Final answer:
To reflect the relationship between inflation rate and unemployment rate, plot the data on a graph and identify the Phillips curves. A Linear Equation often describes the short-run Phillips curve, while the long-run curve suggests a fixed inflation rate regardless of changes in unemployment.
Step-by-step explanation:
The task involves establishing a relationship between the inflation rate and unemployment rate which is typically represented by the Phillips curve. The first step in analyzing this relationship is to plot the data points with inflation rate on the Y-axis and unemployment rate on the X-axis. According to the information provided, the graph that emerges will resemble something akin to Figure 13.7, Figure 26.7, or Figure 12.7, variations of which may appear in economic textbooks.
Upon inspecting the graph, we look for evidence of the Phillips curve(s). In the short term, we should be able to identify a downward-sloping trend illustrating the inverse tradeoff typically observed between higher unemployment rates and lower inflation rates. This is referred to as the short-run Phillips curve. Conversely, over the long term, we might observe a vertical line of data points, signifying a long-run Phillips curve that correlates with the natural rate of unemployment—commonly suggested to be around 4%.
To answer the student's question regarding the equation for the change in the inflation rate as a function of the unemployment rate, the specific mathematical representation would depend on the exact nature of the relationship between these two variables as shown in the graphical data. However, since the question mentions a tradeoff between inflation and unemployment rates, a Linear Equation (Choice A) might often be used to describe the short-run Phillips curve, whereas the long-run Phillips curve would suggest no correlation, and thus, no change in the inflation rate, regardless of unemployment, suggesting that no function exists for the long-run curve.