Optimal values for decision and outcome variables

Managerial Economics (ECON 3551)

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Choose any five spreadsheet problems (tabs on the spreadsheets in the Course Materials / Lecture Slides folder), except Ch. 2 App. On each spreadsheet,

(1) Identify what the key variables and data are. (2) Analyze the baseline scenario: calculate the optimal values for the decision and outcome variables. (3) Create and analyze a change scenario: discuss a possible change in the data and its effect on the decision and outcome variables.

See the example and details below. The deliverable is a Word or PDF file, submitted through Blackboard.

Deadline

Sunday, June 10, 11.59 pm

Note: There is no possibility of extension because of the grading deadline two days later.

Example and Details

CH. 2 APP

1. What to do

Here is what you see when you first open the spreadsheet:

The decision variable (Quantity) is colored blue; the target variable (Profit) is colored red.

Identify the “data.” You do this by clicking the green-colored entries and see if there is a formula behind them that contains independent information. In this case, price comes from an assumed demand function:

The demand function is P = 170 – 20*Q, since the cell reference (B7) points to quantity Q. Also, cost comes from an assumed cost function:

The cost function is C = 100 + 38*Q. Some other cells have formulas, but they derive from the demand function (MR) or the cost function (MC), so they are not new information. You have to use your understanding of economics to recognize what they are, and that the information is not new. Alternatively, you could look up the actual spreadsheet problems in the book and see what the data are that are given.

Now you optimize the target variable, probably by using Solver (which I explained in class, and in the Ch. 2 slides). Solver tells you that the optimal quantity is Q0 = 3.3, and the optimal price is P0 = 104. Then, profit is π0 = 118. Make a note of these values.

Next, you choose one of the formulas that contain data and think of a scenario that could affect the data. Let’s say, you pick the demand function, and you imagine that consumer incomes increased, and this is a normal good. Then, the demand function might change to P = 200 – 20*Q. You modify the spreadsheet accordingly. Recognize that, when demand changes, the formula for MR does as well. It becomes P = 200 – 40*Q, and you need to make that modification.

Note that the decision variable will not be at its optimal value anymore, after the change. Run Solver again to reoptimize.

It turns out that the firm’s optimal quantity increases to Q1 = 4.05, the optimal price increases to P0 = 119, and the optimal profit increases to π1 = 228. Again, note down these values.

2. How to report your work

This is how you might show your work in this example. Whichever format you choose to follow, make sure it includes:

– The spreadsheet you’re working on (chapter number and the name of the worksheet tab).

– The primary data that are being assumed (given functions and values). – The decision variable(s) and the target / objective(s). – The initial optimal value(s) of the decision variable(s) and the target / objective(s), as

well as any affected variables that might be of particular interest. – How you are modifying primary data and your justification, i.e. the scenario you are

considering and any further assumptions that may be required, so that it produces a change in that direction.

– The new optimal value(s) of the decision variable(s) and the target / objective(s), as well as important affected variables. Also express any changes in percentages, so that they are on a common scale. E.g. the percent change in profit is 100*(π1 – π0)/ π0.

You do not need to include screen captures.

Ch. 2 (App)

Primary Data:

– Demand function P = 170 – 20*Q – Cost function C = 100 + 38*Q

Key Variables:

– Sales (decision variable) – Profit (target variable)

Baseline Scenario Optimal Values:

– Sales: Q = 3.3 (Price P = 104) – Profit: π = 118

Sensitivity Analysis:

Suppose there is an increase in consumer incomes. I will assume that this is a normal good. Then demand will increase. Specifically, consider an increase in the demand function to P = 200 – 20*Q, which means that consumers are willing to pay $30 more. In this case, the company should increase sales by 23% to 4.05, while raising the price by 11% to $115. This will increase profit by 93% to $228.

Change Scenario Optimal Values:

– Sales: Q = 4.05 (Price P = 115) – Profit: π = 228

3. How I will grade

There are four points per spreadsheet. Two points are for correctly evaluating the baseline scenario (i.e. determining the data and initial optimum); two points are for coming up with a reasonable change scenario and evaluating it (reasonable justification, new optimum). For each scenario (baseline, change) you get 1 point if your answer is basically right, but imprecise or flawed in a minor way (say, you forgot one of the given data in the baseline scenario, or you omitted a necessary assumption in your change scenario). You get 2 points for an answer that is clear, complete, and correct.

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