1. TruePoo is a small startup company that sells shampoo in southeastern Michigan. TruePoo currently prices each bottle of shampoo at $18 per bottle. Historically they have sold about 600 bottles of shampoo each week. The CEO hires you out of business school to help improve the profitability of the company. You realize that you need to understand both their production costs and their demand curve.

a. After interviewing Managers and examining the accounting books, you discover that the company pays $300,000 per year in salaries and benefits (which are paid unrelated to the amount of shampoo sold), and $6000 per month in rent on their factory in Detroit. Their marketing and advertising costs, which are determined at the beginning of each quarter (i.e., before actual production is known), came out to an annual total of $4.20 per bottle sold. The company pays $0.40 for each plastic bottle the shampoo is packaged in, and $1.50 for the ingredients used in each bottle of shampoo. Last year, TruePoo also paid a graphic design firm $22,000 to re-imagine their branding and re-design the logos on the bottles. What is the marginal cost of production for each bottle of shampoo?

b. Having understood the company's cost structure, you now set out to understand the demand curve. To do so, you convince the CEO to run an experiment where you lower the price of shampoo from $18 per bottle to $16 per bottle for a few weeks. You specifically pick weeks to run this experiment when you are comfortable assuming that nothing else major has changed in the market environment. During your price experiment, the company sells, on average, 700 bottle per week.

i. What is your own-price elasticity of demand (at the initial price of $18 per bottle)? Note: you are estimating a point elasticity at $18/bottle, not an arc elasticity an arc elasticity would be the average elasticity over the price range $16 to $18.

ii. If you are willing to assume that your demand curve for shampoo is linear, what is your estimated equation for TruePoo's demand curve?

iii. What is your profit maximizing price?

c. Suppose that you learn one of your biggest rivals is planning on launching a major advertising campaign. If you change nothing about your marketing:

i. What will your rival's advertising campaign probably do to your own-price elasticity of demand?

ii. what (qualitatively) would this probably do to the profit-maximizing price you should charge?