Pricing Decisions at PoolVac, Inc

PoolVac, Inc. manufactures and sells a single product called the "Sting Ray," which is a patent-protected automatic cleaning device for swimming pools. Pool Vac's Sting Ray accounts for 65 percent of total industry sales of automatic pool cleaners. Its closest competitor, Howard Industries, has captured 18 percent of the market.

Using the last 26 months of its sales data, PoolVac wishes to estimate demand for its Sting Ray_ Demand for Sting Rays is specified to he a linear function of its price (P), average income for households that have swimming pools in the U.S (MAVG) and the price of the competing pool cleaner sold by Howard Industries (PH). The general linear form of the demand function

\[{{Q}_{d}}=a+bP+c{{M}_{Avg}}+d{{P}_{H}}\]

The attached Minitab worksheet presents the last 26 observations (monthly data) on the price charged for a Sting Ray (P), average income of households with pools (MAVG), and the price Howard industries charged for its pool cleaner (PH)

Problem 1: Write out the equation for the empirical (estimated) demand equation for Pool Vac.

Problem 2: Evaluate the statistical significance of the three estimated slope parameters using a significance level of 0.05. Explain how you decided each parameter was statistically significant or not.

Problem 3: Are any of the estimated slope parameters significant at the 0.01 significance level? Explain how you know.

Problem 4: Discuss the appropriateness and/or expectations of the algebraic signs of the three slope parameters, based on your theoretical expectations.

Problem 5: The manager of Pool Vac believes Howard Industries is going to price its automatic pool cleaner at $250, and average income in the US is expected to be $65,000. Based on this information, solve for the estimated (simple) demand function and the inverse demand function. Show all work.

Problem 6: Assume that the profit-maximizing quantity is approximately Q = 1725. What price should Pool Vac charge for the Sting Ray if it wants to sell 1725 units?

Problem 7: Assume that the current price is $296 and the current quantity is 1725.

(a) Compute the point price elasticity of demand.

(b) Using the definition of price elasticity we get

(c) Is the total revenue expected to rise or to fall as a result of the price cut?

Problem 8: Assume the same current quantity (1725) of Sting Rays, and the same expected average income ($65,000).

(a) Compute the income elasticity of demand for Sting Rays.

(b) As stated before, the sign is expected to be positive, which is the case in this example.

(c) A 10% increase in \({{M}_{AVG}}\) would be predicted to increase the quantity demanded of Stingrays by 8.0713%.

Problem 9: Assume the same current quantity (1,725) of Sting Rays, and the same price is charged by Howard industries ($250).

(a) Compute the cross-price elasticity of demand for Sting Rays

Price: $28.95

Solution: The downloadable solution consists of 7 pages, and 808 words
Deliverable: Word Document and pdf