See attachment.

Worksheet

NAME: ____________________________________________________________

NOTE: Use this Word File to TYPE your answers. (I will subtract 2 points (10%) if your homework is not typed).

Show your work. Explain all the steps. Justify the values you assign to utility weights and observe levels of attributes. When in doubt, explain MORE rather than less.

The situation is similar to the last assignment. You have applied to work at the same two firms. They still have offices in Chicago, Columbus, and Los Angeles. If you get the job, the firm will assign you to one of these cities. Assume that, if the firm assigns you to a particular city, you will live in the neighborhood listed in parentheses.

The overall goal of this assignment is to evaluate which FIRM represents your better choice.

Differences

I eliminated the category that compares costs of living across the cities. As discussed in class, we will account for those differences by adjusting the expected income.

I am introducing:

1. State dependent preferences

2. Computation of discounted present value of expected earnings, adjusted for cost of living differences in each city

3. Uncertainty in Year 1 (the second year)

As before you will need outside information. I am providing it here:

A. Rate of interest = 6 percent

B. Your consumption rate of time preference (use to discount future utility)

Note B.1: You must decide it.

Note B.2: You must explain why you chose that value and what that value implies about your preferences

Note B.3: You MAY NOT use a consumption rate of time preference that is equal to “1.”

C. Total income tax rate in each city

C.1: California 13.5%; Los Angeles: 10.5% - total 24.0%

C.2: Illinois: 12.9%; Chicago: 9.9% - total 22.8%

C.3: Ohio: 10.0%; Columbus: 12.2% - total 22.2%

D. Cost of living difference (Columbus is the reference city)

(if spend $1.00 in Columbus, how much must spend to get same amount of goods in the other city)

D.1: Los Angeles: 1.40

D.2: Chicago: 1.25

D.3: Columbus: 1.00

Like last time: Follow the process described in class to calculate a total utility associated with the “bundled” good of each city.

1. LIST CHARACTERISTICS

2. Assign your UTILITY WEIGHT for each characteristic that gives you utility

Note 2.1: Explain the weight you assign

3. Assign a value that reflects the LEVEL of each CHARACTERISTIC present in each city

Note 3.1: This value has nothing to do with your preferences;

Note 3.2: Use the information you found (cited) and explain how you decided the value.

4. LIST AN INFORMATION SOURCE for each characteristic and rationalize the value you assign

Note 4.1: Should be the source of the information you used to gauge the characteristics in each city;

Note 4.2: Use Google/internet or other objective sources, not family members or personal experience.

Task 1. Compute a baseline (Year 0) total utility associated with each city.

NOTE: The utility value is NOT the one you use to decide if you prefer firm 1 or firm 2.

Year 0

State dependent preferences

We will incorporate state dependent preferences and uncertainty in the following way.

In Year 0 you will be single.

In Year 1, you will have a partner (with certainty) and there is some chance you will have a child.

Probability have a child = 0.35

Probability do not have a child = 0.65

Task 2. Compute a Year 2 total utility associated with each city under two different states of the world

For each of the two “states” you might be in in Year 1:

1. Reevaluate how much you value each of the characteristics given your situation (partner, with/without child)

2. Assign a new weight (be sure to justify why your utility weight changed)

3. Compute a total utility score for each city for each state of the world

As a resource, you can download templates to make decision trees here: https://templatearchive.com/decision-tree/;

If you want to read more about them, see https://www.ibm.com/topics/decision-trees

Year 1-State 1 – With a partner, no child

Year 1-State 2 – With a partner, with a child

Task 3. Create a utility decision tree

The decision tree will be almost exactly the same as the one you construct(ed) for earnings. Instead of earnings in each city, you will list the values from above - the total utility each city offers.

Task 4. Compute discounted expected utility associated with taking a job at Firm 1 and taking a job at Firm 2

For this task, you have to multiply the probabilities along each path then sum the products. Discount with your consumption rate of time preference (NOT the interest rate)

Discounted present value of expected disposable income, adjusted for cost of living differences in each city

Previous information holds

That information:

Prob. of Probability firm assigns you to … Monthly salary in each city …

Firm Offer Chicago Columbus Los Angeles Chicago Columbus Los Angeles

1 0.65 0.35 0.40 0.25 $4,300 $3,200 $4,600

2 0.80 0.40 0.20 0.40 $3,800 $2,700 $4,150

1. Multiply the monthly salary by 12 to get your annual income.

2. Compute disposable income (as in class) for Year 0

3. Adjust for cost of living differences in each city in Year 0

Introduce uncertainty in disposable earnings in Year 1.

C. Year 1 total income tax rate in each city

C.1: Los Angeles: 24.0% (stays same, p=0.15); 27.0% (increases, p=0.85);

C.2: Chicago: 22.8% (stays same, p=0.05); 25.0% (increases, p=0.95)

C.3: Columbus: 22.2% (stays same, p=0.50); 24.0% (increases, p=0.50)

You must re-compute the discounted present value of expected disposable income, adjusted for cost of living.

Task 5. Create a decision tree like last time but add new branches for the two possible states of the world in Year 1

Guided by the decision tree, use the above information to compute

1. Discounted present value of cost-of-living adjusted expected earnings at each firm.

(Use the interest rate to discount future expected earnings)

2. Discounted present value of expected utility at each firm.

Note: show your work, explain the steps. (Use your consumption rate of time preference to discount future utility)

Based on these values, conclude with a statement about:

The FIRM that represents your better choice.

Why? In your explanation, be sure to discuss how your preference for risk or attitude about risk affects your choice. Explain what factors were most important for you.