Problem Set #1
Directions: Answer all of the following questions and show all your work. Submit your via ELMS answers as *ONE* pdf or Word file, plus *ONE* Excel file (for question 1).
Calculus Review
- You solved this problem in the quiz.
Consider a perfectly competitive firm producing bags of potato chips (selling for $900 per box of 10,000 bags) that has the following cost function:
C(q) = q2 + 10q + 90.
What is the profit-maximizing choice of output (i.e. find q, the number of boxes of potato chip bags)?
Now repeat this problem using the Solver tool in Excel to derive the answer. You can easily set up your excel worksheet to use Solver as follows:
| A | B | |
| 1 | q | Profits |
| 2 | = “formula” |
Notice row 1 has labels for the variables in row 2. This is purely for presentation purposes. The “formula” in cell B2 should be your formula for given the information from this problem, and it should reference cell A2, which is the level of output. Using Solver, you will maximize B2 (i.e. profits) by varying A2 (i.e. quantity).
Submit your Excel spreadsheet with the Solver solution (with your name in the file name like this: “Richard_Stahnke_Q1_xlsx”). Please also include 1) a screenshot of your Excel spreadsheet *OR* 2) a picture of your Excel work (simply select the cells showing your Excel work and paste special as a picture into your Word document).
Expected Utility
- Your current wealth level is W = 49, and you have the option of making the following wager: if a fair coin comes up heads you get 15; if it comes up tails you lose 13. Your utility function is U = W1/2 .
- What is the expected value of this gamble?
(Hint: This answer is independent of your level of wealth.) - What is the expected utility of the gamble?
(Hint: Here your wealth enters into the calculation.) - Explain why you would or would not opt to take this wager.
- Illustrate your answer graphically.
- What is the expected value of this gamble?
- Go to L05, Slide 2 for the Lottery A vs. Lottery B example information. Between us, we have calculated the expected income and expected utility of both lotteries. Now, illustrate both lotteries on one expected utility graph showing why Lottery A is preferred to Lottery B. Make sure to label clearly your axes and different key points on the graph.
