Hello and welcome to this session of Econ 9:15, microeconomic analysis.
I hope that you have had a good week.
And enjoy learning the contents of the last two lectures.
Today we're going to look at the supply side of the market, and instead of.
Starting from the general equilibrium style of model, looking at a perfect competitive market, I thought it might be a bad idea to start with models that can.
Batch capture, what do we observe in real markets?
And the starting point today would be the monopoly market.
While you might think that it may not be that common that a market is completely supplied by only one firm.
However, this is also a very useful model because in many markets firms have substantial market power, or sometimes people also say they have substantial monopoly power firms like Apple for instance. They produce products that are so superior that many people will not consider any other products, and being a substitute to an Apple product.
So to this second segment of consumers, Airport has has substantial market power, so a lot of their pricing behavior would be better captured by a monopoly model compared to another different model, for instance, or that's.
Such a firm large firm Inger?
Bing Free quote, unquote in a free market and in many other cases, monopoly.
Is a feature of the technology. For instance, for instance, utility markets. We often have a monopoly supplying a special specialized market. For instance the water company.
I was in a.
Certain area is only makes sense too.
To construct only one water supply insistent instead of two because.
Having two redundant services, would it be? Would it be?
Efficient so.
In such utility markets, an often we see that the firms are the only supplier to a certain area.
And this these are the. These are the examples of monopolies.
Right, so today we're going to look at.
In more detail, the pricing behavior and all the production behavior of monopoly firms.
Right so.
Let's, let's start with the model, right right from the model, so a monopolist faces two sorts of constraints.
And it chooses its price.
It's price and output levels. First it faces the standard technological technological constraints. It's convenient to summarize the technology.
By the use of a cost function.
Here we use the function C of Y.
And see is the total cost producing Y units of the product.
The second set of constraints.
Is consumer behavior.
So consumers are willing to purchase different amounts at different prices.
Then we can summarize the market demand by this defunction.
D. Would it be the total amount being demanded by the consumers at the price of P?
So as a monopolist.
Its profit maximization problem is to maximize the revenue which is P * Y. The Price times units they produce, minus the total production costs.
And the monopoly can choose any combination of price and output level. However, there is a constraint set by the demand function, because when you produce why units of output, you have to make sure that the demand will be above that. Otherwise you have. You cannot sell all those why units, so the constraint would be the price you set has to be able to sell.
Or the units you produce.
And often you would not set a price.
Often for the monopolist Fillmore monopolist.
Um?
This constraint is bonding.
The market they have to make sure.
The price it says would order would sell or the units that produce because if if this if DP is not bonding, meaning that demand at P is larger than Y then.
The monopoly can reduce the price. A note increase the price. You can increase the price because the demand would decrease as price increases so the monopoly can increase price and still being able to sell. This why units on the other hand the revenue would go up so.
As a result of maximizing its profits.
The constraint has to.
Satisfied with the quality, if it's larger than then why? If the demand it lies in, why the properly can increase its price?
So the monopolies, property market maximization problem becomes.
This.
This function and it is maximized only on P.
Right, because the constraint is bonding so.
It's often.
Easier to work.
The proper work on the problem from a different perspective. For instance, the instead of understanding or choosing what price it sets by maximizing this profit function.
It's it would be the same for the.
For the monopoly.
To choose the level of output.
Such that the.
It says that the price is automatically determined by the inverse demand function, which means that the price it has to set to clear the market or sell the sell the units they produce.
So this is this is often convenient to have the inverse demand function where you're on the vertical access you have price on the horizontal axis you have why the output? And often we can represent the demand function P of Y as a downward sloping function.
So the monopoly, given this inverse demand functions are monopolies. Maximizing problem would be to set the output level.
Such that the revenue minus the total production costs is maximized, so that's the same problem from two different perspective. Why is to set the price?
And you produce up to that demand level. The other is to set the ultimate level and the price will be determined by the market supply. The demand function. That or the units you produce or be.
Purchased so that's the same maximization problem from two different perspectives.
So we know we all know how we all know how to find the solution to this.
To this problem. So to understand the output level that maximizes problem, we have this first order condition as follows.
P + P prime awai the.
The marginal effects of outputs on price because the more you produce or decrease your price.
And times why the total output? This is the marginal revenue has to equal to marginal cost of production. That's the 1st order condition.
Normally with a downward sloping demand function, the 2nd order condition is also satisfied, but it needs to be because the profit function to be maximized need to be concave, so the 2nd order conditioning need to be negative.
Which also means that.
The 2nd order condition requires that the derivative of the marginal revenue must be less.
Then, the durative of marginal costs.
So.
The margin, in other words, the marginal revenue revenue curve has to cross the marginal cost curve from above, because if you if you have a producer less than the 1st order condition output level, then marginal revenue has to be above marginal cost. If we produce more than the optimal level than the model revenue has to be below marginal cost so it crosses.
The major cost of frontier above, and only once.
In our way.
So why don't we look at a graph representation here we have downward sloping demand function. This is downward sloping demand function, and we know that the marginal revenue curve is.
Is like this almost 1/2 of the?
Between them
it's it's easy to calculate. For instance PY of Y, that's revenue.
And the marginal revenue curve is PY.
Plus T.
And that's it. And this is the demander.
Is this is the demand function inverse demand function, the price right? And this is less than zero because it downward sloping so the marginal revenue function has to be to the left of the demand curve and we can draw it as here marginal revenue curve and this is the marginal cost curve. Normally a production technology is convex, the more you produce the higher the marginal cost would be. So this is the monopoly.
Monopoly level, as you can see, the marginal revenue curve cross the marginal cost curve from the above and only crosses and once.
So on this page.
When the monopoly monopolistic considers selling DY units.
Of more output, it has to take to take into account two effects. First, the revenue will be increased by P * D Y the extra unit you sell at the price P will give you a boost in revenue. Second, in order to sell this additional output, it must reduce its price by this much.
So then this is depending on the curvature of the.
Of the demand of the inverse demand function, and this is negative.
To the monopolies.
Revenue because.
The price has to be decreased for every unit it sells.
So the marginal revenue.
When you produce a little bit more is captured by this aggregate level.
Of impacts
so the 1st order condition would say that the revenue marginal revenue has to equal to marginal cost.
Which gives us this condition. First you can see that the simple algebra will tell us that when the marginal cost equal to marginal revenue, this has to hold.
And when we write epsilon, the.
Demand the price elasticity of demand, which is we look at how much demand is affected by and.
Change in price and normalize it by.
Normalize it by the percentage.
Of the change and which is.
Equal to Pete.
Divide by YDYDP.
Normally if we increase the price, why should decrease? So this is less than zero. So and this is, pricing is still demand, and if you if we use this notation.
Then we can write.
The 1st Order condition in this way, so price times 1 + 1 over epsilon.
Has to equal to the marginal cost of production.
And it follows from the first or condition that the at optimal level of output the elasticity of demand must be greater than one in absolute value. What does it mean?
It means.
I can erase this part.
Because the marginal cost of production is positive, so this is 1 /. 1 over epsilon has to be larger than zero as well, because the price is positive and marginal cost of production is causative and this has 2 equal to 0, so there one over epsilon has 2 equal to minus. A has to be large than wireless one.
And we times both sides by epsilon because epsilon is negative, so we need to switch to a sign of switch the inequality sign when we multiply both sides by epsilon. This will be one less than 1 -- 1 times epsilon. Then you can see that the absolute value of epsilon price elastic demand has to be greater than one.
That means that the monopoly has to set its price at the.
Elastic part of the demand function instead of the elastic part of the demand function.
So that's the economic inside of how monopoly set its price, or how monopoly set its own output level at. This is output level, and this is the price level. At this point the price elasticity of demand.
In absolute terms, has to be larger than one.
So.
Right so.
That's a monopoly case.
I think from from there.
The basic microeconomics modules that you might have taken in your undergrad studies. We all know that the monopoly produces what is socalled data weight loss, meaning that the level it produces is not socially efficient socially optimal, and this and I would say that in many markets in reality that firms to some degree they enjoy some level of market power or monopoly power.
So.
This type of inefficiency is rather norm rather than the exception because if we look at the general equilibrium model, we see that the market is always efficient and the marketing cribbing is pretty efficient to any. Protein efficient can be implemented by a marketer Caribbean, so it's all very nice there, but in reality.
What are firms does in the market does not always.
Does not always maximize the social welfare in the country where they maximizes their own profit is oftentimes is different from.
From the social welfare so.
That's the important different different sides of the general model would be 1 extreme and here today we look at another.
Spectrum of the of the modeling choice where we look at the monopoly.
So to understand.
Social welfare. Let's consider any car economy with only one consumer.
And with the quasi linear utility function so we can separate this market from the rest of the consumption.
You can think of why as amount of money the consumer possesses, X is the unit, the.
The consumer consumes these products in question.
So.
In this case, the inverse demand function from the utility function is given by P equal to the marginal utility of consumption. In other words, is that when the consumer maximizes utility, there will be.
Utility of Consumer X units you originally have why units or numeria RY units of currency you would have if it helps so and then you have to pay for the P unit at the exit units of the product that you consume.
And the price is P. So if you maximize this, you with respect to X, naturally the marginal utility of consumption has to equal to P, the price and this price if you.
Consider.
If we look at this function is a function. This actually gives us the inverse demand function, right? So this is penises X, so this is the inverse demand function when P decreases.
The marginal utility has to decrease, and when does the marginal decrease? When consumer consists more so X increases, P decreases, so this is actually the inverse demand function.
And.
As before, let's.
Call CX
let's say Expedia production costs of Monopoly.
The social welfare.
Which is the sum of consumer Sir plus plus profits?
Anne.
But in other words, if we look at this look at the system that how many units being produced.
Anne.
Oh, and being being consumed were bring UX of utility, UX of utility.
And the total cost of production.
Is C of X, so this is.
We have social welfare function quite.
So.
So if we would like to be more precise so the welfare equal to consumer Sir plus.
Plus
the monopoly profit.
Consumer Sir, plus consuming X units would be UX.
Plus Y minus PX right?
Because that's.
Your consumption and this is the price you pay.
This is consumer Sir plus plus the profit the monopoly would get their revenue. That's what the consumer pays for the product products they consume minus.
C of X right?
That's the production cost of the monopoly. So in total it would be would be U of X. This cancels out.
Plus why?
Minus 6.
So then you would wonder why did we left?
Why did we leave the leave the Y out here?
Well, as you know, that utility function is all only in this context only serves the ranking of the preferences for instance. So any monotonic transform transformation of the utility function would be equally good. Utility function for this representation.
And this why is a constant as well. So if we ask the question whether the social welfare is maximized or not, this is as good as this one and for simplicity we can leave the constant out because when this is maximized and this is maximized as well, right?
So.
And this is the.
Social welfare total consumption utility derived from X and total production costs. The difference of these two represents social game from having this market.
And socially efficient outputs.
Would imply that you prime of X should be equal to see prime of X, so marginal utility should be equal to marginal cost and this should be the market price.
Market price so that so the market is only efficient when the price is equal to marginal minor cost.
So in the previous example having of this.
Market is only efficient when the price.
Let's call it a quiet prior P, not.
Price equal to marginal cost only when this point and you can see that in this case the efficient level output is larger than the monopoly case since the only one.
Michael Casa equal to marginal utility. Marginal utility is represented by the downward sloping demand curve, and only when these two equal to each other do we have an efficient allocation. And in this case we can see the monopoly.
Is not producing to the efficient level right? And this is a rather general?
That's it.
Monopoly.
At the monopoly level, marginal cost marginal revenue. So if we evaluated the marginal minor impacts of outputs on welfare.
At the monopoly ultimate level, then the marginal utility minus the minor cost marginal marginal cost equal to this part due to.
Monopoly the monopolists profit maximization behavior. So if we substitute this to this part.
And note that you prime.
Of XM is equal to PM.
Equal 2 PM.
Or rather equal to P of XM.
And if we put this part into it and use this for that one, then we know that the marginal impact of ultimate only welfare is minus P. Prime Times XM, and this is.
The derivative of the demand function is the 2nd order derivative of the utility function, which is less than zero because we have a minus sign in front of it. Then we have a positive sign here. So at the utility level, social welfare will increase out. No enter the monopoly ultimate level. Social welfare will increase when we.
Um?
When we increase outputs.
In this sense, in a sense, in this diagram.
If we increase from the majority of monopoly also output a level then.
The.
Social welfare will increase. What is social welfare actually is measured by this area in the monopoly output. This area.
For instance, the blue part is the total cost of producing that many units, because if we integrate, if you integrate from zero to YN, the marginal cost.
Of the Y is equal to Cy.
Evaluated from YN 2 zero, which means say an. So if you integrate this part in the sense that you have this, you calculate the area below the marginal cost curve. Then you have the total cost of production. On the other hand, if we integrate.
Below the.
Below the price curve, so zero to YN of P of YDY because.
PRY equal to marginal utility of the Y marginal utility. This is you.
Why evaluated from zero 2 YN is equal to U?
YN
assuming.
If utility is zero when you can consume nothing of this product. So what is social welfare? The social welfare is the blue parts.
Social welfare is the year, the.
The part marked by this area, right? So the consumer Sir. Plus and this is serious and this is cost. This is cost consumers of consumer welfare minus.
The consumption supplies minus the cost. This is a social welfare and and then you can see if we increase why a little bit then this area increases.
Right so this.
The social welfare increases as we increase the output from the monopoly level, and this process continues until we reach this parts and in this part is nothing but the part of our P equal to marginal cost, and only when we have this only when we are in this area this point.
Then if you further increase the output, then the cost is above the utility marginal utility. So you only create a negative impact to social welfare so.
This is efficient part. The lesson is at at the monopoly level. It's not efficient. So in this is.
And capture here.
So increasing output at the front utility level will increase utility.
We can also write the social objective function as consumer Sir plus profits process the profits and this is what we have done before.
And do it if of profits with respect to X is 0. So if we take dirt of this part is 0 gum.
And dirty will consumer Sir plus at XM.
Is.
Logic is larger than zero, so that's easy to to look at, because if we look at this point will be you prime minus P prime of X -- P of X.
And then we have this part evaluate, evaluate it at the.
At the monopoly case.
Then we have this part and because.
The consumer is.
Is optimizing its consumption? The minor utility has to equal to price, so this is zero and we only left with this parts. And because this is negative in front of it, there's negative sign. So the entire thing is positive. So these are the two perspectives and how we can get that Monopoly is producing too little compared to the efficient outcome, right? There's someone out because.
So let's take a break and.