Empirical: In this question you will explore the 3D shapes of two utility functions. The end result of this exercise should be (1) two plots of the 3D shape of the utility functions and (2) two plots of the indi?erence curves for the same utility functions and (3) a brief (1 paragraph or less) analysis of your plots for each utility function.
(a) Download the Excel spreadsheet from bcourse called PS1QE. There should be two tabs labeled *Utility function 1* and *Utility function 2*.
(b) For each utility function, plot a surface chart of the utility function using the 3D surface chart. Make sure you have sensible scales and grid lines for each axis. We suggest a scale of 0 to 100 and major units (gridlines) every 10 units on the z-axis for utility function 1, and a scale of 0 to 10 with major units (grid lines) every 0.5 units on the z-axis for utility function 2. (Hint: you can change the scale of the z axis by right clicking on it and selecting Format Axis. The grid line controls are under Scaleand the lines that are drawn are the Major unit.)
(c) For each utility function, plot the indi?erence curves using the contour-keeping the same scale as the previous part. (Hint: You may need to ?rst create the same 3D plot to have access to the z-axis and then change type to contour.)
(d) Describe each of the utility functions you have just plotted. For example: What is the shape of the indi?erence curves? Do the utility functions satisfy our assumptions (completeness, transitivity, more is better)? Are the goods imperfect substitutes, perfect substitutes or perfect complements?