Business
 PRODUCTIVITY GROWTH HYPTHESIS
 
         In this assignment, we will attempt to study the effects that difference
 in Income Ratio (henceforth known as I.R.) between the years 1980 and 1990
 have on the Productivity Growth (P.G.) during the same period of time. 
         The Income Ratio of one specific year can be found if we take the average
 income of the richest faction of a country (the richest 20% of the
 population) and divide it by that of the poorest faction (the poorest 20%).
 In this assignment, the Income Ratios that were used were those of 13
 different countries. The I.R.'s on both 1980 and 1990 were taken for all
 these countries and, to find the difference between them, the I.R. for 1990
 was divided by the I.R. for 1980, for each country. These new numbers
 illustrate the change of  I.R. between the two years so that we can compare
 how the P.G. changes in relation to the changes in the I.R..
         On this assignment, we use inductive reasoning to examine the data and
 find a theory (a hypothesis) that would combine the data given in a way
 that would make sense, based solely on our data. How do we know if the
 "theory" that we formulate makes sense? In this case we will plot the
 points (derived from the column "I.R. 1990/1980," going on the x-axis, and
 the column "Productivity Growth 79-90," on the y-axis). According to how
 the points are on the graph in relation to the Average Point (0.94,1.45)
 (point that is an average of all values and which divides the graph into
 four Quadrants), if 80% of these points are where they would be expected to
 be to conform to the hypothesis, then there is no reason to reject this
 hypothesis. If, on the other hand, the majority of the points does not
 conform to our hypothesis (are not where they were predicted to be), then
 it is rejected. 
         Another method of reasoning frequently used by Mainstream economists is
 "deductive knowledge," as opposed to "inductive," described above. Their
 theory is formulated and only then it is applied to the data. Their theory
 on this subject suggests that productivity within a country grows when the
 population has incentives to work harder (or to work more). When the gap
 between rich and poor increases (an increase in I.R. form 1980-90,
 resulting in a larger ratio on the column I.R. 1990/1980), so does the
 population's eagerness to work, therefore increasing the Productivity
 Growth. Since when one variable goes up the other also goes up, there is a
 positive (or direct) correlation between the two. Mainstream economists use
 deductive reasoning to deduce that there exists a positive correlation
 between the two factors. In short, their hypothesis is that when the Income
 Ratio increases, the Productivity Growth also increases, since people are
 more motivated. For this to be true, we would expect a line going up and to
 the right on the graph, passing by Quadrants II and IV. Most points (80% or
 more) would have to be on these two Quadrants. This, however, is not the
 case (see graph), since only about 30.77% of the points plotted satisfy
 these conditions.
         Since the original hypothesis was rejected, we might want to see if there
 is a negative correlation between the two variables (that is, as one goes
 up, the other goes down). Our new hypothesis would then be "as the Income
 Ratio increases, the Productivity Growth decreases." Then, in the case of a
 high I.R., people in lower classes would rationally start to feel insecure
 and that their work is not being recognized by society, therefore losing
 motivation and producing less. In this case, since there's a negative
 correlation, one would expect the line on the graph to go downwards, from
 left to right, passing on Quadrants I and III. If this hypothesis were
 valid, 80%+ of the points would have to be on these Quadrants. This is also
 not the case, for only 69.32% of the points are on the appropriate
 Quadrants. Like the first, this second hypothesis also has to be rejected.
         After analyzing these two relationships and seeing that neither is valid,
 we conclude that there is no direct relationship between the two variables
 tested. That does not mean that one has no effect on the other (it probably
 does), only that there may be other factors and influences involved that
 have not been accounted for in this assignment and that one is not the only
 factor responsible for the changes in the other.
 DATA SHEET
 
         Country    Income Ratio            1980     Productivity   Growth
 1979-90     Income Ratio           1990    Income Ratio      1990 / 1980        
 United States   9.0     0.4     11.0    1.2     
 Australia       9.6     0.8     9.6     1.0     
 New Zealand     8.8     1.4     8.8     1.0     
 Switzerland     8.7     1.0     8.0     0.91    
 Canada  7.0     1.1     7.0     1.0     
 Britain 6.8     2.0     7.0     1.03    
 France  6.5     2.4     6.0     0.92    
 Italy   6.1     2.0     5.8     0.95    
 Germany 5.8     1.6     5.0     0.87    
 Holland 5.6     1.5     5.0     0.89    
 Belgium 4.7     2.2     3.8     0.81    
 Sweden  4.7     1.5     3.8     0.81    
 Japan   4.2     1.0     3.6     0.85    
 
 
 Average Income Ratio 1990 / 1980: 0.941
 Average Productivity Growth 1979-90: 1.45
 No. of points conforming to first hypothesis: 4/13 = 30.77%
 No. of points conforming to second hypothesis: 9/13 = 69.23%
 
 By: Leonardo Santos