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Chapter 1
Principle 1 - people face trade offs
All decisions involve trade-offs, examples:
· going to a party the night before your midterm leaves less time for studying
· Having more money to buy stuff requiring working longer hours which leaves less time for leisure.
· Protecting the environment requires resources that might otherwise be used to produce consumer goods

Principle 2 the cost of something is what you give up
· making decisions requires comparing the costs and benefits of alternative costs
· The opportunity cost of any item is whatever must be given to obtain it
· It is the relevant cost for decision making

Principle 3 - rational people think at the margin
A person is rational if she systematically and purposefully does the best she can to achieve her objectives
· many decisions are not “all for nothing,” but involve marginal changes - incremental adjustments to an existing plan
· Evaluating the costs and benefits of marginal changes is an important part of decision making

Principle 4 - people respond to incentives
· incentive: something that induces a person to act I.e. the prospect of a reward or punishment
· Rational people respond to incentives because they make decisions by comparing costs and benefits.
Examples: in response to higher gas prices, sales of “hybrid” cars (eg. Toyota Prius) rise. In response to higher cigarette taxes, teen smoking falls

Principle 5 - trade can make everyone better off
Rather than being self - sufficient, people can specialize in producing one good or service and exchange it for other goods
· countries also benefit from trade and specialization
· Get a better price abroad for goods they produce
· Buy other goods more cheaply from abroad than could be produced at home

Principle 6 - markets organize economic activity
· a market is a group of buyers and sellers
· Organize economic activity means determining
· What goods they produce
· How to produce them
· How much of each they produce
· Who gets them
· In a market economy, these decisions result from the interactions of many households and firms
· The interaction of buyers and sellers determined price of goods and services
· Each price reflects the goods value to buyers and the cost of producing the good
· Prices guide self-interested households and firms to make decisions that, in many cases, maximize society’s economic well being

Principle 7 - government can sometimes improve well being
· people are less inclined to work, produce, invest, or purchase if large risk of their property being stolen
· A restaurant won’t serve meals if customers don’t pay before they leave
· A music company won’t produce cds if too many people buy copies illegally
· Government may alter market outcome to promote efficiency.
· Externalities: when the production or consumption for a good affects bystanders (pollution)
· Market power: a single buyer or seller has substantial influence on a market price (monopoly)
· In such cases, public policy may increase efficiency. Government may alter market outcome to promote equity

Principle 8 - a county’s standard of living
· standard of living is dependent on the productivity of labour.
· Labour more productive = standard of living will be higher.

Principle 9 - price rise when the government prints too much money
· inflation: increases in general level of prices
· In the long run, inflation is almost always cause by growth in the quantity of money which causes the value of money to fall
· The faster the government creates money, the greater the inflation rate

Principle 10 - society faces trade off
· Times when reducing inflation may lead to greater unemployment
· Reduction of unemployment may lead to inflation










Chapter 1

Economics methodology is the same as any science discipline. Partly science, called social science.

What is an economy?

Fundamental properties –

Property ownership –
Freedom of choice – choices have two dimensions, choice on the consumption side and on the production side. Free to make choices on both sides. No such thing as absolute freedom.
Self-interest – improve lot, freedom is guided by self-interest. In journalistic writing, self-interest is assumed to be selfishness. Selfishness comes out of self-interest, every action taken in self-interest is not a reflection of selfishness. Selfishness is pursing self-interest at somebody else’s expense. Self-interest is genuine but selfishness is not. Self-interest is the driving force of the economy.
Price signals - A market economy, how resources get allocated to various goods and services
Competition – significance of competition in reducing the excesses that could be committed in a market economy when self-interest is pursued. Without consideration of welfare.
The economic role of government - not an essential characteristic of a market economy/price system.

What is economics?
- Economics is the study of efficient allocation of a society’s scarce resources to produce goods and services that satisfy human wants, and how those goods and services are distributed among the members of the society.
- Two things being emphasised, functions of an economic system. Allocation function (efficiency) and distribution function (equity).
- Sometimes will be conflict between achievement of goals relating to these two functions.

Wants/needs – every need is also a want, every want is not a need. Wants include things that are not needed but enjoyable.
Goods and services – good are tangible, services are intangible. Goods have a physical existence whereas services don’t. Goods can be stored (gap between production and consumption). Services are produced and consumed simultaneously.
Resources – things that are used in the process of production. Three categories: Raw materials, energy, factors of production.
General form of resources: Labour (human work, skilled labour, political labour etc.), Capital – physical: produced means of production something that has been produced previously (Machines/tools/factories), Land (natural resources), entrepreneurship
Scarce -

Adam smith, father of economics. The wealth of nations 1776. The one who systemized economic ideas and put them in a package, which is now called economics.
The idea of invisible hand, leads to desirable market outcome.

7th principle, role of the government: if there are deficiencies, society would respond to those deficiencies through a collective institution. Natural for economics to assume these additional functions can be assigned to the government.
In economics, we split these deficiencies in two categories:
I. Market Weaknesses,
II. Market Failures.


Market weaknesses – distribution of income in the economy may not be desirable which means that there may be a higher unequal distribution of income, rich people and poor people.
- Ask government to redistribute income by adopting various policies.
- May result in excessive market power in the hands of few people.
- Split in four broad categories: perfect competition, monopoly, monopolistic competition and oligopoly.

Market failures: market outcomes fails to satisfy allocative efficiency.
- Allocative efficiency: best outcome from the society’s point of view. When the best is not achieved, market has failed to achieve that best. 1 External effects (if consumption or production leads to positive or negative effect on bystanders), 2 Public goods (provision is not possible through the market therefore there is a market failure)
- Governments economic rule is connected to the allocative function (allocative efficiency) and the distribution function (equity)

That is to say that government actions –or interventions in the market mechanism – can be helpful to achieve:
1. The goal of efficiency
2. The goal of equity
Chapter 2 – Thinking like an economist


Methodology in economics:
- Scientific method involves observation, theory, and more observation
- Social scientists/economics/scientists build models to test those theories.
- Models come in a variety of forms: tables (tabular models), diagrams, figures (diagrammatical models), equations (mathematical models)
- Diagrammatic model – most useful model because of visual information conveyed by that model.
- Two dimensional diagrams - only two variables can be included. Diagrammatic models have the deficiency that you include more than two models
- Every model is constructed on the basis of assumptions. Assumptions come in two forms: behavioural assumptions (what are producers/consumers trying to achieve?), simplifying assumptions (ceteris paribus)

Economic models:
- May represent a relationship between two variables, x and y. this relationship may be a relationship of correlation. A more sophisticated relationship maybe be called a cause and effect relationship; one variable is a cause (independent variable), effect (dependent variable)
- Constructing a two dimensional diagram, with 5 independent variables, you can only pick 1 out of 5 to focus on. The other variables will be called the left out of excluded variables

- There are two independent variables in this model – price and income. Both of these cause changes in quantity when they change

- When plotting data in a diagram, there are two very important parameters: vertical intercept and slope.






Mathematical models:


- QD (quantity demanded is a function of p)
- Exact relationship between p and QD is given by the equation, a – bP
- A is the constant of the equation, shows up as the vertical intercept
- B is the coefficient of the variable, shows up as the slope
- Independent variable is P, negative sign shows that the relationship between p and QD is negative
- The slope mathematically is: Vertical change divided by horizontal change

if y is on the vertical axis and x is on the horizontal axis, it will be changed in y divided by change in x.
- Slope can be calculated by picking any two points (end points/middle points) if it’s a straight line
- Vertical change is 2, horizontal change is 8, therefore slope is 2/8 = ¼
- The slope of a nonlinear curve, a linear line must be drawn as a tangent to the point for which the slope is to be computed and then the above procedure is to be applied



The PPF model:
- The PPF model can be constructed for diverse scenarios. It could be constructed for an individual, a firm, a sector of the economy, or an entire economy
- Model will be constructed on four assumptions:
- Two goods – computer and cars
- Given resources (tradeoff between two goods)
- Given technology (technology change can lead to a change in production)
- The law of increasing opportunity cost – as you produce more and more of a good, its opportunity cost keeps on in terms of quantity, increasing


- Two goods, computer and cars
- Whenever you produce more of one good, the quantity of the other good will be decreased. As you move down the curve, more cars are being produced and less computers.
- As you move from down to up (E – A), you’re producing more computers but less cars.
- D represents that the resources are being wasted
- When you move down the curve (F – E), more cars are being produced and less computers.
- Opportunity cost is increasing




Shifts:
- When changing things that are kept constant, the curve will shift. The shifts include: non-neutral shift and a neutral shift.



NON NEUTRAL SHIFT NEUTRAL SHIFT

- Technological change Is applicable to both goods, then PPF will shift in a neutral way (right graph)
- If more labour/capital/land resources are available then the shift will be a neutral shift.
- Sometimes natural disasters destroy the capital stock, if capital is decreased and population is reduced then PPF will shift inward rather than outward.


In a diagrammatic form, it is important to distinguish between a movement along a curve and shifting a curve
Slope is the effect of an independent variable and shift is the effect of a left out
variable
Whenever a left out variable changes, the constant of the equation changes. Positively or negatively so it may be a upward or downward shift





Chapter 3 - INTERDEPENDENCE AND THE GAINS FROM TRADE

- Trade makes everyone better off
- Trade requires an interaction between two parties – a buyer and a seller
- Trade interaction makes buyer and seller better off; These parties could be two persons, two cities, two provinces or two countries
- Trade is based on specialization, and implies specialization

To provide a proof of this proposition, we will use a model that we have studied in the previous chapter - the PPF model. To keep things simple we will not use a mathematical model, and thus we will use only the other two forms – tabular, and diagrammatic forms. Since every model is constructed under certain assumptions, that is therefore the starting point of our discussion.
Assumptions of the model:
1. Two neighboring parties – a Rancher (Rose) and a Farmer (Frank)
2. Two goods – Meat and Potatoes
3. Given resources
4. Given Technology
5. Constant opportunity cost
The last assumption is made to keep the model as simple as possible – a methodological principle. The results will remain unchanged if we keep the law of increasing opportunity cost.

. Economics has long noted that trade is based on ‘comparative advantage’ and is not connected to what is known as ‘absolute advantage’. It may also be noted that comparative advantage may exist even in the presence of absolute advantage. Comparative advantage could also be referred to as ‘relative advantage’ – in line with that being the general term used in economics – but economics retains the term in honor of David Ricardo, a 19th Century economist, who first figured this out and used the term ‘comparative’ in his exposition.
Understanding the difference between these two terms is crucial to follow the argument. This difference can be explained in two alternative ways: i) in terms of of productivity, or ii) in terms of opportunity cost. It may be noted that:
§ Absolute advantage would exist if one party is more productive in the production of both the goods. In such a situation, that party would have the lowest opportunity cost figures - the opportunity cost of producing any one of those goods in terms of the other good – an idea that was introduced in the last lecture.

Comparative advantage is based on relative productivity, or opportunity cost, advantage. It is quite easy to see that if each of two parties is more productive in the production of one of the goods. Each party would have comparative advantage in the good in which it is more productive.
A complication arises in the case where one of the parties has absolute advantage – i.e., it is more productive in the production of both the goods. In such a situation, it is difficult to see the existence of comparative advantage. Thus, it may be concluded that the party which is more productive in the production of both the goods does not need to participate in trade with the other party.
However, this conclusion is not warranted. Even when one of the parties is more productive in the production of both the goods, its productivity advantage may be more in one of the goods. It practice, it is almost impossible that the productivity advantage may be exactly of the same proportion in both the goods. Therefore, normally the party with absolute advantage will have a comparative advantage in the production of the good where it is relatively (or comparatively) more productive.

Viewed from the opportunity cost point of view, each of the parties will have relatively lower opportunity cost in the production of one of the goods. And this would imply that the party with productivity disadvantage in both goods will have relatively lower disadvantage in the production of one of the goods. This may seem complicated until we come to compute these values, once the model has been constructed, a little later.
We may note, though, that it was precisely this idea that was explained by Ricardo in the parliament when nobody understood it when supporting the arguments that proposed trade restrictions.
Let us proceed to the construction of the model by noting that both farmer and rancher can produce both the goods, and in absence of trade, they will consume whatever they themselves produce. Such a situation is one of self-sufficiency which in economics is referred to as ‘autarky’. In such a situation, each will produce what he/she would like to consume, and thus their PPFs also become their ‘Consumption Possibilities Frontiers’ (CPFs) – a new concept.

When it comes to selecting the form of the model to be used, we will use two forms: i) the tabular form, and ii) diagrammatic form, as noted earlier. This has the advantage of showing that what can be represented in one form may also be represented in the other. This will also show certain advantages of using a particular form, as will be shown a little later.
Based on the data at our disposal, we have constructed these models in the next slide in a situation of autarky where PPF coincides with CPF as shown there for both the parties.
The gains from trade are less obvious, however, when one person is better at producing every good (in the present case both the goods) for self-consumption, a point made earlier.



When we look at the numbers somewhat closely, we find that the rancher is 3 times (= 24/8) more productive than farmer in the production of meat and is only 1.5 times (= 48/32) more productive in the production of potatoes. Ricardo concluded that rancher had a comparative advantage in the production of meat and thus, he concluded, in a similar situation his country will be better off when specialization and trade is permitted – indeed encouraged.
Thus, the parable continues with the rancher seeing this clearly after many years of autarky, and goes to the farmer to propose to him that he should specialize in the production of potatoes, and that he/she will supply him with whatever quantity of meat he needed for consumption from his/her own production of meat only – as a result of his/her specialization in meat.


Specialization and Trade
Before we show how the rancher (indeed Ricardo, to begin with) reached this conclusion, we also need to adopt the alternative approach for this subject – to argue the case in terms of the opportunity cost differences – which is the usual approach followed in the textbooks.
We may note – or rather recall from the last chapter – that the opportunity cost of the good on the horizontal axis in terms of the good on the vertical axis is given by the slope of the PPF. It may also be noted that we can represent any of the goods on the horizontal axis. The logic here is very simple. It assumes that we are moving down the PPF from any starting point, and thus are producing more of the good on the horizontal axis by giving up some quantity of the one on the vertical axis.
We may select the end points of the two PPFs to compute their slope values. For the farmer, the opportunity cost of potatoes in terms of meat is ¼ (= 8/32), and for the rancher, the number turns out to be ½ (=24/48). This means the farmer has lower opportunity cost in the production of potatoes as compared to the rancher – this being a reflection of lower productivity disadvantage we saw earlier. Thus, he should specialize in the production of potatoes.

The easiest way to do this is to inverse the axes – put meat on the horizontal axis and potatoes on the vertical axis - instead of moving from a lower point to a higher point on the PPF to compute the needed opportunity cost. The opportunity cost numbers will get inversed as a result of inversion of the axes. Thus for the farmer, the opportunity cost of meat in terms of potatoes will be 4 (32/8), i.e. 4 kgs of potatoes will have to be sacrificed to produce 1 kg of meat. When we compute that number for the rancher, we get 2 (= 48/24) – i.e. Rose will have to sacrifice only 2 kgs of potatoes to produce 1 kg of meat. She has lower opportunity cost for meat as compared to the farmer – a reflection of the higher productivity advantage in meat, as we saw earlier.
Therefore, the conclusion is that the rancher has a comparative advantage in the production of meat, and once the comparative advantage of one of the parties becomes clear, the logical conclusion is that the other party has comparative advantage in the production of the other good. Thus, the farmer has comparative advantage in the production of potatoes, as we saw earlier.
This means the rancher will specialize in the production of meat and the farmer in the production of potatoes, and this will make both of them better off by making it possible for them to consume more of both, or at least one good, in contrast to autarky, as a result of specialization and trade – as we will see a little later. It may be noted that trade can also be referred to as ‘exchange’.

Let us assume that the rancher was successful in convincing the farmer to proceed with the proposal of specialization, and they became well off. Here, though, it is not difficult to see that any beginner would be somewhat skeptical of this argument, and thus would like a rigid proof for this. Let us proceed with this proof. Here, I will adopt a slightly better approach than the one used in the textbook: I will focus on constructing the CPFs for both the parties. While in the case of autarky, a CPF coincides with the corresponding PPF, in the case of specialization and trade, the CPF will diverge from PPF, and the nature of this divergence will provide the needed proof.
The first thing to note is that trade cannot occur without an exchange ratio – the rate at which a unit of one good will exchange for another good. Thus, in the present context, we need an exchange ratio (ER) between meat and potatoes. How this ER is actually determined in a market economy is a question that we will return to a little later. Here we are interested in focusing on the theoretical basics of this issue.
























Market Equilibrium – Chapter 4

Prices are determined through market mechanisms by the interaction of the market forces.
A market is an institution which brings buyers and sellers into contact through various modes so that they may be able to conduct transactions. As far as the market forces are concerned, there are two forces: one associated with the buyers (demand), and the other with the sellers (supply). Thus, we are going to work with demand and supply forces.

Markets are perfectly competitive. At this stage, there are a large number of buyers and sellers meaning that none of the participants in the market will have any power to influence the outcome of the market – this is also called ‘price taking behavior’.
Demand and supply forces brought together is to see how market equilibrium is obtained. This is called a market equilibrium model.

Determinants of Demand:
One can think of many things that influence demand of different buyers but here we would like to identify the ones that we think are the most important ones, and these will include:
1) Price of the good or service – henceforth the price.
2) Income.
3) Prices of the related goods or services.
4) Price expectations
5) Tastes, and for the market demand
6) Number of consumers.

what sort of effect on demand will each of these forces have?
Price is the most important of these variables that will now be called the ’determinants’ of demand. A little reflection on this variable will lead to the conclusion that it will have a negative effect on the quantity a consumer will purchase, i.e. the quantity demanded. In economics, this is a very important relationship, and is denoted as the ‘law of demand’.
In view of its importance, let us formally define it (a definition that must be kept in mind throughout this course): “There is an inverse (or negative) relationship between price and quantity demanded”. What this law means is that whenever price increases, the quantity demanded will decrease and vice versa, as we will see when we construct a demand curve in the model. Also keep in mind the significance of the word ‘law’ throughout our coverage of economics.
The second variable is income of the consumer. Income represents his purchasing power, and thus it is easy to understand that whenever this purchasing power changes, the consumer’s behavior towards his/her purchases will change. However, this effect is slightly more complicated than the price effect considering a varied basket of goods and services consumed by every consumer.

A careful look at the consumer behavior reveals that this effect may be positive or negative for a particular consumer depending on the nature of the good under consideration. And if that is the case, it may in some cases be even zero.
We note that normally this effect will be positive. When income increases, the demand will increase. Pay attention to language: ‘demand’ and not ‘quantity demanded’ as was the case earlier. This will become clear a little later when we construct the model curve in the model. But then there may be cases where this effect may be negative. Considering these possibilities, we need to note:
v When income effect is positive, the good will be called a ‘normal good’ – the normal situation.
v When it is negative, the good will be called an ‘inferior good’ – no ethical connotations though.
v When it is zero, it will be called a ‘zero income effect good’.
It may be pointed out that the same good may be normal (in most cases), inferior, or zero income effect good.

The negative effect may seem odd to a novice, but it is quite possible that when income of a family increases, they may reduce their consumption of margarine by moving on to butter. One can think of many such examples. What we need to note is that, in general, these odd cases are only a few among a large number of consumers.
When it comes to prices of the related goods, we are focusing on the goods that are related on the consumption side. Such a relationship may be one of ‘substitutability’ – when the two goods serve the same want – or one of ‘complementarity’ – when those are consumed together.
When two goods are substitute goods, and the price of one of those changes, the demand for the other will be influenced. For example, when the price of a soft drink increases, it will become relatively expensive compared to another soft drink whose demand will increase in response, and vice versa when the price decreases. This is called a ‘substitution effect’.

Such an effect will work in the reverse direction in the case of complementarity. Consider coffee and cream that are complementary goods. In this case, if the price of coffee increases, and thus leads to a decrease in its quantity demanded – the law of demand – the demand for cream will also decrease – for now less cream is needed. The reverse will happen when the price of coffee decreases.
We now come to price expectations – that is what is expected about the price change in future. Expected changes in future will lead to changes in the current demand – people will respond to those expectations to reduce the impact of those changes on their future purchases. For instance, if the price is expected to increase, consumers will increase their purchases now for future consumption to avoid paying higher prices later. Thus if price is expected to increase, current demand will increase (a positive effect). If the price is expected to decrease, the reverse will happen. In this case the current demand will decrease (again, a positive effect – a negative into negative).

Next variable to evaluate is ‘tastes’. This is a very general variable to account for all sorts of other effects on demand such as cultural, religious, fashions etc. that lead to changes in demand. These effects will vary from source to source of these effects, and these could be positive or negative. Consider that source to be fashion: fashion could change favorably – when something becomes fashionable (a positive effect) – or unfavorably – when something becomes unfashionable (a negative effect).
Finally, the number of consumers will have a positive effect on demand, i.e. the larger the number of consumers, the higher the demand. This effect is related directly to the ‘market demand’ rather than the previous cases where our focus was only on individual demands, and we must note that changes in individual demands will also change market demand. We may think of these as an indirect effect on the market demand.
We are now ready to start building the model. Our primary focus will be on diagrammatic model, although we will also see the tabular form here. Although we can use the mathematical mode – which will have certain advantages, as will become clear, in our discussion – but we will focus on the diagrammatic model to keep things as simple as possible.

In contrast to the mathematical models in which we can include as many variables as we want, in diagrammatic model we are forced to reduce that number considerably. How many variables can be included in a diagrammatic form? Well, the answer is at the most three: one dependent variable and two independent variables. In such a situation, we will need to construct a three-dimensional diagram, which is a very complicated task.
Throughout this course, we will construct only two-dimensional diagrammatic model. This means, we can include only one independent variable along with a dependent one. To begin with, we will focus on the individual demand curve, and this means we can select only one of the five variables listed above for inclusion in the model. Since price is the most important of those variables, therefore that is the one to be included in the model.
What we now need to do is to plot the individual demand curve. In the model we are going to construct, price will be represented on one of the axes, and quantity on the other. Although the mathematical convention is to put the independent variable on the horizontal axis, in economics we don’t follow that convention and put price on the vertical axis. In the following model, we will assume that other things remain unchanged – that is, other determinants don’t change.


Individual Demand Schedule or Demand Curve






§ Whenever the price changes, the quantity demanded changes, such a change will show up as a movement along a given demand curve: upwards when P increases, and downwards when it decreases: these are the manifestations of the ‘law of demand’.
§ The demand curve was plotted in a two-dimensional model under the assumption that other determinants of demand remain unchanged – the ceteris paribus assumption. But, then, if a change occurs in any one or more of those variables, something will happen to the demand curve as we will see a little later.


Market Demand versus Individual Demand

§ Market demand: The sum of all the individual demands for a particular good or service. Thus the market demand curve is derived by a horizontal – the quantity side – summation of the individual demand curves.

Market Demand as the Sum of Individual Demands



Shifts in the Demand Curve

Any change in the left-out variables will cause a shift in the entire demand curve. Thus when such an effect is positive – an increase - the demand curve shifts to the right, and it is called an increase in demand.
On the other hand, when such an effect is negative, the demand curve shifts to the left and is called a decrease in demand.
We can relate these shifts to any change coming from those left-out variables. For example, any change in income may cause a positive shift in the case of a normal good, and reverse in the case of an inferior good. Similar effects will occur in the case of substitutes and complementary goods.


On the supply side, we proceed in the same steps as we did on the demand side. We begin with:
§ The Law of supply: ‘There is a direct (or positive) relationship between price and the quantity supplied.’ Just like the demand side, there are other variables, besides price, that influence supply. These shift the supply curve.
§ Factors that shift the supply curve: The Determinants of Supply
1. Input prices
2. Technology
3. Expectations about future price
4. Number of sellers
Let us begin with the price variable to build the model on the supply side.

Market Supply versus Individual Supply

§ Market supply: The sum of supplies of all sellers.
§ Thus, the market supply curve is derived by a horizontal summation of all the individual supply curves.




Market Supply as the Sum of Individual Supplies


Shifts in the Supply Curve
§ Any change that increases the quantity supplied at every price shifts the supply curve to the right and is called an increase in supply.
§ Any change that reduces the quantity supplied at every price shifts the supply curve to the left and is called a decrease in supply.
These are the effects of the left-out variables.
Analysis of the Shifts in the Supply Curve

- It is easy to understand that when the number of suppliers increase, the market supply curve will shift to the right, and vice versa when they decrease. On the other hand, when price is expected to increase, the suppliers will decrease their current supplies to take advantage of the higher price that is expected to prevail in future.
- The effect of the other two forces is not as simple. However, something that may help understanding the effect of those is the realization that supply curve is very intimately linked to the cost of production - something that we will focus more closely upon in Chapter 13. Here, all we need to note is that anything that increases the cost of production – say on average – will decrease the individual supplies, and thus also the market supply. This will show up as an upward shift in the supply curve. The reverse will happen when that cost of production decreases.

In light of this clarification, it is not difficult to see that when any input price increases - be it of raw materials of the factors of production – the result will be an increase in that cost of production, and thus the supply curve will shift up (a decrease in supply), and vice versa when the reverse happens.
When it comes to change in technology of production – due to what is known as technological change – the result will be an increase in the productivity of the inputs, the factors of production in particular.
As a result of technological improvement, the supply curve – individually and collectively – will shift to the right, or downward. It may be noted that there is no such
thing as technological dis-improvement. Thus this effect will be only unidirectional.







SUPPLY AND DEMAND TOGETHER

Equilibrium: Equilibrium is a state of balance between the two market forces. It represents a situation in which the price has reached the level where quantity supplied equals quantity demanded.
The result is a unique pair of price and quantity called equilibrium price and equilibrium quantity. Note that when we mention any one of these, we imply the existence of the other.
§ Equilibrium price: The price that balances quantity supplied and quantity demanded.
§ Equilibrium quantity: The quantity supplied, and the quantity demanded at the equilibrium price.

This figure shows the market supply curve and market demand curve together. There is ONLY one point at which the supply and demand curves intersect. This point is called the market equilibrium point. The price at this intersection is called the equilibrium price, and the quantity is called the equilibrium quantity.
Here the equilibrium price is $2 per cone. The equilibrium quantity is 7 ice cream cones. At the equilibrium price, the quantity of the good that buyers are willing to buy exactly balances the quantity that sellers are willing to sell. The equilibrium price is sometimes called the market clearing price because, at this price, everyone in the market has been satisfied. Buyers can buy all they want to buy, and sellers can sell all they want to sell.

Whenever the price diverges from its equilibrium value, there will be a state of disequilibrium. As a result, there may be either:
Surplus: Quantity supplied is greater than quantity demanded, at any price higher than equilibrium price – Excess Supply
Shortage: Quantity demanded is greater than quantity supplied, at any price lower than the equilibrium price – Excess demand






Markets Not in Equilibrium



Restoration of Equilibrium

Market disequilibrium, however, is a temporary phenomenon. In a market system, the prices are flexible, and thus free to adjust whenever surplus or shortage arises. It may, therefore, be noted that in free market economy, a state of disequilibrium will be self-correcting.

• How quickly equilibrium is reached varies from market to market, depending on how quickly prices adjust. In most free markets, surpluses and shortages are only temporary because prices eventually move toward their equilibrium levels.
• Indeed, this phenomenon is so pervasive that it is called the law of supply and demand: the price of any good adjusts to bring the quantity supplied and quantity demanded for that good into a state of balance – the equilibrium.

§ When analyzing how some event affects the equilibrium in a market, we note that when surplus exists, there will be pressure on price to adjust downwards, and vice versa when there is shortage.
§ Note that when only either demand or supply changes, things are quite simple – such cases are known as simple cases. There could be 4 simple cases in the model: Demand increase or decrease, and similarly supply increase or decrease.
But, then, there are four complex cases where greater attention is required to arrive at a conclusion as to what will happen in the new state of equilibrium.
How an Increase in Demand Affects the Equilibrium


Complex Cases

There are four complex cases:
1. D increases and S increases
2. D increases and S decreases
3. D decreases and S increases
4. D decreases and S decreases
These cases are complex because sometimes, both these changes may have similar effects, so these will reinforce each other in the same direction of change – increase or decrease. But in other cases, the two effects may work in opposite directions and thus it may not be possible to conclude what the final outcome will be unless we know the two changes in quantitative terms – as happens in a diagrammatic model.

The best way to handle the complex cases is to understand that each of the complex case is a combination of two simple cases. In simple cases, the outcome is known for sure without even any knowledge of the quantitative changes.
Take the first case: D increases and S increases. In both these cases, equilibrium quantity increases, and thus we know that the outcome in the complex case will be the same as far as the equilibrium quantity is concerned.
But when it comes to price, in the case of D increase, the price increases while in the case of supply, the price decreases. Thus the two forces are working in opposite directions, and we don’t know what the final outcome will be unless we see the two shifts quantitatively in a diagram.
D increases and S decreases.
The effect in both these cases is an increase in price, and therefore that outcome is guaranteed. But as far as the equilibrium quantity is concerned, the effect in the first case is increase
in quantity while in the second case, it decreases. Thus we are not sure what the final outcome will be unless we see the quantitative changes in a diagrammatic model, as we do in the next slide.

What Happens to Price and Quantity When Supply or Demand Shifts?







§ Market economies harness the forces of supply and demand to achieve:
§ Supply and demand together determine the prices of the economy’s many different goods and services; prices in turn are the signals that guide the allocation of resources – as required by the allocation function.
So far, the only time we encountered the problem of quantitative changes was in the complex cases. Other than that, we only focused on the qualitative changes: increases, decreases. But, the issue of quantitative changes in the context of the markets is extremely important. For example, if a price changes by let us say 5, by how much will the quantity demanded change?




ELASTICITY AND ITS APPLICATION - Chapter 5

Broadly speaking, elasticity is a measure of how much buyers and sellers respond to changes in market conditions. Thus:
§ Elasticity, in general, is a measure of the responsiveness of quantity demanded or quantity supplied to one of its determinants. All elasticity measures will be computed in percentage terms, for such calculations will be unit-free.
§ Price elasticity of demand: Generally called the elasticity of demand is a measure of how much the quantity demanded of a good responds to a change in the price of that good, computed as the percentage change in quantity demanded divided by the percentage change in price. Thus Ed will be: defined as:



THE ELASTICITY OF DEMAND

For example, suppose a 10 increase in the price of an ice-cream cone causes the amount of ice cream you buy to fall by 20

The Ed value of of ‘2’ means that for 1 change in price the quantity demanded will change by 2. It may be noted that theoretically this value is negative, but usually the sign is disregarded.



Ed = (△Qd / Qd) . 100 / (△P/P) . 100 which can be written as:
= (△Qd / Qd) . (P/△P)
= (△Qd / △P) . (P/Qd)
= ( 1/ slope) . (P/Qd) and for Es = ( 1/ slope) . (P/Qs), something relevant a little later.
The last expression tells us that slope of the demand curve is very important in the value of the elasticity coefficient. Since we mostly work with linear demand curve – having a constant slope – it may give the wrong impression that Ed will be constant. That conclusion is unwarranted because the ratio given in the second expression continuously varies. This means that Ed will continuously change along a linear demand curve.
It may also be noted that the larger the slope value – and thus lower the value of the first ratio – the less elastic the curve for any given value of the second ratio. We will see that when the slope value becomes infinite, the elasticity coefficient will be zero. These points will also be true on the elasticity of supply side as will be discussed below.


Point A:
Price = $4
Quantity = 120
Point B:
Price = $6
Quantity = 80
From point A to point B, the price rises by 50, because the base value for this computation is 4, and the quantity falls by 33, and thus Ed = 33/50 = 0.66.
From point B to point A, the price falls by 33, and the quantity rises by 50, and thus Ed = 50/33 = 1.5. This shows the same data gives different answers because the base values differ in the two movements.
The solution is to use the mid-point formula, as shown below.

The Midpoint Method
What this mean is that when ‘p’ changes, we end up at two different points on the demand curve, and thus there will be two different Ed values. We don’t have a unique value for the elasticity. To solve this problem, we use an approximation by getting an average value between those two points by using the ‘midpoint’ formula, as:



The average – the midpoint solution - in the above case will be 1.08, an average of the two values computed above.

Since Ed can be different at different points on a given demand curve, note the following possibilities along a given linear demand curve:
1. If Ed > 1, demand is said to be ‘elastic’. This happens when the numerator is larger than the denominator. That means quantity changes are larger than the price changes.
2. If Ed < 1, demand is said to be ‘inelastic’, the reverse of the previous case.
3. If Ed = 1, demand is said to be unit elastic. In this case both the changes (in numerator and denominator) are equal. On linear demand curve this happens at the mid-point.
We will also consider two polar cases shortly: i) Ed = 0, and ii) Ed = ∞, and these will be cases where the law of demand gets violated.
The same classification, and conclusions, will also be applicable in the case of elasticity of supply, Es , as we will see a little later.
This classification is relevant in a very important way when it comes to the effect of price changes on the sales revenues of a firm or industry. We will turn to that subject shortly.

1. Availability of close substitutes. Demand will be more elastic the larger the number of substitutes available.
2. Necessities versus luxuries. Demand will be more elastic for luxuries as compared to the necessities.
3. Definition of the market. Demand will be less elastic in the case of broader definition of the market. Consider market for apples (broader market) vs market for gala apples (narrower market) for which more substitutes will be available, and thus demand will be more elastic.
4. Time horizon. Demand is more elastic in the long run as compared to short run.





Total Revenue (TR) and the Price Elasticity of Demand


§ Total revenue (in a market): The amount paid by buyers and received by sellers of a good, computed as the price of the good times the quantity sold.
• If Ed > 1 (elastic demand), a decrease in price will lead to an increase in TR, and vice versa.
This is because ’Q’ increase will more than offset the effect of price decrease on TR.
• If Ed < 1 (inelastic demand), a decrease in price will lead to a decrease in TR, and vice versa.
This is because the price decrease proportion is larger than the offsetting quantity increase.
• If Ed = 1 (unit elastic demand), TR will remain unchanged when price changes.
Note that the reverse conclusions will be applicable in the reverse movements than the ones noted above. We can see these results in the following diagrams.



TR is represented by the area under the demand curve at the selected point – the point representing the corresponding ‘P’ and ’Q’.





While the elasticity can be calculated for any determinant of demand, we will select only two: i) Income, and ii) Prices of the related goods. Let us begin with (i) denoted as Ei:
i) Ei = tage ∆ in Demand / tage ∆ in Income
1. If Ei > 0, the good is a normal good – it is the case of positive income effect.
2. If Ei < 0, the good is an inferior good – negative income effect.
3. If Ei = 0, it is a zero income effect good.
ii) Prices of the related goods: Consider good ‘X’ as the good under consideration, and good ‘Y’ as the related good. The elasticity symbolism will include both of these letters in the sub-script – with the good under consideration being noted first, i.e. EXY.

Now EXY = tage ∆ in demand for x / tage ∆ in price of Y
If EXY > 0, The two goods are substitute goods. When price of ‘Y’ increases, the demand for ‘X’ increases. People start consuming less ‘Y’ by replacing it with ‘X’. The larger the value of this elasticity coefficient, the greater the degree of substitution between those goods. On the other hand:
If EXY < 0, The two goods are complementary goods. When price of ‘Y’ increases, less quantity will be demanded – the law of demand – and less ‘X’ will be demanded because of the complementarity relationship.
We now turn to the price elasticity of supply, commonly referred to as elasticity of supply, and symbolically Es.


There is not much difference between this, and the Ed dealt at some length above. The only difference is of the sign: While Ed is negative – though the negative sign is usually ignored, and omitted – Es is positive, as a reflection of the ‘law of supply’.
Note that:
If Es > 1, supply is elastic; same was the case for absolute value of Ed.
If Es < 1, it is inelastic. And
If Es = 1, it is unit elastic.
This is a repetition of what we did earlier in the case of Ed. The only determinant of Es is the time duration. Supply will be more elastic in the long run as compared to a shorter run. This is because the suppliers get the flexibility of adjusting their production plans when more time is available. We will also look at the two polar cases as we did earlier in the case of demand.


The Variety of Supply Curves

Because the price elasticity of supply measures the responsiveness of quantity supplied to the price, it is reflected in the appearance of the supply curve. And now, we will also look at the polar cases:
If the slope of the supply curve is infinite – the curve is vertical -, Es = 0, perfectly inelastic supply.
If the slope is zero – the horizontal curve -, Es = ∞, perfectly elastic supply, and If Es = 1, we have a case of unit elastic supply. It may be noted that in the previous two cases, the law of supply does not hold, just as it would be the case on the demand side – the law of demand does not hold, a point noted above.

















CONSUMERS, PRODUCERS, AND THE EFFICIENCY OF MARKETS - Chapter 7

Considering the question just raised, the first thing that we need to pay attention to is that we cannot even proceed to provide an answer until we have a criterion that forms the basis of what is ‘good’ for the society. Economics proceeds to answer this question by saying that if the quantities of various goods and services produced in the economy are right, the society will achieve the best result from the resources at its disposal. In the technical language of economics, the allocation of resources will be best. Such an outcome is called ‘efficient allocation of resources’ – something that was hinted upon in the definition of economics, in the first lecture. This answer is the fundamental part of what is known as welfare economics.
In welfare economics, this criterion is given the technical name as: ’Allocative efficiency conditions’, which can be expressed in two alternative forms: one in terms of ‘total’ values, and the other in the form of ‘marginal’ values. These values take both ‘benefits’ and ‘costs’ into consideration. Benefits are generally the result of consumption, and costs are generally associated with ‘production’. It may be noted that theoretically benefits may be labelled as negative costs, and costs as negative benefits.

The two forms of allocative efficiency are:
1. Maximization of ‘Net Social Benefits (NSB)’. These benefits come in two forms, one relating to consumers – the Consumers’ Surplus’ – and the other to the producers – the ‘Producers’ Surplus’. Total Surplus is the summation of these two.
2. Equalization of ‘Marginal Social Benefits (MSB)’ to ‘Marginal Social Cost (MSC)’.
Satisfaction of (1) implies satisfaction of (2), and vice versa. The most commonly used criterion is the second one, as we will see in a number of chapters. From now onwards, it will be expressed as:
MSB = MSC
We may note at this stage that ‘social benefits’ come in two forms: private benefits and external benefits. And similarly, ‘social costs’ come in these two forms. And thus, we note:
MSB = MB + MEB where MEB represents marginal external benefits
MSC = MC + MEC where MEC …………………………………..costs.


Our analysis will lead to the important conclusion that under certain circumstances, market outcome leads to the maximization of NSB (Net Social Benefits). Put slightly differently, market outcome leads to maximization of total surplus (TS) = CS + PS.

Let us begin with the subject of CS. We define Willingness to pay (WTP) as the maximum amount that a buyer will pay for a particular unit of a good. And What is Actually Paid (WAP) being equal to P.Q. We note that WTP is given by the area under the demand curve up to the relevant quantity. We begin with the following information:



And now in terms of the demand curve










Using the Demand Curve to Measure Consumer Surplus

Because the demand curve reflects buyers’ willingness to pay, it can also be used to measure consumer surplus.
CS = TWP - WAP
Further: How much does buyers’ well-being rise in response to a decrease in price?
The concept of consumer surplus helps answer this question, as we see next.

What Does Consumer Surplus Measure?

§ Consumer surplus, CS, measures the net benefits that buyers receive from a good as the buyers themselves perceive it.
§ Thus, consumer surplus is a good measure of economic well-being, also called economic welfare, (if policymakers want to respect the preferences of buyers).

Cost and the Willingness to Sell

Cost: The value of everything a seller must give up to produce a good (i.e., the producer’s opportunity cost).
§ Producers’ Surplus (PS): The amount a seller receives - as paid by the consumers (WAP) - for a good minus the seller’s cost.



§ The area above the supply curve and below the price measures the producer surplus in a market.
§ The logic is straightforward: The height of the supply curve measures sellers’ cost – more appropriately marginal cost (MC) as we will see in Ch. 13 - and the difference between the price and the cost of production is each seller’s producer surplus.
§ Thus, the total area is the sum of the producer surplus of all sellers, and thus represents net surplus, or benefits, of producers.


Measuring Producers’ Surplus (PS) with the Supply Curve





How a Higher Price Raises Producer Surplus

§ It is not surprising to hear that sellers always want to receive a higher price for the goods they sell.
§ But how much does sellers’ well-being rise in response to a higher price?
§ The concept of producers’ Surplus (PS) offers a precise answer to this question.








Ch. 7 (Contd.) & CH. 6

MARKET EFFICIENCY

Benevolent social planner, who is an all-knowing, all-powerful, and a well-intentioned dictator, to make it a parable. This planner would wish to maximize the economic well-being of everyone in society, i.e. total surplus, or let us say TS = CS + PS, from our last meeting.

1. What would be the TS in a state of market equilibrium.
2. Would that be the maximum TS possible as compared to any other situation, a situation of output being more, or less, than the equilibrium value?
3. If the answer to this question is ‘yes’, then the market allocation of resources is the best outcome from the society’s point of view. This, of course, would mean that a perfectly competitive market equilibrium satisfies the allocative efficiency conditions.













Consumer and Producer Surplus in the Market Equilibrium



In this diagram we see the TS realized – area ACE - in a state of market equilibrium. We also need to note that in addition to efficiency, the social planner might also care about equity. Equity would represent the fairness of the resulting distribution of well-being associated with the equilibrium outcome among the members of society. This is a somewhat complicated issue because there is no unique distribution of income, and therefore fair outcome, that may be acceptable to everyone in the society.
Simply put, economics recognizes that this issue better be handled at the political level. But it also notes, given a politically acceptable distribution of income, we may run into situations where there is a trade-off between the allocative efficiency and equity objectives – a situation where both objectives may not be achievable simultaneously.
Let us now focus on the question raised above. For this we need to note that the demand curve represents MSB, and the supply curve represents MSC provided there are no external effects on either consumption or production side, i.e. MEB = 0, and MEC = 0
as we defined them in our last lecture. In light of that, we note that MSB = MB, and MSC = MC.
MSB = MSC

We can see that this allocative efficiency condition is satisfied at point ‘E’ – the equilibrium point. To reiterate, it is now quite clear that at the equilibrium output, where the two curves intersect one another, this condition will be satisfied, and thus NSB (= TS) is shown by the area ACE as noted above. The question now is: Is this the maximum NSB that can be realized out of all the potential output levels? A satisfactory answer hinges on the proof that any other output level – higher or lower – than the equilibrium output will reduce NSB.
Consider the possibility where output produced is ‘Q1’. At this output MSB are given by the height ‘JQ1’ and MSC is given by the height ‘KQ1’, and thus we can see that MSB > MSC, and the surplus associated with this unit is given by the distance ‘JK’.

If this unit is not produced, society will lose this net surplus – which in the technical language of economics is called ‘Deadweight Loss (DWL)’. It is represented by the distance between the D and S curves. For any unit up to the equilibrium output, we see DWL in absence of production of that unit. This implies that as more output is produced beyond Q1, DWL is avoided, and society gains in terms of increased TS. This area is identified as DWL area – JKE - in the diagram, an area defined over any lesser output level produced as compared to the equilibrium output.

The answer is a definite ‘No’. This is because, beyond the equilibrium output level, MSC is higher than MSB, and thus any unit produced will decrease NSB. For instance, at output level Q2, MSB are given by the height Q2J’ whereas the corresponding MSC is given by the height Q2K’ – thus resulting in a net loss (DWL) of K’J’ distance. The conclusion now is that if output Q2 is produced, the DWL to society will be given by the area EJ’K’. For any unit produced beyond the equilibrium output there will be a DWL. This important conclusion will recur all along in the following chapters.
Chapter 6 - Supply, demand, and government policies

Government Intervention in the Market

§ We are now able to study the effects of government interference in the market. This interference can take two forms:
1) Direct interference in the form of price fixing, and
2) Indirect interference where prices get indirectly influenced.
Let us consider direct interference. This interference can take two forms:
Price ceiling: A legal maximum on the price at which a good can be sold.
Price floor (or support): A legal minimum on the price at which a good can be sold

How Price Ceilings Affect Market Outcomes

Assume the government imposes a price ceiling on the market for ice cream. Two outcomes are possible in each case:
i. The price ceiling is not binding on the market and the market price will equal the equilibrium price. In such a situation, price ceiling does not make any sense. If price ceiling is to be effective, it must take the following form:
ii. It must be set below the equilibrium price for it to become a binding constraint on the market, and in this situation the market price will equal the price ceiling, as we see below. In such a situation, the market will run into a state of disequilibrium.

It needs to be emphasized that such a policy is implemented to safeguard the interests of the low-income families. However, it is quite clear that at the ceiling price there will be a shortage. This can give rise to a black market for that product, and in the black market the price may turn out to be even higher than the free market equilibrium price. This would make the policy counter-productive. Thus, it is very clear that when such a policy is implemented, care must be taken to ensure that black market does not develop. This may require some sort of rationing arrangement.

Let us now turn to the other form of market interference: Support price, or floor price. Floor price is the minimum price guaranteed by the government. This is to support the low-income producers - generally the low land holding farmers. Clearly, to be sensible, this support price must be set at a higher level than the equilibrium price; for otherwise it will not make any sense. The following diagram shows this possibility.
In chapter 4 discussion, we saw that a bumper crop may lead to a decrease in the TR of the farmers – remember this happened because demand for food is usually inelastic – as we will see below.




We must note that such a policy will lead to excess supply – surplus – as seen in the diagram. The government must purchase this surplus for the policy to be effective. Otherwise, the price will fall – and may fall even below what it would have been in absence of any interference. This way the policy may become counter-productive.
The alternative to manage the possibility of surplus would be to ration output among the producers – the ration set at the level where with the support price the farmer will get an acceptable income level.


How the Minimum Wage Affects the Labor Market

The second form of government intervention – the one called indirect intervention – occurs as a result of taxation. Imposition of a tax changes the price inclusive of tax in the market. Although all taxes change the market price, for the sake of simplicity we will focus on the sales tax. Note that the conclusions reached under this form will be quite general.
One of the pertinent question that we will focus on is: Who bears the burden of the tax? In the technical terminology of economics, this is referred to as economic incidence of a tax. Economic incidence of a tax may be, and generally will be, quite different than its ‘legal incidence’ which is based on the legal responsibility of tax payment to the government. The question is very important because it is the economic, and not legal, incidence which people would care about.
While the common understanding would be that economic incidence would be same as legal incidence, what we are going to learn today is that this is not true: and that the tax burden falls on both the buyers and sellers.

Now, we also face the question: If buyers and sellers share the economic burden, what determines how that burden is divided?
To see how the tax incidence falls on both the parties, we need to proceed in three steps we covered in Chapter 4 for analyzing supply and demand:
1. Does the law affect the supply curve or demand curve?
2. What is the nature of the shift in the curve?
3. Examine how the shift affects the original equilibrium to establish a new one.
Suppose the legal incidence is on the buyers; that the buyers are held responsible to remit the tax amount to the government. Suppose this tax is $0.50 for each ice cream cone. The original demand curve will now need to be adjusted as the one that will be relevant for the seller; i.e. the one faced by the seller. We will need to shift the original one down by the tax amount: 50 cents, as seen below.


A Tax on Buyers


The shift is shown by the red curve
And the new equilibrium is identified by a new intersection, with the eq’m price of $2.80 received by the seller – though the buyer actually ends up paying $3.30, and the eq’m quantity being 90 now, as compared to 100. The tax proceeds are .50 x 90 = 45 dollars.
TAXES

Implications: Who pays the tax?
The analysis yields two lessons:
Taxes discourage market activity. When a good is taxed, the quantity of the good produced is smaller in the new equilibrium, a reduction from 100 to 90. Thus the allocation of resources does not remain efficient as per our understanding in Ch. 7. Tax introduces allocative inefficiency, and thus a DWL, shown by the triangular area between the two curves from 90 to 100.
Buyers and sellers share the burden of taxes. In the new equilibrium, buyers pay 30 cents more for the good, and sellers receive 20 cents less than what they received before the imposition of the tax. They are now responding to different signals – because the tax has drawn a wedge between the price paid and the price received - as compared to the original position of eq’m thus leading to the DWL identified above.

TAX on Sellers

Now suppose the legal incidence is on the seller.
Now, it is the supply curve that will shift, but upwards. The tax amount is now perceived as a cost, just like any other cost, and this shifts the supply curve up by the amount of the tax, i.e. 50 cents, as we will see in the next figure.
It is obvious that the price net of tax will be 50 cents less than what the seller will receive from the buyers – as the original supply curve will indicate.
Thus, the end result will be the same as was the case earlier on: i) the two parties will be responding to two different price signals, and ii) the quantity produced in the new eq’m will be different than what it originally was – leading to a misallocation of resources, and thus a DWL.
Both parties end up bearing the economic burden of the tax, just as we saw earlier - in the case of legal incidence being on the consumers.


A Tax on Sellers


As we can see the price paid and the price received are exactly the same as previously. Thus it does not matter whether we deal with the tax as being legally on the consumers or on the producers. Generally, we follow the first approach.













Distribution of tax burden on buyers and sellers

Elasticity and Tax Incidence

We now know that when a good is taxed, buyers and sellers of the good share the burden of the tax. But how exactly is the tax burden divided?
Only rarely will it be shared equally. It all depends on Ed and Es. To see how the burden is divided, consider the impact of taxation under two different scenarios – different with regard to Ed and Es:
1. A market with very elastic supply and relatively inelastic demand, and
2. A market with relatively inelastic supply and very elastic demand.
Both of these cases are presented below. What we see there is that a greater burden falls on the party with less elastic response - a very important conclusion. This theme will recur in the next lecture.

How the Burden of a Tax Is Divided

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