Learning Outcome By the end of this chapter you should be able to: ■ Identify the importance of theory, data and forecasting
Economic An important role of economics is its use to answer questions pertaining to economic Theorizing behaviors, trends and outcomes. Economists can develop theories based on observation of facts and figures and subsequently attempt to test these theories in order to answer such questions. These theories can answer questions such as the impact of the internet on economic growth or the expected demand for wheat in Pakistan in a certain month of the year. We now take a detailed look at what such theories mean and their importance in understanding economic issues. Theories Theories are constructed to explain various issues that arise in an economy.
For example, what determines the number of eggs sold in Lahore in a particular week? As part of the answer to such a question, economists have developed the
theory of demand
.Like any other theory, the theory of demand is built around definitions, assumptions^fid predictions.The basic elements of any theory are its variables. A variable is a magnitude that can take on different possible values. For the theory of the demand for eggs, we define the variable demand as the number of cartons of eggs consumers wish to purchase during a particular time period.
A theory’s assumptions concern motives, physical relationships, lines of causation, and the conditions under which the theory is meant to apply, whereas a theory’s predictions are the propositions that can be deduced from it. For example, a proposition in the theory of demand states, “if the price of eggs rises, consumers will purchase fewer eggs”. This negative relationship between a product’s price and the amount people wish to buy applies to all commodities. These propositions are then taken as predictions about real-world events. Economic Data
Economists seek to explain observations made of the real world. Why, for example, did the price of wheat rise in some years even though the wheat crop increased? We would be aware of this issue only if we had numbers for the wheat crop and the price of wheat, and we would need a lot of additional data (such as on incomes and other prices) to come up with a comprehensive answer.
Real-world observations are also needed to test the predictions of econo • theories. For example, did the amount that people saved in a partic year rise when a large tax cut increased after-tax incomes? By theory prediction is that it should have, as more income was made available
47 people. To test this prediction, we need reliable data for people’s incomes and their savings.
In economics there is a division of labor between collecting data and using it to generate and test theories. The advantage is that economists do not need to spend much of their scarce research time collecting the data they use. The disadvantage is that they are often not as well informed about the limitations of the data collected by others as they would be if they collected the data themselves.
Once data is collected they can be displayed in different ways, all of which we will see later in this chapter. It can be laid out in tables and can be displayed in the various types of graphs that we will study later. Where we are interested in relative movements rather than absolute ones, the data can be expressed in index numbers.
Index numbers
Table 1.3-1 Price of sugar and wheat(average price in each year, Rupees per kg)
Index numbers as relatives
Comparisons of relative changes can be made by expressing each price series as a set of index numbers. To do this we take the price at some point of time as the base to which prices in other periods will be compared. We call this the
base period
In the present example we choose the first’
year as the base period for both series. The price in that year is given a value of 100. We then take the price of wheat in each subsequent year and then express it as a ratio of its price in the base year and multiply the results by 100. This gives us an index number of wheat prices. We then do the same for sugar. The details of the calculations for wheat are shown in Table 1.3-2.Table 1.3-1 shows how the prices of sugar and wheat varied during the past five years. How do these two sets of prices compare in instability? It may be difficult to tell from the table because the two prices start at different levels. It is easier to compare the series if we concentrate on relative rather than absolute price changes. (The absolute change is the actual change in the price; the relative is the change in the price expressed in relationship to some base price.)
Year Sugar ACTUAL PRICES Wheat
(1) 100.4 146.7
(2) 104.5 146.4
(3) 100.8 129.7
(4) 121.8 126.4
Economics | I Quarter
Index of Wheat Prices
index numbers are calculated by dividing the current price bytte I base-year price and multiplying the result by 100 For example, thewtT price in 2001(4) was Rs.126.4 per kg. Dividing by the base year pnce of 146.7 Rs (in 2001(1)) and multiplying by 100 gives an index of 86.2 for this quarter.
Table 1.3-2 Calculation of an index of wheat prices The formula of any index number is.
Value of index in period t = value in period x100
Value in base period
An index number merely expresses the value of some series many] period as a percentage of its value in the base period. Thus the Ye~ Index of sugar prices of 148.4 tells us that the Year 5 price of sugar — 48 4% higher than the Year 1 price. By subtracting 100 from an> i we get the change from the base year. To take another example, thew index of 93.1 in Year 5 tells us that the price of wheat at this timci only 93.1% of the price in Year 1,or, what is the same thing, that the fhad fallen by 6.9% over the 4 year period.
Index numbers as averages
Index numbers are particularly useful if we wish to combine different series into some average. Suppose that we want an mdot* drink beans, and cocoa and coffee beans are the only two prod^ are interested in.
An un-weighted index, for any one year, could be added to Acl indexes for cocoa and coffee and the average could be taken n— would give us a hot-drinks beans index. However, equal weighti given to the two prices by the index. Such an index is called an Iin index, .
An output weighted index
Wheat is a much more important commodity than sugar
mM
that much higher volume is produced of wheat than of su~cJ purpose of illustration, we assume that 9 kg of wheat is every 1 kg of sugar. To get our weighted index of wheat prices, wiej the wheat index value in Table 1.3-3 by 0.9 and the sugar mdj and sum the two to get the final index. The results are shown .1.34. The quite different behavior of the two indexes shows the ~ of the choice of weights. (1) (146.7/146.7) x 100 = 1 0 0 Q < 146.4/146.7) x 100 = 99.8 (3) (129.7/146.7) x 100 = 88.4 | (4) < 126,4/146.7) x 100 = 86.2 i ^ j m (136.6/146.7) x 100 = 93.1 j
49 An index that averages the changes in several series is the weighted average of the indexes for the separate series, the weights reflecting the relative importance of each series.
Price indexes
Economists make frequent use of the price level covering a broad group of prices apross the whole economy. One of the most important of these is the Rafail Price Index. RPI covers goods and services that people buy.
... — Wheat = 0.9 Sugar = 0.1 ACTUAL PRKES
labie
^S-4: Comparison of Index with Equal Weight Index and a Weighted Index
W eights matter a lot. The equal weight index is calculated for each period £>' adding Wheat and Sugar indexes from Table 3.3 and dividing by 2.
--- > e c o n d index is calculated for each period by multiplying the wheat index
by 0.9 and sugar index by 0.1 and then adding the results. These series act quite differently as a result of using different weights, as chi be seen in Figure 3-B.
i price indexes are compiled using the same method. First the relevant ■rim -"d the base year are chosen. Then each price series is converted
■ B "B
L, n u mb e r s . Lastly, the index numbers are combined to create i"med average index series where the weights indicate the relative timnce of each price series. For example, in any retail price index a -O - iianged into index numbers, which are later combined to create it- erage index where the weights show the relative importance n <1 e series; for example, the price of sardines would be given a iisrakr weight than the price of living accommodation, as what te the price of accommodation is much more important to —than the price of sardines.
economic data
txo; !ri:c variable such as unemployment or GDP can come in
Year Sugar Wheat
(1) 100.4 100.0
(2) 101.9 100.2
(3) 94.2 89.6
(4) 103.7 89.6
(5) 120.7 98.6
Table 1.3-3 Index of sugar and wheat prices
Year (2) (4) (5) Equal Weights 100.4 101.9 ■ 100.0 100.2 89.6 89.6 98. 6 J 103.7 120.7
Economics | I 14.00% ! 12.00% 10.00% -] 8.00% 6.00 %
Unemployment of 10 cities of Pakistan in a certain: 4 2.00 % 0.00 % Cross sections
The first is called cross-sectional data, which means a number of different observations on one variable taken in different places at the same point in time. Figure 3-A shows an example. The variable in the figure is unemployment as the percentage of the workforce. It is shown for ten selected cities of Pakistan in a certain year.
Figure 1.3-1 Time series
The second type of data is called time series data. This involves surve on one variable at successive points in time. Figure 1.3-2 shows a I series for the two indexes of two commodities that were calculated section on the index numbers.
Sygar-0 : 1
Figure 1.3-2 — Weights matter. The two trend lines represent 1 of prices, however both depict different pictures. The equal wt line indicates an overall rise in prices over the 5 year perioa. Index trend line indicates that prices have in fact dropped < period.
Logarithmic scales
A logarithmic scale is a scale of measurement using the logarithm of a physical quantity instead of the quantity itself. It is useftil when percentage of data is more important than absolute changes. When data is graphed on the logarithmic scale, equal distances indicate equal percentage changes. Also, with a log scale a straight line indicates a constant rate of growth.
Scatter diagrams
Data can also be presented in the form of a scatter diagram. This is the most analytical type of chart. Its purpose is to show the relationship between two different variables, such as the price of flour and the quantities of flour sold. To plot a scatter diagram, values of one variable are measured on the x axis and the values of the second variables are measured on the y axis. Any point on the diagram relates to a specific value of the other. The two series plotted on a scatter diagram may be either cross sectional or time series. An example of cross sectional would be a scatter of the price of flour and the quantity sold in a certain month at different places in Pakistan. Each dot would represent the price-quantity combination observed in a different place at the same time. An example of a scatter diagram using time series data would be the price and quantity of flour sold in Karachi for each month over the last ten years. Each of the 120 dots would show a price-quantity combination observed at the same place in one particular month.
Table 1.3-5 shows data for the income and the savings of ten households in one specific year. They are plotted on a scatter diagram in Figure 1.3-3. Each point in the fipre stands for one household, showing its income and its saving. The positive relationship between the two stands out. The higher the income, the higher the saving tends to be.
■come Annual savings 10,000 Figure 1.3-3: Savings and Income 14 12 10 20 40 60 80 100 120
Economics | I
52
Graphing
economic theories
Savings tend to rise as income rises. The table shows the amount of income earned by ten selected households, together with the amount they saved during the same year.
The theories are constructed on the basis of assumptions about relationships between the variables. For instance, the quantity of generators is assumed to fall during summer as its price rises, and the purchasing power of an individual tends to increase with an increase in his total income. How| do we express such relationships mathematically? When one variable is related to another in such a way that to every value of one variable there | is only one possible value of the second variable, we say that the second variable is a function of the first variable. When we write these variables j down we are writing down the functional relationship between them.
We can express functional relationship using mathematical equations* j graphs, numerical schedules or even in words.
Assume a relationship between a famil/s monthly income, which K shown by the symbol
Y
and the totalamount it spends on goods anfl services during that year, which is represented by the symbol q Verbal statement: When income is zero, the family will spe*J| PKR 800 a year (either by savings or borrowing), and for 1 rupee of income that it obtains its expenditure will increase llj
0. 80 paisa.
Schedule, The schedule shows the value of the family’s inco«J and the consumption pattern.
Table 1.3-6: Schedule of the family's monthly income and consum|M|
Monthly Income Consumption
Reference I
0 ... 800 2,500 5. 0 7,500
10.0
Mathematical (algebraic) statement: C = PKR 800 = equation of the relationship just described in words., you can first see that when
Y
is zeroC
is PKR 800. Then| substitute any two values ofY
that differ by 1 rupee, r each by 0.80, and see that the corresponding two ^ consumption differ by 0.80 pai
aisa.
Geometrical (graphical) statement: Figurel.3-4 shotisl points from the schedule above and the line repi equation given in point 3.
Figure 1.3-4, Income and Consumption 1000 8000 4000 2000 0 4000 6000 8000 0 Consumption 2000 10000 Household income (PKR)
Comparisons of the values on the graph with the values in the schedule, and with the values derived from the equation just
stated, shows that these are alternative expressions of the same relationships between C and Y. All these modes of expression show the same relationship
between total
consumption and total income. Functions
After looking at the relationship between income and consumption expenditure, we can state the general expression for it which is detached from the specific numerical above, and we use a symbol to show the dependency of one variable to another. Using cf, for this purpose, we can write: