# What price (p) maximizes total contribution (TC)?

Accounting Excel
Paper , Order, or Assignment Requirements

Demand and Revenue Management
Name ______________________
READ “DRM_Week3_ONLINE_Notes.doc” in this same folder.
ANSWER the questions and e-mail to me by end-of-day 10/8/2017. (Late submissions will be penalized.)
RENAME this file as “lastname_firstname_Week_3and5.doc” but with your name, of course!
NOTE: This assignment mostly covers material from Chapters 2-3 of PRO and Chapters 3-5 of DM, but may use concepts from earlier material as well.
This is a Word document, so just add space as needed between questions, but leave the original questions!
If you have any doubt, show work or explain for partial credit, or else the answers will be graded as “all or nothing”.
Hint: Clever use of Excel might make some answers much easier to answer!
Maximum of 100 points on assignment
Tactical Questions:
1. (10 pts total) Chapter 2, Problem 1 on page 36 of PRO (“Brain and Company…”)
a. (5pt) see text
b. (5pt) see text
2. (10-15 pts total) If price elasticity of demand (ϵ) is 3,
a. (5pt) How does demand change if the price is increased 1%
b. (5pt) How does demand change if the price is decreased 5%
c. BONUS (5pt) How does demand change if the price is decreased 50%
3. (15-20 pts total) The Basic PRO Problem. Dizzy Toys © has created a new toy, RoboWoman™, loved by girls and boys alike, that costs \$5 to make. They are not sure what price they should charge for this awesome new toy, but they want to maximize profits. Initial market research has hinted at a linear PRF of d(p)=14000-700p.
HINT: See slides 59-60 of Week 3 ONLINE slides!
a. (5 pts) What price (p) maximizes total contribution (TC)?
b. (5 pts) What is the demand at the optimal price (p*)?
c. (5 pts) What is the TC at p*?
d. BONUS (5 pts) What is the satiating price (P)?
4. (20-30 pts total) Pricing with Competition: The Multinomial Logit (MNL). Consider Example 3.7 on page 57 of PRO. It is relatively easy for a company to change its price, but difficult to change its price elasticity since this is based on factors such as brand reputation and customer loyalty. Re-create the chart from the example in Excel using Equation 3.13 (Note that I divided price by 1000 to keep the numbers reasonable and prevent rounding errors in Excel). You should get a result like this:
Model Price bj e^(-bipi/1000) Market Share (μi(p))
Audio Two 400 2.5 0.368 30.8%
Koshiba 650 3.077 0.135 11.3%
Takata and Fuji 500 2.4 0.301 25.3%
Soundmaster 750 2.4 0.165 13.9%
Cacophonia 1200 1.25 0.223 18.7%
1.193 100.0%
Assuming elasticity (bj) does not change (which is of course a BIG assumption for a large price change!), what is Takata and Fuji’s market share if it…
a. (5pt) decreases its price to \$400?
b. (5pt) increases the price to \$625?
c. (10pt) At \$400, Takata and Fuji is at the same price point as Audio Two. Assuming their costs are exactly the same, which company is in the “better” position? Why? (Hint: Use more than just the market share to explain!)
d. BONUS (10pts) If it costs \$350 to make an item (and elasticities don’t change), find the price that maximizes Takata and Fuji’s Total Contribution.
5. (20-30 pts total) The Logit Price-Response Function. (Based on Problem 3 on page 70 of PRO) An auto manufacturer can manufacture compact cars for an incremental cost of \$5,000 apiece. She faces a logit price-response function for sales in the next month (see equation 3.11 on page 53), with parameters C=40,000, b=0.0005, and market price ṕ=\$12,000.
a. (5) Keeping the price as variable p, what is the unit margin (contribution) from each additional sale?
b. (5) What is the price-response function, d(p), for this manufacturer?
c. (5) At a price of \$10,000, what is the demand?
d. (5) Roughly, what is the shape of the willingness-to-pay distribution?
e. BONUS (5 pts) What price maximizes Total Contribution?
f. BONUS (5 pts) What price maximizes Revenue?
Strategy Questions:
g. (10 pts total) Accurate demand plans are crucial for a company. They are used by Finance to predict revenues and cash flows. They are used by Operations to help determine long-term capacity and short-term scheduling. How can Sales and Marketing (the organization that should be in charge of forming the demand plan) be held accountable for:
h. (5pts) Underestimating the demand
i. (5pts) Overestimating the demand
6. (5 pts) Explain the roles of demand plan “dashboards” and the benefits they offer.
7. (10 pts) What is the goal of “demand management” and “integrated business management”? What 4 repeating steps are used to execute a “proper” DM process?

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