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 faces its closest competitor, Howard Industries, also selling a competing pool cleaner. Using the 26 observations report we calculated pricing and cash flows.
The General Demand equation used is
QD = a + bP + cMavg + dPh
Where a is the dependent variable, bP is the price of the PoolVac good, cMavg is the average household income, and the dPh is the price of the related good (Howard Industries). . An estimated demand equation for PoolVac is: Qd = 2729 – 10.8P + 0.0214Mavg + 3.17Ph
Where, bP is the price of the PoolVac good, cMavg is the average household income, and the dPh is the price of the related good (Howard Industries). So, we see the good sold by PoolVac (the Automatic Swimming Pool Cleaner) is considered a normal good. We know this due to the general demand formula and the LAW OF DEMAND, for every $1 dollar increase in the price of the PoolVac good, we see the quantity demanded decreases by 10.8 units. We can also state, the Howard Industry good is a substitute good. We know this based on the values from the general demand function formula. So for every $1 dollar increase in the price of the Howard Industry good, we see the quantity demanded of the PoolVac good increases by 3.17 units (when holding Income and the Price of the PoolVac good constant), this is due to the direct relationship between the change in quantity demanded and the change in price and the value for the related good is positive. Regression Results
Variable(Predictor)| Coefficient Estimate| Standard Error| T-ratio| P-value| P| -10.758| 1.33| -8.09| 0.000|
MAVG| 0.021420| .009452| 2.27| 0.034|
PH| 3.166| 1.344| 2.36| 0.028|
Since the P values of all 3 variables are within the 5% confidence interval, each variable should be considered as statistically significant in determining the demand of the pool vacuums. We should look at the P value for each of the slope parameters and in doing so, we find that price is 100% significant, average income (Mavg) is 96.6% (100-.034) and price of competition (Ph) is 97.2% significant (100-.028).
So, if the price of the product goes up, demand for the product goes down because of the negative coefficient associated with the price variable. The negative coefficient makes sense, because people are going to be less interested in buying something if it’s more expensive. Looking at the F stat which is 211.1, we can say the overall regression equation is significant since the absolute value is large. The P value is 0 so there is no chance that this regression equation doesn’t explain the relationship between the given variables and quantity demanded.
Suppose PoolVac decides to price their automatic poolvac at $240 and the average income is $60,000 the demand function would be as followed: Qd=2729-10.8P+0.0214(5,000)+3.17(240)
Average income is 60,000 a year divided by 12 months to get $5,000 for the monthly income. Qd=2729-10.8p+107+760.8
Qd=3596.8-10.8p Direct Demand Equation
Inverse demand function is:
While the profit max quantity is 1650 and the inverse demand for the product is Q=3596.8-10.8P. We substitute Q for 1650 and solve the inverse demand equation. 1650=3596.8-10.8p
If PoolVac wants is to sell 1650 Sting Ray machines they will have to reduce their prices to $180 for each machine.
Assuming that the following variables for the estimated slope coefficient equations are a followed the: P= 290
Price elasticity of Demand formula is E= B(P/Q)...