COU 4: Graphing a Tent-Shaped Utility Function

Instructions

Print out this pdf. Then, answer each of the following prompts by drawing on the graph or writing in the space at the appropriate prompt in the pdf. Once you’ve written all your answers on the printed out pdf, scan and upload your work to Gradescope following the instructions here.

Prompt 1

Notice that the location of an ideal point I is marked on the horizontal axis of the graph for this prompt. Use the graph to draw a tent-shaped utility function for a person with ideal point located at the point marked ‘I’ on the horizontal axis. Use the tick marks on the vertical axis to make sure the the level of the utility function you draw is correct at each location along the horizontal axis.

Prompt 2

Notice that the graph for this prompt marks the location of an ideal point I on the horizontal axis, just as in the graph for the Prompt 1. In addition, this graph marks the locations of three policies labeled A, B and C. First, draw the graph of the tent-shaped utility function for a person with ideal point located at the point marked ‘I’ on the horizontal axis. Notice that since the location I in this prompt is exactly the same as the location marked ‘I’ in prompt 1, the graph of the utility function you draw for this prompt should be identical to the graph you drew for Prompt 1! Second, use dotted lines to trace the locations of each of the policies A, B and C up to the utility level that the utility function you’ve drawn assigns to the policy.

Prompt 3

In the spaces provided under Prompt 3 in the pdf, write the approximate utility levels assigned by the utility function you drew in response to the prompts above at each of the policies A, B and C.

Prompt 4

In the spaces provide under Prompt 4 in the pdf, write the preference ordering over policies A, B and C of the person whose preferences are represented by the utility function you drew in response to Prompts 1 and 2.

Rubric

Prompt 1

You can earn up to 1 point on Prompt 1. You earn 1 point if you draw a graph that correctly depicts the utility level assigned at every location on the horizontal axis. You earn 0.5 points if you draw a graph that is tent-shaped, with the peak of the tent located at the correct point on the horizontal axis but an incorrect level of the graph is incorrect at one or more locations on the horizontal axis. You earn 0 points otherwise.

Prompt 2

You can earn up to 3 points on Prompt 2. To earn more than 0 points, you must first of all draw a tent-shaped graph with the peak at the correct location along the horizontal axis. If you do not draw a tent-shaped graph with a correctly located peak, you get 0 points regardless of what else you draw. If you draw a tent-shaped graph with a correctly located peak, but the level of the graph is incorrect at one or more points, we evaluate the other elements of what you’ve drawn as if the levels you drew are all correct. Specifically, you earn 1 point for correctly tracing the utility levels assigned by the graph you’ve draw at each of the policies A, B and C.

Prompt 3

You can earn up to 3 points on Prompt 3. To earn more than 0 points, you must have earned 3 points on Prompt 2. If you earned 3 points on Prompt 2, then you earn 1 point on this prompt for each of the correct approximate utility levels you write. The levels you write must match the levels indicated in the lines you traced in Prompt 2. They must match even if the levels of the graph you drew in Prompt 2 are incorrect!

Prompt 4

You can earn up to 3 points on Prompt 4. To earn more than 0 points, you must have earned 3 points on Prompt 3. If you earned 3 points on Prompt 3, then you earn 1 point on this prompt for each unique pair of the policies A B and C for which you provide a ranking that matches the relative utility levels you wrote in response to Prompt 3.