Chapter 1 - Appendix - Appendix Problems - Page 27: 3

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Graphs can be used to represent economic relationships by showing the relationship between two variables on the x and y axis. Inverse relationship is when an increase in one variable results in a decrease in the other variable. This is represented on a graph as a downward slope, where as the x-axis variable increases, the y-axis variable decreases. A direct relationship is when an increase in one variable results in an increase in the other variable. This is represented on a graph as an upward slope, where as the x-axis variable increases, the y-axis variable increases. (a) The number of inches of rainfall per month and the sale of umbrellas would have an inverse relationship. As the amount of rainfall per month increases, the sale of umbrellas would decrease. However, other variables such as temperature, time of the year, and location could also affect the sale of umbrellas. (b) The amount of tuition and the level of enrollment at a university would have an inverse relationship. As tuition increases, the level of enrollment would decrease. However, other variables such as the quality of the university, the availability of scholarships, and the job market could also affect enrollment. (c) The popularity of an entertainer and the price of her concert tickets would have a direct relationship. As the popularity of an entertainer increases, the price of her concert tickets would increase. However, other variables such as the location of the concert, the timing of the concert, and the size of the venue could also affect the price of concert tickets. Historically, enrollments and tuition have both increased, which is not consistent with the graph of an inverse relationship. This could be because tuition increases have not been large enough to significantly decrease enrollment, or because other factors such as the quality of education or the job market outweigh the effect of tuition increases on enrollment. _____ I first identified that the question was asking for an explanation of how graphs can be used to represent economic relationships, and the difference between inverse and direct relationships. I explained that graphs can be used to represent economic relationships by showing the relationship between two variables on the x and y axis. I defined inverse relationship as when an increase in one variable results in a decrease in the other variable and direct relationship as when an increase in one variable results in an increase in the other variable. I then provided examples of an inverse relationship (a) and direct relationship (c) between the number of inches of rainfall per month and the sale of umbrellas, and the popularity of an entertainer and the price of her concert tickets. For the example of inverse relationship (b) between the amount of tuition and the level of enrollment at a university, I explained that as tuition increases, the level of enrollment would decrease. I also mentioned that other variables such as temperature, time of the year, the quality of the university, the availability of scholarships, and the job market could also affect the relationship between the variables, and pointed out the historical fact that enrollments and tuition have both increased, which is not consistent with the graph of an inverse relationship.