Question

After coming up with an innovative idea for a new product, you paid $2000 to an industrial designer to draw the blueprints and found a factory in China that agreed to produce the product for you for $3.5 per unit (the price includes the shipping cost from China to you). Since this is a totally new and unique product, you have no idea how the demand for it would be. Therefore, before you start pricing the product and ordering large amounts from the Chinese factory, you decide to run an experiment (or a pilot study): you talk to Target and they allow you to sell your product at 11 different Target stores for 11 different prices (a different price at each store). These stores are located in areas whose residents have similar average income, so you can be certain that price (and not income) is the only factor varying among these stores. After 2 weeks, Target sends you the sale numbers for your product.

Price    Quantity Demanded

4          231

5          210

6          170

7          162

8          150

9          122

10        102

11        81

12        59

13        44

14        20

B. Using regression, find the demand line that is the best fit for the observed data points. (in other words, add a trend line to the graph you had in part (a)).
Write the demand function in the form of Q = a – bP = Q = 600 – 20P

Given the demand equation found in part (b), if you eventually decide to sell your product at $8 per unit for the first year, how many units do you expect to be sold and how much will your revenue and profits be that year?

Can you please help me with the bold question. I'm a little confused with the profits. - Thank you

Answer 1

In the beginning of the question, it says that the cost of production and shipping is $3.5 per unit. If you set the price at $8, contribution per unit is $4.5. So first we find the number of units sold, then multiply it with $4.5, to get total contribution. Then we subtract amortization of the $2,000 that was paid for the blueprints to get the profit.