Question 1:
Rooms = C + b price
Regression results:
Marriott price:
The Marriott price coefficient is negative; this means that as price increases, the number of rooms booked decline.
Significance:
The R squared value is 0.97, this means that the price explains 97% of fluctuations in rooms booked. The p value is also less than 0.05 meaning that the coefficient is significant at this level.
Interpretation:
The coefficient value is -2.76, this value means that when price is increased by one unit, the number of rooms booked decline by 2.76.
Question 2:
Prediction:
The model:
Rooms = 2006.58 -2.76 price
$99
Rooms = 2006.58 -2.76 *99
Rooms =1733.07
$399
Rooms = 2006.58 -2.76 *399
Rooms =904.27
If the price was $99, the number of rooms booked would be 1733.07. If the price was $399, the number of rooms booked would be 904.27
Arc Elasticity:
(904.27-1733.07)/(( 904.27+1733.07)/2) = -0.63
(399-99)/ (399+99)/2 = 1.20
-0.63/1.20
Elasticity = -0.52
The elasticity value is less than 1, this indicates inelastic room booking and therefore in order to increase revenue the hotel should raise its prices.
Question 3:
The revenue value is determined and the following plot is generated:
Question 4:
Break even point:
Advertising = $500,000
Price = 300
At price 300, the number of rooms will be
Rooms = 2006.58 -2.76 *300
Rooms = 1178.58
Increase in room demand by 20% will result into
1178.58*120% =1414.296 rooms
The variable cost is 35, for the rooms its
1414.296* 35 = 49500.36
Question 5:
Results:
The model:
Rooms = 1846.44 – 2.75 price + 1.53 best price
The best western price coefficient is a good predictor given that the p value is 0.42 which is greater than 0.05. This price matters given that an increase in best prices will result into an increase in demand for Marriot rooms.
Question 6:
Results:
The coefficient of Hilton price is significant; the p value is 0.00 which is less than 0.05 and therefore significant.
The value 2.51 means that as Hilton prices by one unit, and then the demand for rooms at Marriott increases by 2.51 units.
Question 7:
Variable cost per room = 35
Fixed cost = 30,000
Price = 279
P = 279
Demand equation
Q = 758.68 -1.37 Marriott price + 2.51 Hilton price
Q = 758.68 -(1.37 *279) + 2.51 Hilton price
Total revenue
R = P * Q
R = 279 * Q
Total cost
TC= Q*35 +30,000
Total profits
Total profit = R - TC
Question 8:
Profit maximization:
Assume demand is
Q = 758.68 -1.37 P
The results are summarized below:
The optimum price is 294, the number of rooms booked at this price is 356.
