Problem 1 (10 points)
Denote Golden State Warriors as g and Cleveland Cavaliers as c. Also, denote the relation “better than” by B and “at least as good as” by A.
(2 points) Use the notation above to write,
Golden State Warriors is better than Cleveland Cavaliers:
Cleveland Cavaliers is at least as good as Golden State Warriors:
Golden State Warriors is better than Golden State Warriors:
(2 points) From question (a) above, which subquestions (1, 2, and 3) state weak or strict preference relation?
(3 points) Introduce the third team, New York Knicks, and denote by N. Using the notation above, for the preference relation B, state the condition for transitivity. You can use any order.
(3 points) Using the notation above (and for the three teams), state what it means for the preference relation A to be complete (you will need to define the universe first and state possible relations for the universe).
Problem 2 (4 points)
Assume you have 3 possible actions, a1, a2, and a3. Each action is associated with utilities 2, 3, and 10, respectively.
(2 points) What is the opportunity cost of each action?
(2 points) Assume the fourth action, a4 has been added, which is associated with the utility of 3. What are the opportunity costs of each action?
Problem 3 (6 points)
Assume we judge pizza based on two components, pizza sauce, and cheese quality. Both components could be measured on a scale from 0 to 10. There are only two pizza producers in the town, Good Pizza and Super Pizza. Good Pizza has a pizza sauce quality of 7 and a cheese quality of 5, while Super Pizza has a pizza sauce quality of 5 and a cheese quality of 7.
(2 points) Imagine currently Good Pizza is consumers’ preferred pizza. Put sauce quality on the X-axis and cheese quality on the Y-axis. Using an indifference map represent the scenario from above.
(2 points) Super Pizza company wants to create a new product (new company) which they can use as a decoy to make their current product look better. Explain (with words not on the graph) how can they achieve their goal.
(2 points) Copy the graph from the question (a) and add a point which will summarize your explanation from the question (b). In other words, the point that you select should show pizza quality and cheese quality of the decoy product (notice, there could be many such points, just pick one).
