CONSULTING PROJECT

Pricing and Production 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. PoolVac's Sting Ray accounts for 65 percent of total industry sales of automatic pool cleaners. Its closest competitor, Howard Industries, sells a competing pool cleaner that has captured about 18 percent of the market. Six other very small firms share the rest of the industry's sales. Using the last 26 months of production and cost data, PoolVac wishes to estimate its unit variable costs using the following quadratic specification:

\(A V C=a+b Q+c Q^{2}\) The monthly data on average variable cost \((A V C)\), and the quantity of Sting Rays produced and sold each month \((Q)\) are presented in the table below.

PoolVac also wishes to use its sales data for the last 26 months to estimate demand for its Sting Ray. Demand for Sting Rays is specified to be a linear function of its price \((P)\), average income for households in the U.S. that have swimming pools \(\left(M_{\text {avg }}\right)\), and the price of the competing pool cleaner sold by Howard Industries \(\left(P_{H}\right)\) :

\(Q_{d}=d+e P+f M_{\text {avg }}+g P_{H}\)

The table below presents the last 26 months of 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 \((P_H)\) :

PoolVac, Inc. incurs total fixed costs of $45,000 per month.

1a. Run the appropriate regression to estimate the average variable cost function (AVC) for Sting Rays. Evaluate the statistical significance of the three estimated parameters using a significance level of 5 percent. Be sure to comment on the algebraic signs of the three parameter estimates.

b. Using the regression results from part 1a, write the estimated total variable cost, average variable cost, and marginal cost functions (TVC, AVC, and MC) for PoolVac.

TVC =

AVC =

MC =

c. Compute minimum average variable cost.

\(Q_{\min} = \quad AVC_{\min }=\)

2. a. Run the appropriate regression to estimate the demand function for Sting Rays. Evaluate the statistical significance of the three estimated slope parameters using a significance level of 5 percent. Discuss the appropriateness of the algebraic signs of each of the three slope parameter estimates.

b. The manager at PoolVac, Inc. believes Howard Industries is going to price its automatic pool cleaner at $250, and average household income in the U.S. is expected to be $65,000. Using the regression results from part 2a, write the estimated demand function, inverse demand function, and marginal revenue function.

Demand:

Inverse Demand:

Marginal Revenue:

3. Using your estimated cost and demand functions from parts 1 and 2, what price would you recommend the manager of PoolVac, Inc. charge for its Sting Ray? Given your recommended price, estimate the number of units PoolVac can expect to sell, as well as its monthly total revenue, total cost, and profit.

P:

\(Q\) :

TR:

TC:

Profit:

4. For the profit-maximizing solution in question 3, compute the point elasticity of demand for Sting Rays.

E=

In the profit-maximizing situation in question 3, a 5 percent price cut would be predicted to (increase, decrease) quantity demanded of Sting Rays by percent, which would cause total revenue to (rise, fall, stay the same) and profit to (rise, fall, stay the same).

5. For the profit-maximizing solution in question 3, compute the income elasticity of demand for Sting Rays.

\(E_{M}=\)

1. Is the algebraic sign of the income elasticity as you expected? Explain.
2. A 10 percent increase in \(\mathrm{M}_{\text {avg }}\) would be predicted to (increase, decrease) quantity demanded of Sting Rays by percent.
3. A 10% increase in \({{M}_{AVG}}\) would be predicted to increase the quantity demanded of Stingrays by 8.1%.

6. For the profit-maximizing solution in question 3, compute the cross-price elasticity of demand for Sting Rays.

\(E_{X R}=\)

1. Is the algebraic sign of the income elasticity as you expected? Explain.
2. A 3 percent decrease in \(\mathrm{P}_{\mathrm{H}}\) would be predicted to (increase, decrease) quantity demanded of Sting Rays by percent.

7. If total fixed costs increase from $45,000 to $55,000, what price would you now recommend in order to maximize profits at PoolVac? Compute the number of units sold at this price, total revenue, total cost and profit:

P

Q:

TR:

TC:

Profit:

8. If the manager of PoolVac wanted to maximize total revenue instead of profit (a bad idea), the manager would charge a price of $______

At this price, PoolVac's profit would be $____ which is (higher than, lower than, the same as) the profit in question 3 .

Price: $24.05

Solution: The downloadable solution consists of 12 pages, 1205 words and 5 charts.
Deliverable: Word Document