A ski resort hotel has 20 rooms. The full price of each room is $160. The manager would like to sell one room at an advance-purchase discount. The manager knows that the probability is 0.60 that demand at the full price will be no higher than 19 rooms, but is not sure what should be the size of the discount. Based on the course material on revenue management, which of the following advance-purchase discount prices would likely result in increased revenue for the hotel?

Question

BlackTom AI · Accepted Answer

We start by restating the core setup and options clearly, so the reasoning that follows can be checked against them.
Question and options:
- A ski resort has 20 rooms. Full price per room is $160.
- The manager will offer one advance-purchase discount (i.e., a lower price now to encourage demand).
- It is known that there is a 0.60 probability that demand at the full price will be no higher than 19 rooms. Revenue-management intuition suggests choosing a discount that converts the remaining potential demand into sold rooms without sacrificing too much per-unit revenue.
- Answer options: $40 off (price $120), $60 off (price $100), $80 off (price $80), or None of these.

Now, assess each option in turn, considering how revenue would be affected under the given information.
Option 1: $40 off (price $120)
- What this implies: You lower the price to $120 and try to fill more rooms.
- Why this might or might not increase revenue: Lowering price generally increases quantity demanded, but it also reduces per-unit contribution margin (from $160 to $120). To determine revenue impact, you would compare expected revenue under this price with expected revenue under the current full-price scenario. Given that there is a 0.60 probability that demand at full price is only up to 19, there is a potential to fill the one remaining room by discounting. However, the gain in units sold would have to exceed the loss in price times the additional rooms sold to beat full price revenue. Since we only know the probability structure for the full-price case and not the exact demand distribution, it is not guaranteed that discounting to $120 would increase expected revenue. In many revenue-management cases, a modest discount can help but is not guaranteed to beat the full-price outcome when demand uncertainty is as described.
- Potential pitfall: If the 0.60 probability of selling at most 19 rooms under full price already implies the hotel would not exceed 19 in most scenarios, lowering to $120 may or may not produce a higher total revenue depending on how much incremental demand is generated and how many units actually sell beyond 19. Without precise demand distributions, we cannot conclude a sure revenue gain.
Option 2: $60 off (price $100)
- This option further lowers price, increasing the incentive to buy but decreasing per-unit profit further.
- Reason for caution: While a lower price can attract additional demand, the proportional decrease in price from $160 to $100 is steeper. The expected revenue could improve if the price-elasticity of demand is high enough to fill all 20 rooms with close to full probability, but the direct computation would require the exact demand distribution at $100. Given only the 0.60 figure for the full-price case, we cannot confidently assert a revenue increase.
Option 3: $80 off (price $80)
- Price is substantially reduced to $80.
- Consequences: If enough of the 0.60 probability scenario shifts toward selling all 20 rooms, the total revenue could rise or fall depending on how many rooms are actually sold at $80 versus at $160. However, dropping price to $80 dramatically reduces per-room margin, and unless the demand increase is substantial and certain, total revenue is unlikely to exceed the full-price revenue, especially since the full-price revenue already accounts for up to 20 rooms when demand is high. With only the given probability (0.60 forDemand ≤19 at full price) and no precise demand function, it is risky to assume that a steep discount would yield higher revenue.
Option 4: None of these
- This option asserts that none of the proposed discount levels would likely increase revenue relative to selling at full price.
- Why this can be reasonable: With only the information that demand at full price is no higher than 19 with probability 0.60, there is a significant chance you cannot reliably fill all 20 rooms even at the discounted prices, and the additional revenue gained from selling more rooms at a lower price may not compensate for the loss in per-unit contribution margin. Since the exact demand response to each discount is not provided, and the full-price scenario yields up to 20 sales when demand is high, it is entirely plausible that none of the discounts would improve expected revenue compared with selling at full price.
Synthesis and decision: Given the absence of precise demand distributions for the discounted price points and the fact that the full-price case already allows for selling up to 20 rooms when demand is sufficient, the most cautious and defensible conclusion is that none of the discounted prices can be guaranteed to increase revenue without additional demand data. The 0.60 figure alone does not provide enough information to positively conclude that any of the discount levels would outperform full price.
As a result, the option most consistent with a conservative interpretation of the available information is: None of these.

MGT355H5 F LEC0101 Term Test 2

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