Calculating maximum sales loss and net profit , Microeconomics

The Healthy Spring Water company sells bottled water for offices / homes. The price of the water is $20 per 10 gallon bottle and the company currently sells 2,000 bottles per day. The company's daily income and costs: Sales revenue: $ 40,000 Variable cost: $ 16,000Fixed cost: $ 20,000

1. What is the maximum sales loss (in % and in units) that the firm could tolerate before a 20% price increase would fail to be worthwhile? (No change in Fixed Cost).

2. Following competition, the firm considers a 10% price cut. At present, the delivery capacity is exhausted. To serve more customers, the company will have to add one or more additional trucks and drivers. Each truck would deliver up to additional 400 bottles daily, at daily operating costs (wage, fuel, etc) of $500. What is the minimum sales gain (in % and in units) that the firm must obtain to make a 10% price cut worthwhile?

3. If the actual sales gain following the 10% price reduction were 700 bottles daily, what would be the change in net profit resulting from the price change? (Please show relevant computations).

4. A competitor with a very similar price is rumored to reduce his price of a bottle by 15%. Please suggest a well based (i.e. calculated) advice to the firm's reaction.

5. If on average, a customer who buys a bottle, buys from the firm 2 boxes of disposable cups, each box costs the firm $3 and priced at $7 - How would your answers to Question 2 above change ? Under such circumstances, can a promotional campaign of a price of $7 a bottle, be profitable? Explain your answer and support it with the proper calculations.

6. Derivation Question: Derive the expression for Iso-Contribution relative change of sales quantity (assume no change in fixed costs) when there is a relevant change in the Variable Cost per unit (for all units - not just the additional ones). Give a realistic example of such a change. Show how it was derived and express it so as to make clear that it is a generalization of the basic expression derived in class.

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