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OUTLINE OF THE LECTURE
A. Graphic Presentation of Data
B. Graphing Economic Models
C. The Production Possibility Frontier
A. Interrelationships between data and models
1. Time series
2. Cross section
1. Tables
2. Graphs
D. Graphing Economic Data
1. Cartesian analytical plane
2. Ordinate and abscissa
3. Quadrants
E. Scatter Diagrams
1. plotting data
2. Econometrics
F. Time series
1. Average levels
2. Variability
3. Patterns (Trends, Cycles)
4. Zero base
A. Y = f (X)
B. Supply and Demand
C. Basic patterns of relationships
1. Positive
2. Negative
3. Maximum and minimum
D. Slope
1. Linear relationships
2. Non-linear relationships
E. linear relationships in macroeconomics
1. C= a + b(Y)
2. C = Y
3. C = a (horizontal)
4. a = Y (vertical)
F. 3 variable relationships
A. Definition of PP Frontier
1. Fixed resources
2. Given technology
B. Points on or off the frontier
1. Inside
2. On
3. Outside
C. Opportunity Cost
1. Slope of PP Curve
2. Law of increasing opportunity cost
D. Economic growth
1. Methods of increasing the PP frontier
2. Application to VN
A. Presentation of economic data
1. Graphing Data
2. Scatter Diagrams and Time Series Graphs
B. Graphing Economic Models
1. The Slope of a relationship
2. Linear relationships
3. Relationships Involving more than two variables
C. The Production Possibility Frontier
1. Opportunity Cost
2. Economic Growth
A. Economic Data and models are interrelated
1. Data suggests the possibility of a relationship
2. Data allows you to quantify the relationship
3. Models tell you what data to collect
4. Data allows you to test models.
B. Types of Economic Data
1. There are two main types of economic data,
a. time series data and
b. cross section data.
2. A time series is a sequence of measurements of a variable over time.
1991 8.3%
1992 8.7%
1993 7.8%
3. Cross section data record at a point in time, the way an economic variable differs across different individuals or groups.
Country Population Per Capita Income
U.S. 240 million $25,000
V.N. 70 million 400
C. Ways of presenting data
1. Tables
a. Advantages
i. Easier to understand
ii. Public more familiar with tables
iii. Good for reference volumes
iv. Usually more precise than graphs
b. Disadvantages
i. Difficult to portray relationships
2. Includes only a fraction of possible values
2. Graphs
a. Advantages
i. Convey understanding of relationships
ii. Good for developing or explaining theories
b. Disadvantages
i. Some people not familiar with them
ii. Not as precise
iii. Can be used for deception
a. 3 dimensional pictogram distorts relative sizes
b. Graph not at zero distorts variability
II. Graphing Economic Data
A. Cartesian anaytic plane
B. Graphs represent quantity as a distance
C. Two-variable graphs use two perpendicular scale lines
(division of the analytical plane into 4 quadrants)
1. The vertical line is called the "ordinate" or "y-axis"
2. The horizontal line is called the abscissa or "x-axis"
3. The intersection of the two axes is called "the origin"
D. The four quadrants are as follows
1. First (y is positive, x is positive)
2. Second (y is negative, x is positive)
3. Third (y is negative, x is negative)
4. Fourth (y is positive, x is negative)
III. Scatter Diagrams and Time Series Graphs
A. Two common ways of presenting economic data are:
1. scatter diagrams and
2. Time series graphs
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A. A scatter diagram plots the value of one variable that is associated with the value of another variable
1. Good for cross section data
B. A scatter diagram shows a series of points whose coordinates correspond to the values of two variables.
or
C. A scatter diagram plots pairs of values, simultaneously observed, for two different variables
1. Scatter diagrams can indicate the nature and consistency of the relationship.
a. Example, rice production and rice exports.
2. A scatter diagram can be used to plot cross section or time series data
a. (as long as there are two time series)
3. It is possible to calculate mathematically the line which best describes the relationship shown by the scatter.
a. Sum of deviations from line equal zero
SUM of d = 0
b. Sum of squared deviations are a minimum
SUM of d2 = min
c. The techniques for doing this are part of the discipline of econometrics.
4. Econometrics is the branch of economics devoted to measuring relationships and testing hypotheses using statistical methods and economic data.
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A. A time series graph plots:
1. time along the horizontal axis and
2. the economic variable along the vertical axis.
B. A time series graph shows
1. The average level of the variable,
2. Whether it changes rapidly or slowly (variability)
3. and whether there are patterns (trends and cycles) in the movement.
C. When writing articles on economic topics and using time- series graphs, be careful that the full y axis is shown.
1. Otherwise you may give false impression of variability.
D. When comparing two time series on the same graph, you may wish to use two different scales.
1. (e.g. production and price level)
2. e.g. inflation rate and exchange rate
2. One on left y-axis, and one on right y-axis
A. A relationship between economic variables can be expressed as Y = f(X) .
1. That means that the value of the dependent variable, "Y", will depend on the value of the independent variable "X".
B. Normally,
1. the dependent variable (Y) is measured along the ordinate (y axis) and
2. the independent variable (X) is measured along the abscissa (x axis).
C. In economics, we violate this convention in one of or most important analytic techniques (supply and demand)
1. This is a historical accident.
a. We use Alfred Marshall's graphs,
b. with Leon Walras' demand and supply equations
2. Why don't we correct our error?
a. Now that everyone is so familiar with the wrong way of graphing,
b. we think it would be too confusing to return to the right way.
3. That is questionable.
a. It depends how familiar student's are with mathematical conventions.
D. Graphs often have one of four basic patterns that can immediately convey the nature of the relationship between variables:
1. A positive relationship is illustrated by the two variables increasing (or decreasing) together.
2. A negative relationship is illustrated by one variable decreasing while the other is increasing.
3. No relationship (independence) is illustrated by a movement of one variable with no change in the other.
a. It would appear as either a vertical line
b. or a horizontal line.
4. A relationship which has a negative range and a positive range.
a. It will have a maximum or a minimum (or both).
A. The slope of a curve equals:
1. the change in the value of the variable on the vertical axis divided by
2. the change in the value of the variable on the horizontal axis.
DELTA X / DELTA Y
3. Slope = Change in vertical distance
Change in horizontal distance
4. Sometimes slope is called "rise over run"
5. In terms of symbols, the slope equals dx/dy.
6. The slope will depend on the units of measurement
a. (e.g. liters per kilometer) vs. (gal / km)
b. (dollars per liter) vs (dong per liter)
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A. Linear relationships (Straight Lines).
1. Linear relationships are extremely important in macroeconomics.
a. Most of the key relationships are approximately linear.
b. in our models, we assume they are linear for simplicity.
2. The slope of a straight line is constant.
3. The slope is positive if the variables are positively related
a. e.g. overweight charge = f ( kilos)
4. The slope is negative if the variables are negatively related.
a. e.g. surplus travel money = f ( kilos)
5. Equation for a linear relationship (straight line) is:
a. Y = a + b * X
i. "a" is the ordinal intercept
ii. "a" is the value that Y takes when X is zero.
iii. "a" can be positive or negative
iv. "b" is the slope
v. "b" is the change in Y per unit change in X.
b = DELTA Y / DELTA X
vi. "b" can be positive or negative
b. An example is:
Y = 10 + 4 * X
i. "a" = 10
ii. "b" = 4
5. Schedule for a linear relationship (straight line)
a. Select arbitrary values of independent variable (X)
b. Compute corresponding values of dependent variable (Y)
c. Fill in the table
X Y
0 10
1 14
2 18
3 22
6. Graph of a linear relationship (straight line)
a. Can prepare graph two ways
i. Plot schedule
ii. Plot equation directly
b. Plot points from schedule
1. Connect points (could have been computed)
c. Plot equation directly
1. Plot ordinal intercept -- (A) or (10)
a. At 0 on x-axis
b. move up (or down) "a" units on y-axis
2. Plot the slope -- (b) or (4)
a. move z units on X axis and
b. move up (b * z) units on Y axis if "b" is positive
c. move down (b * z) units on Y axis if "b" is negative.
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A. Non linear relationships (Curved Lines)
1. Non linear relationships (Curved lines) are especially important in microeconomics
a. Many of the most important relationships are non-linear.
b. Microeconomics is about optimizing
i. Finding maximum points and
ii. Minimum points
2. Nonlinear relationships are important to macroeconomics because the behavioral assumptions of macroeconomic models are derived from microeconomics.
a. Microeconomics is the foundation for macroeconomics.
3. Some important Macroeconomic relationships are beleived to be non-linear
a. Full range of the Aggregate Supply (AS) curve.
b. Full range of Keynesian Liquidity preference curve
c. Production possibility curve
B. Slope of a curved line at a point.
1. It is equal to the slope of the tangent drawn to the point. (the first derivative)
2. A tangent is a straight line which touches a curved line at a single point. The slope of the curve is the same as the slope of the tangent at that point
C. The slope of a curved line at its peak (maximum) is zero (0). (and falling)
D. The slope of a curved line at its trough (minimum) is zero (0) (and rising)
E. Slope of a curved line across an arc.
1. It is equal to the strait line between the two points on the curve.
2. it is an estimate of average slope between two points.
V. More on Linear relationships
A. In macroeconomics many relationships are assumed to be linear:
1. This corresponds to the facts or
2. for the sake of simplicity.
B. The equation for a linear relationship has two parameters, the slope and the intercept e.g.
Y = a + b * X
1. e.g. Hours in course = 6 + 3 * Number of Lectures
H = 6 + 3*L
C. The intercept is:
1. the value of the dependent variable (Y) when
2. the independent variable (X) is zero
D. Given the slope (b) and the intercept (a) it is possible to construct a table or a graph corresponding to a straight line.
E. A ray from the origin
A ray from the origin is a straight line with an intercept of zero.
Y = 25 * X
F. The 45 degree line
1. It is misnamed, it would be 45 degrees only if the scales were the same.
2. It should be called "the ray with a slope of one"
b = 1
Y = 1 * X or Y = X
3. At every point on the line:
a. the Y value equals the X value.
4. This ray from the origin is very important in macroeconomics
1. e.g. Where aggregate planned expenditure (APE) equals actual real GDP (Y)
2. it is a set of possible equilibrium points
3. Along a ray, the rate of growth of X = rate of growth of Y
DELTA Y / Y = DELTA X / X
4. Along a ray, marginal equals average
a. Marginal equals Delta Y / Delta X
b. Average equals Y / X
DELTA Y/ DELTA X = Y / X
G. A horizontal line
Y = a
e.g. Y = 10
1. Horizontal lines are very important in macroeconomics
2. They describe spending which is autonomous (A)
a. (not dependent on the level of real GDP (Y).
i. e.g. I, G, X, Autonomous Consumption
3. They describe price levels that do not change as GDP increases
a. (the Keynesian range of the Aggregate Supply curve)
4. They describe a range of the Keynesian "Speculative Demand for Money"
H. A vertical line
10 = X
1. Vertical lines are also very important in macroeconomics.
2. They describe the case of the supply of a fixed stock.
1. e.g. The currency in circulation (M)
2. The stock of gold in the country
3. The assumed "natural rate of unemployment"
4. The maximum possible GDP. (The Classical range of the Aggregate Supply curve)
V. Graphing Relationships Among More than Two Variables.
A. Ceteris Paribus is a Latin phrase meaning "all other things being equal".
1. When a two variable relation is graphed
a. we assume all other variables are constant.
B. In macroeconomics we are often interested in relationships with two independent variables.
Price level = f ( real GDP, the Money supply)
P = f (Y, M)
Aggregate Planned Expenditure = f (Y, P)
C. We can only graph two variables in 2 dimensions
D. When a relationship involves more than two variables,
a. A curve is drawn for a given value of the second independent variable.
b. A new curve is drawn for a new value of the second independent variable.
E. We illustrate a third variable by a series of "contour" lines
a. each corresponding to a different value of the third variable.
b. This is widely used in macroeconomics to show the shift of a relationship
1. Shift of APE curve (government spending levels)
2. Shift of APE curves for different price levels
3. Shift of SAS curve (increased wage rates)
4. Shift of LL curve (as Y rises)
VII. The Production Possibility Frontier
A. Production can be defined as the transformation of inputs into outputs of factors of production (land, labor and capital) into economic goods.
1. Production is limited by:
a. the scarcity of productive resources and
b. the technology available.
B. The production possibility frontier (PPF) shows:
1. for each level of output of one good,
2. the maximum amount of the other good that can be produced.
C. The production possibility frontier (PPF) marks the boundary between:
1. the combinations of goods and services that are feasible to produce and
2. the combinations that are not.
D. Every point on the curve represents maximum productive efficiency.
1. Productive Efficiency means:
a. Achieving as much output as possible with a given number of inputs, or
b. Achieving a given level of output with as few inputs as possible.
C. Examples of Production Possibility Frontiers (PPFs)
1. two commodities,
a.(corn and sheep)
b. (food and education)
c. (tanks and trucks)
2. Fixed resources (e.g. no capital formation)
3. Fixed technology (no research and development)
D. The Production Possibility Curve separates two regions
1. Combinations above the curve are not attainable
2. Combinations below the curve are attainable but inefficient
3. Combinations on the curve are efficient and attainable
E. For every point inside the curve,
1. there will be a preferable point on the curve.
2. From the short-run perspective, it always pays to move towards the curve.
3. That is what Viet Nam has done in recent years.
a. rice production
b. clothing
VIII. Opportunity Cost
A. The opportunity cost of an action is the best alternative forgone.
B. If you are on the PPF, the opportunity of producing more of one product (more corn) is
1. the output of the other good sacrificed (e.g. less cloth).
C. The slope of the production possibility frontier (PPF) measures the opportunity cost.
1. An increase on the X axis causes a decrease on the Y axis
a. DELTA Y / DELTA X = slope = opportunity cost
D. The PPF is usually not drawn as a straight line.
1. The slope increases.
2. Meaning the opportunity cost increases.
E. The "Law of Increasing Opportunity Cost" states:
1. As more of a particular commodity is produced, larger and larger quantities of the alternative good must be sacrificed.
2. Hence, the opportunity cost of additional units of a good rises.
F. The bowed out shape (concave to the origin) of the production possibility frontier is a reflection of "the law of increasing opportunity costs".
1. The "Law of increasing opportunity costs" is due to the fact that not all resources are equally effective in producing both products.
2. As you increase the production of one product,
a. You must use progressively less suitable resources;
i. (e.g. farmers and teachers in education and agriculture)
(Cultural Revolution in China)
ii. (e.g. meadow and hillside in corn and sheep)
b. You must draw away resources that a progressively more suitable for the other good suitable.
c. If all resources were perfectly adaptable to alternative uses, the PPF would be linear.
G. Applications to the Real World
1. Resources are limited.
a. so there is a boundary between what is attainable and what is not.
2. When you are at full employment and full technical efficiency,
a. The only way you can produce more of one good is to produce less of another good. (opportunity cost)
3. As a country begins to specialize in some product, the opportunity cost of that product is likely to rise.
a. The result is partial specialization in most countries.
H. Applications to macroeconomics
1. Discussions of economic growth
2. Discussion of international trade and finance
a. Gains from specialization
i. Absolute advantage (Adam Smith)
ii. Comparative advantage (David Ricardo)
iii. Static versus dynamic comparative advantage
Learning by doing
East Asian Countries
IX. Economic Growth
A. Economic growth is the process of pushing outward the PPF.
B. The PPF can be shifted outward in one of two ways:
1. Increasing the quantity or quality of the resources, and/or
2. improving the technology of production (broadly defined)
a. Includes institutional changes
C. The quantity and quality of resources can be increased by:
1. Capital accumulation (Physical and human capital)
a. Physical capital can be increased by producing capital goods (e.g. factories, machines and inventories)
b. Human capital can be augmented by devoting resources to education and training.
c. To increase capital formation, you may have to sacrifice current consumption (C).
i. That is what is meant by "saving"
2. Growth of the labor force through:
a. Population Growth
b. Increased rate of labor force participation
c. Hours of labor per year.
3. Increased natural resource base due to
a. Search and discovery
b. Research on extraction and productive utilization
D. The rate of technical progress can be increased by:
a. devoting resources to research and development.
b. Giving incentives for research and development. e.g.
a. Prizes
b. Enforceable patents and copyrights
c. Tax deductions for R and D costs
c. Importing foreign technology
d. Altering institutions
a. Decontrol of US transportation system
e. Building new capital goods
E. The greater the rate of capital formation or technological progress,
1. the more rapid the shift of the PPF.
2. Application to rate of capital formation in Viet Nam:
a. Rate of growth of GDP (Y) = 8%
R of G = DELTA Y / Y = .08 = 8%
b. rate of capital formation 12% of GDP
RCF = DELTA K / Y = .12 = 12%
c. oil-production capital coming on line
d. Labor force growing at 2% per year
DELTA LF / LF = .02 = 2%
3. Increased efficiency
a. Incremental Capital-Output Ratio (ICOR) of 1.5
i. ICOR = DELTA K / DELTA Y = .08 / .12 = 1.5
ii. Typically ICOR > 3
b. Viet Nam is using its new capital very efficiently or
i. It is moving towards the PPF.
c. ICOR is likely to rise as Vietnam approaches the PPF.
i. Viet Nam will need higher savings rates to maintain growth rates of GDP.
F. If a nation is already on its PPF,
1. Economic growth is not free.
2. Both capital accumulation and technological change have opportunity costs.
a. To increase capital goods production or R&D, you must decrease consumer goods production.
b. Compare Japan and the US
G. If a nation is below its PPF,
1. It may be able to increase capital goods, R&D and consumer goods all at the same time by increasing efficiency.
a. US in Great Depression, WWII
b. USSR in 1980s below PPF
c. Viet Nam in Doi moi
2. After a nation's economy grows,
a. it can have more of everything
b. Self-sustaining growth
X. Summary of the Lecture
Graphing data
There are more than two main types of graphs used to represent economic data: scatter diagrams and time-series graphs. A scatter diagram plots the value of one economic variable associated with the value of another. Such a diagram reveals whether or not there is a relationship between two variables and, if there is a relationship, its nature.
A time-series graph plots the value of one or more economic variables on the vertical axis (x-axis) and the horizontal axis (x- axis). A well constructed time-series graph quickly reveals the level, direction of change, and speed of change of a variable. It also reveals the trends. Graphs sometimes mislead, especially when the origin is omitted or when the scale is stretched or squeezed to exaggerate or understate variability.
Graphs of economic models
Graphs are used in economic models to illustrate relationships between variables. There are four cases: positive relationships, negative relationships, no relationships and graphs that have maximums and minimums.
The slope of a relationship
The slope of a relationship is calculated as the change in the value of the variable measured on the y-axis divided by the change in the value of the variable on the x-axis. That is delta x / delta y. A straight line has a constant slope, but a curved line has a varying slope. To calculate the slope of a curved line we either calculate the slope at a point or the slope across an arc between 2 points.
Graphing relationships among more than two variables
To graph a relationship among more than two variables, we hold constant the values of all variables except two. We then plot the value of one of those variables against the value of the other. Then we draw a new curve corresponding to the two variables when the value of some other variable has changed. Holding all other variables constant except the two in question is a graphic illustration of the "ceteris paribus" assumption- the assumption that other things remain the same.
The production possibility frontier
The production possibility frontier is the boundary between what is attainable and what is not attainable given available resources and technology. Production can take place at any point inside, or on, the production possibility frontier; but it is not possible to produce outside the frontier. For every point inside the frontier, there will always be a better point on the frontier.
Opportunity cost
The opportunity cost of any action is the best alternative action forgone. The opportunity cost of acquiring one good is equivalent to the amount of another good that must be given up. The opportunity cost of a good will increase as the quantity produced of that good increases.
Economic growth
The production possibility frontier does not remain fixed. It changes over time, partly because of natural forces and partly because of the choices we make about saving and investing. If we use some of today's resources to produce capital goods and research and development instead of producing consumer goods, we will be able to produce more goods and services in the future. The economy will grow. But growth cannot take place without incurring costs. The opportunity cost of consuming more goods and services in the future is consuming fewer goods and services today.
Key concepts
1. Axes
2. Capital Accumulation
3. Capital goods
4. Capitalism
5. Ceteris paribus
6. Consumption
7. Consumption goods
8. Coordinates
9. Cross section data (So lieu cheo)
9. Curve
10. Data (So lieu, du lieu)
10. Economic growth
11. Econometrics (Kinh te luong)
12. Function (Ham so)
11. Goods and services
14. Growth rate (Toc do gia tang, toc do tang truong)
12. Human capital
13. Linear relationship
14. Negative relationship
15. Model (Mo hinh)
15. Origin
16. Other things equal (Cac dieu kien khac giu nguyen)
17. Percentage change (Chenh lech tinh bang pham tram)
16. Positive relationship
17. Production
18. Production possibility frontier
19. Productivity
20. Scatter diagram (Do thi rai)
21. Slope
22. Technological progress
23. Time series data (Day so lieu theo thoi gian)
23. Time-series graph
24. Trend
25. x- axis
26. x- coordinate
27. y- axis
28. y-coordinate
Questions based on lecture 2
1. In writing an economics article for the general public is it best to express a relationship between economic variables by an equation, a schedule (table) or a graph?
2. What can be learned from a careful analysis of a time-series graph of the Retail Price Index in Viet Nam?
3. If an economist wishes to illustrate a relationship involving three variables, what options are available to her (or him)?
4. Is it possible to draw a production possibility frontier (PPF) that does not illustrate the problem of scarcity?
5. Did the decline of the CMEA cause the production possibility frontier (PPF) of Viet Nam to shift inward? Did "Doi Moi" cause the production possibility frontier (PPF) of Viet Nam to shift outward?
6. Is the economy of Viet Nam currently operating on its Production Possibility Frontier?
7. How are the choices being made now by households and the government of Viet Nam influencing the rate of economic growth in the future?
8. Does the "law of increasing opportunity cost" apply to the production of rice and fruits in rural Viet Nam?
9. If all of the countries of ASEAN (the Association of South East Asian Nations) opened their borders to absolutely "free" trade with each other, would that shift outward the production possibility curve of Viet Nam.
10. Viet Nam has licensed the assembly of automobiles within the country and raised the tariff on imported automobiles to 200%, do these actions move the economy closer to the nation's production possibility curve?
Problem based on lecture 2
Relationships can be represented in algebraic form by an equation. For example, the points along a demand curve can be demonstrated by the following equation:
Y = 10 - 2X
The value of Y can be found by inserting different values of X and solving the equation for Y.
1. Find the values of Y for the following values of X and enter them in the table below.
X Y
0
2
4
6
8
2. Draw this relationship on the graph below using standard mathematical conventions.
3. What is the slope of the line between the first and second points? __________
4. Is this curve a straight line? ___________