was your strategy, Ryan? Can
you tell the class? Mm-hmm. Amazing. That's
exactly right. So as you can see here,
the marginal product of labour for green
eggs and the marginal product of labour for
ham were different. So as you can see
for ham, each worker you added would always
give you an output of 16. No matter if
you move from 1 to 2 or 11 to 12, it would
always give you 16. But as Ryan said,
green eggs, as you go from 0 to
the first worker, you get 23 units
of output, and then this decreases
by 2 every time. So, from 0 to 4,
you're always better putting 4 workers
into green eggs. Because as you move
from the 3rd to the 4th worker, that's
17 units of output. Whereas, if you're
on 3 and you put the extra worker into
ham, you'd only get 16 units of output. So,
you're leaving a dollar on the table there.
But once you hit the 4th worker, adding
an extra one into the 5th only gives you
15 units. So this is now below the marginal
product of labour for ham, and you
should put the rest of the workers in ham,
exactly as Ryan said. And this is where
we also want to differentiate
between marginal product and
average product. Because 5 units of
green eggs gives us 95 units, so that's
what? That is 17? No, it would be 19. 19.
So the average product here is 19. So some
people think they should put the fifth
here because the average product is still higher
than one unit of the average product in
here. But we don't think about the average. We
want to think about the marginal product.
How a one unit change affects output. So this
game here was hopefully getting you into the
mindset of thinking of the margin as a manager
of where to allocate your resources. And
yeah, well done, Ryan. That's the exact way
to think about this. okay so the role of
the manager in the production process so
they produce output on the production function
and the idea is to align incentives to
induce maximum worker effort this is harder
than it seems so i'll give you an example of
of me in this situation then we can talk about
a manager an actual company so i have
this principal agent problem with all of
you so ideally and i've kind spoken about this
if I could just monitor how much effort you
put in to this course and how much you learn
then I wouldn't need any assessment so I
could just base it on that but I'm not
privy to that I don't observe how much effort
you put into the course outside of the 50
minutes you spending class three times so I
kind of know what you do at home you could
do anything you could study 24 hours a day
or you could study zero hours a day I couldn't
tell so we use exams and assessments to
try and monitor that but it's not optimal
And it's the same thing with work as well. So
imagine you're paying a labourer to produce
something for you. And let's say you
know that there's a 50% chance every
time they try and make the
product it succeeds. And a 50% chance
that when they try to make it, it
fails. And the amount of attempts they
have at making it depends on the
effort they put in. You don't observe
the effort level they choose. You just
observe the output. They could have gotten
really unlucky and they could have had
10 failures in a row. um statistically
unlikely but this could happen or they could have
had a lot of successes and put in no effort
you can't really monitor the effort so
how does the manager do we induce effort
and this is through the idea of incentive
compatible contracts so we'll speak about this
a little bit later on principal agent
problems but they're very interesting i think
okay and the next thing the manager needs
to do is use the right mix of inputs to
maximize profits so to maximize profits when
labor or capital vary in the short run,
the manager will hire labor until the value
of the marginal product of labor equals the
wage rate. So the value of the marginal product
of labor is just the marginal product
of labor multiplied by the price you get
from selling the good. And you'll
essentially employ people up until
when that equals the wage rate
essentially. So for example, if
they're not equal to each other and the marginal
product of labor is higher than the
wage rate what that essentially means is
you're leaving money on the table you could
hire an extra worker and they produce more
value for you than the cost it is to hire
them so if you're not hiring them you're not
maximizing your profit exact same thing with
capital as well exact same thing with
capital where r is the rental rate of capital
that's just how much you pay for a unit of
capital essentially so you keep producing
if an extra worker or an extra unit of
capital brings in more revenue than the cost
fairly straightforward so the value
of the marginal product is just
the value of the output produced
by the last unit always sink on the
margin law of diminishing returns the marginal
product of an additional unit of output will
at some point be lower than the marginal
product of the previous unit so i kind of um
violating that a little bit in the green eggs
and ham game because one was constantly 16
but at some point it would drop below 16
for the next marginal product so that's what
we're saying here and to maximize profit based
on your input usage you use input levels
at which the marginal benefit equals the
marginal cost shocking shocking stuff here so
when the cost of each additional unit of
labor is w the manager should continue to
employ labor up until the point where w equals the
value of the marginal product of labor in the
range of diminishing marginal product this
is the big caveat here that you haven't
seen what does this mean so this is our
value of the marginal product of labor here
and this is our wage right here so dollars
units of labor so as you can see the value of
the marginal product of labor is increasing
at an increasing rate all the way up until
here then it's increasing at a decreasing
rate all the way up until here and if we
continue with that then it would be negative
so what it's saying is at two points this
intersects with the wage rate over here
and over here it intersects here as we're
increasing an increasing rate and it intersects
here when there's diminishing marginal
product so we have increase in marginal
product and diminishing and the idea here
is all the points above w this is the
amount of value each of these extra workers
are providing you so if you only hide
workers up until this point here you'd
actually be making a loss on every single one
of them except the one here all their value
of the marginal product of labor is
less than w0 but when you go here you get
all this profit here from these workers so
that's why you want to stop at the decrease
in marginal product not at the increase
in marginal product okay so as we as we
just saw below and we saw this idea that at
some point the um the value of the marginal
product of labor will decrease and can even
get into the negatives and i think this is
a nice illustration of that the the the
saying too many cooks is the thing so Gordon
Ramsey's here to evaluate a kitchen and
tell us the issue here So I think this
is a really good illustration
of the value of the marginal
product of labor. Like how much value
do you get from hiring a chef whose job is
to like put a lemon on on each plate so clearly
this is an example of this chef not
optimizing based on on the cost maybe it has
something to do with the idea of fancy
restaurants which i i'm not that familiar with
give me a big bowl of pasta and i'm happy
but clearly gordon ramsay was not impressed
with this so clearly they were employing
laborers below the marginal product of labor
when it was below the wage rate so they
could do better for profits so we talked
about before that the production function is
essentially a technology that maps inputs of
labor and capital into output and here
we have three commonly used algebraic production
functions which are different types of
technology of production so you've actually
seen two of these before in in a kind
of way and then i'll introduce the third to
you as well so linear just assumes a perfectly
linear relationship between all inputs and
total output so it's just the amount of
inputs of capital multiplied by a plus
the amounts of labor, multiplied by b, where
a and b are constants. The Leon-TF production
function assumes that inputs are used
in fixed proportions. So as you can see,
what we have is this minimum
function. So for the engineers here,
you've probably seen this before, but
for those seeing a minimum function
for the first time, nothing to be scared
about. All it says is there's going to be
more than one number in here, and we just
want to take the smallest one. That's
all it's same. So we have a times capital
and then we have a number number b times
labor and whichever one is the smallest
one we're going to take out and that's going
to be our output. Finally we have a
very common production function the Cobb
-Douglas production function and
this assumes some degree of substitutability
among inputs. So this has k to the
power of a multiplied by l to the power of
b where A and B are constants and usually
A plus B equals 1. So this actually is
what gives us our nice kind of convex
shape that we've seen in our indifference
curves. That is kind of a Cobb
-Douglas style function. There are other
ways to get that as well, but Cobb
-Douglas gets us there. So here are
some examples. We have the production
function is linear. It's just 3K plus
6L. When you have 3 units of capital
and 7 units of labor, pretty easy, just chuck
in the three units of capital here and the
seven units of labor here three times three
plus six times seven 51 units of output
nothing groundbreaking this is our leontief
production function we want to take the
smallest number here so inside we have three
multiplied by the capital inputs plus six not
plus and then we have six times the seven
units of labor inputs so we have this 3 times
3 is 9 6 times 7 is 42 the smallest
number in here is 9 that's what we
take out that's what the output
is, 9 units finally we have our
Cobb-Douglas function here you can see a and
b equals 1 so k to the power of 0.7 l to the
power of 0.3 once again just plug in the same
numbers for capital and labour and we get
3.87 which equals 3 units because you're
not producing the 4th you're producing 3 units
you can't produce 0.87 on of a unit that's
an important thing to think about that will
definitely come up on on the exam at some point
so keep this in mind the mathematical answer
isn't the economics answer a lot of the
time so we have these algebraic measures of
productivity so we care about the marginal
product of capital and the marginal product
of labor remember all this is is how much
output we get when we increase the inputs by
either one unit of labor or one unit of capital
so for the linear if we go back here linear
if we want to see the marginal product of
labor we look at the labor sorry the labor
function here we see is l to the power of one
so we take one out the front here multiply
one by b take this to one to the minus one
this disappears and we just get b here so as
you can see the marginal product of labor for
a linear function is b the marginal product
of capital is a the average products are
pretty straightforward you have the whole
production function divided by how many units of
capital you use or how many units of labor
you use respectively. Now Cobb-Douglas
very similar so the marginal
product of capital is raised to the power
of a you multiply the whole function
by a you take the a out from the front
then you reduce the power of k by one
so it's a minus one so you end up with
a multiplied by k to the power of A minus
1 multiplied by L to the power of B,
which is this here. And you can do
the same thing for labor as well, as
you can see this time we're taking
the B out the front and reducing the
power of L by 1. That's how you get
the marginal products in the Cobb-Douglas
function. And once again average products
fairly straightforward. So we can look at the
Cobb-Douglas function in action and see what
the marginal product of labor is. So as
you can see we don't have F of K we have f
of 1 and l and it gives us this function here
and this is telling us that capital is fixed
at one unit and one to the sorry one to
the power of a quarter is just one so this
whole function is just l to the power of three
divided by four so what is the marginal
product of labor when we hire an additional 16
units additional 16 units so we take what
is here out the front so three divided by
4 we take it out the front and multiply L by
3 divided by 4 and then we reduce the power
of L by minus 1 so up here It's 3 divided by
4 minus 1 minus 1 is just minus 4 divided
by 4 So 3 divided by 4 minus 4 divided by
4 gives us minus 1 divided by 4 So that's
our marginal product of labor here Then we
just plug in how many units of labor we're
hiring 16 and it gives us the marginal product
of labor for hiring 16 additional units which
is 3 divided by a. So to finish up
with I want to speak about isoquants
and the marginal rate of technical
substitution. So isoquants are
essentially the indifference curves
of production. They capture the trade-off
between combinations of inputs that
yield the same output when all
inputs are variable. So what this is saying
is if you want to produce 200 units
there are multiple ways that you can do this
by adjusting the labor and the capital so
all these different combinations will produce
the same output so the marginal rate of
technical substitution is the rate at
which a producer can substitute between two
inputs and maintain the same level of output
so we have the marginal rate of substitution
on the indifference curve here we have
the marginal rate of technical substitution
the marginal product of labor divided by
the marginal product of capital. How many
units of labor do you need to give up to
increase by one unit of capital essentially?
Or if you give up one unit of capital, how
many units of labor do you need to add to
get the same output? So these are our
isoquants here. Q0, everything on
this curve, capital on the y-axis, liable
on the x-axis, will produce 100 units. At
A, we have more units of capital, less units
of labor. At B we have more units of labor,
less units of capital. This is kind of
wrong, so don't look at that, but they
produce the same output. As we move up and to
the right, remember that gave us higher
utility on the indifference curves.
Here it gives us higher output as we move
up and to the right. And as you can see, this
is the marginal rate of technical substitution.
So as we start here with eight units
of labor, if we give up one unit of labor
we don't need to get that much of capital
to be able to produce the same amount of output
that's because once you have eight laborers
you've got too many cooks in the kitchen
the eighth one isn't adding much so reducing
that eighth you know worker you need a
little bit of capital to get the same output
but once you move more to the left you can
see from moving from a to b we have to give
up one unit of labor we got to replace it with
one unit of capital to get the same amount
of production 100 units and then let's
say at point c when you only have two workers
then both workers are probably contributing
a lot so giving up one worker means you've
got to replace it with a lot of capital so
you give up one unit of labor from c to d and
you've got to replace it with three units
of capital so this is how you calculate
the marginal rate of technical substitution
the slope is just a change in capital divided by
the change in labor so when there's not
much labor this is going to be really high so
this is minus three and when it's um
you've got a lot of laborers it's going
to be much lower so at eight it's minus one
and down here it would be like minus 0.2 or
something like that so that's for our
Cobb-Douglas function these um iso these
isocorns but we can also look at the isocorns
for the linear and Leontef production
functions so for the linear production
function is just the same as our perfect
substitutes, just linear. The slope is the
same no matter what between the two. The
slope is just going to be the amount of output
you get from each unit of capital and
each unit of labour. Then our Leon Teff
production function is the same as our
perfect complements. So this is the idea you
rely on the least amount of whatever input
you have. So imagine you have one laborer
and a billion units of capital the laborer
can only use so much units of capital at
one time they can't access everything so
whether you have one unit of labor and one
unit of capital you're here or one unit of
labor and a billion units of capital up
here you're still on the same isoquant
it's like having your right one right shoe
and three left shoes you're just as happy as
if you have one right shoe and one left
shoe. Same idea here. So the isocost, so that was
isoquant, the names are way too similar I
know, but the isocost line is the same as
the budget line that we looked at in consumer
theory. So this is a combination of inputs
that yield the same cost. So the wage rate
and the rate of rent of capital multiplied
by the amount of labor you hire and the
amount of capital you hire respectively
equals your cost and we can rearrange this
again in terms of k so k is on our y-axis that's
why we want to do that we take wl to
the other side c minus wl and then divide
everything by r so changes in isa costs for
given input prices isa costs farther from the
origin are associated with higher costs so
if you don't change anything but then you
move up and to the right this just means
the cost c is higher just like i income is
higher as you move up and to the right and
changes in import prices will change the
slope of isocost lines so this is our isocost
line here the y -axis when when labor
is zero it's just your cost divided by
the the amount you're paying on each unit
of capital same with the x-axis it's
your cost divided by the amount you're
paying per unit of labor you can draw
your straight line that has minus W divided
by R is the slope. So like I said before as you move up and
to the right this means the inputs
are the same but you have more money
to spend essentially or the cost is
higher. The cost is higher. It's
probably a better way to think of it.
The cost is higher. So keeping the input
prices the same as you move down and to the
left the costs are small and this will
ultimately depend on your budget as a as
a firm and similar to before if the wage rate
for example increases what this will do is
it will shift from w0 to w1 so at the old
cost you can't produce the same amount anymore
the input prices have changed this
is once again very similar to what we saw
with consumer theory. So previously for C you
could produce anything on this blue line
and interiorly here but now with the wage
rate increasing you can only produce in this
triangle here so all this area here you
can't choose labor and capital combinations
within there anymore. So cost minimization
is when you produce at the lowest possible
cost and the cost minimization input rule
there's two ways to think about it. The
first is producing a given level of output
with a marginal product per dollar spent is
equal for all inputs. So on the left hand
side of this equation we have the marginal
product of labor divided by how much it costs
to pay for labor. That equals the marginal
product of capital divided by how much it
costs to get capital. The reason this needs
to equal each other is if they're not you're
overspending on one and underspending on
the other for example if this is higher than
the other here what this is telling us if
this is higher is that you're probably spending
too much on this because the wage is
too high the marginal part of labor is
decreased so you should decrease how much you're
putting into labor increase how much you're
put into capital until they're equal each
other that's what it's trying to tell us and
from our graphical perspective the marginal
rate of technical substitution marginal
product of labor divided by the marginal product
of capital equals the ratio of the input
prices this is the exact same equilibrium
condition we had in consumer theory it's
where the budget line is tangential to the
indifference curve they're just touching each other
it's the exact same thing here your isocont
is just touching the isocost line and
i think this is a very simple example let's
say you want to produce 100 units and this is
your Isoquant line. You could produce
at point A with a lot of capital and
a little bit of labor and then
you'd be on C1 here. However, we know you can keep
moving the amount of costs down. The slope
doesn't change. If you remember, if we
just change the cost available, we can keep
moving it down until it just touches the
Isoquant line and that's at point b here which
is much lower cost to produce 100 units
of output so it's the same thing here
that we're putting too much into capital
here compared to labor so we want to keep
reducing capital and increasing labor until
we're at the point b so this is how these
two conditions are related and as you can
see mathematically all we're doing is moving
the mpk down here and the w up here
that's all we're doing they're the exact same
equation essentially so to finish up let's
look at this example and this example isn't
a great example but at least shows you
this kind of idea of putting too much into
one thing rather than the other so terry's
lawn service rents five small push mowers
and two large riding mowers to cut the
lawns of neighborhood households these are
the inputs the marginal product of a small push
mower is three lawns per day and the large
is six lawns per day that's how much
output each can create per day The rental
price of a small push mower is $10 per day,
whereas the rental price of a large riding
mower is $25 per day. Is Terry's launch
service utilising small push mowers and large
riding mowers in a cost-minimising way?
And as we just saw, the cost-minimising
condition is the marginal product divided by
how much it costs us. So this is the marginal
product of the small lower, the marginal
product of the large lower. the small mower
can mow three lawns per day and it costs
ten dollars the large mower can do six lawns
per day and cost $25 so currently we're putting
too much money into the large mower this
is larger than this which means we're over
investing in the large mower so what we'd
want to do they don't give us the functions
here so we can't decide how much exactly we
want to reduce the of large mowers we're
investing in and move that to invest in more
small mowers until they equal each other
until they equal each other we're essentially
leaving money on the table when they're not
equal to each other all right that's that's
all i have for today does anyone have any
questions i know there was just a lot of
information thrown out there but it's the exact
same framework as with consumer theory the
exact same framework and we'll pick
up on some more fun stuff we'll
speak about some AI stuff in
the next class