What price maximizes total contribution

Reference no: EM131674010

Assignment

Tactical Questions:

1. If price elasticity of demand (?) is 3,
a. How does demand change if the price is increased 1%
b. How does demand change if the price is decreased 5%
c. How does demand change if the price is decreased 50%

2. 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.

a. What price (p) maximizes total contribution (TC)?
b. What is the demand at the optimal price (p*)?
c. What is the TC at p*?
d. What is the satiating price (P)?

3. Pricing with Competition: The Multinomial Logit (MNL). 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 (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	b_j	e^(-b_ip_i/1000)	Market Share (μ_i(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 (b_j) 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. decreases its price to $400?

b. increases the price to $625?

c. 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. If it costs $350 to make an item (and elasticities don't change), find the price that maximizes Takata and Fuji's Total Contribution.

4. The Logit Price-Response Function. 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, with parameters C=40,000, b=0.0005, and market price ?=$12,000.

a. Keeping the price as variable p, what is the unit margin (contribution) from each additional sale?
b. What is the price-response function, d(p), for this manufacturer?
c. At a price of $10,000, what is the demand?
d. Roughly, what is the shape of the willingness-to-pay distribution?
e. What price maximizes Total Contribution?
f. What price maximizes Revenue?

Strategy Questions:

5. 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:
a. Underestimating the demand
b. Overestimating the demand

6. Explain the roles of demand plan "dashboards" and the benefits they offer.

7. What is the goal of "demand management" and "integrated business management"? What 4 repeating steps are used to execute a "proper" DM process?

Reference no: EM131674010

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