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Take Home Examination.

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Subject: Marketing
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Take home examination.

1. First we will count the cost of attracting one customer:
As the close rate is 20%,to attract one customer we need 5 prospects, the acquisition will be 850/20%= 4250$
Retention per customer = 200/60%= 333,3$
Ongoing service per customer=600*60%=360$
Add on per customer will be 500*90%-25= 425$
Total margin per customer without retention will be the sum of all margins per customer 400+360+425= 1185
Total equity per customer=Total margin without retention- retention per customer=1185-333,3= 851,6$
If retention goes up by 10%, retention per customer will be 200/70%=285$
Total equity per customer will be =400+600*70%+425-285=959$

2. To find the profit maximizing price we have to count the margin for 1 unit for each price in the table: Price -Variable Product cost=Margin for 1 unit
According to the predicted percentage of people who would buy the product we find out the exact number of deals by multiplying the amount of potential customer purchases by the percentage of expected deals.
To find the total margin we use the following formula:
Number of deals*Margin per unit= Total margin for each price.
From the table below we see that the profit maximizing price is 600$ per unit. Price | Would buy | Margin per unit | Number of deals | Total margin | 800 | 0,1 | 450 | 300000 | 135000000 | 750 | 0,2 | 400 | 600000 | 240000000 | 700 | 0,3 | 350 | 900000 | 315000000 | 650 | 0,4 | 300 | 1200000 | 360000000 | 600 | 0,5 | 250 | 1500000 | 375000000 | 550 | 0,6 | 200 | 1800000 | 360000000 | 500 | 0,7 | 150 | 2100000 | 315000000 | 450 | 0,8 | 100 | 2400000 | 240000000 | 400 | 0,9 | 50 | 2700000 | 135000000 | 350 | 1 | 0 | 3000000 | 0 |

3. The formula of Elasticity is the following:

Elasticity=Quantity1-Quantity0Quantity0 Price1-Price0Price0
According to

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