To determine which product(s) would be most beneficial to wait before buying, we need to analyze the historical pricing data provided in the chart.
### Game System:
- Initial Price: [tex]$243
- Price a few months later: $[/tex]229
- Auction Price: [tex]$450
The initial price of the game system is $[/tex]243, and it decreases slightly to [tex]$229 a few months later. However, the auction price is much higher at $[/tex]450, which indicates that the game system's value increases significantly in the future. Thus, it is beneficial to wait before buying the game system, as its future auction price is much higher.
### Smartphone:
- Initial Price: [tex]$99
- Price a few months later: $[/tex]399
The initial price of the smartphone is [tex]$99, and it increases dramatically to $[/tex]399 a few months later. Since the price increases significantly over time, it is advantageous to wait and buy the smartphone later when considering future value.
### DVD:
- Initial Price: [tex]$18
- Price a few months later: $[/tex]19
The initial price of the DVD is [tex]$18, and it increases slightly to $[/tex]19 a few months later. The increase is minimal, suggesting that there is not much benefit in waiting to purchase the DVD. The future price does not significantly impact the decision.
### Conclusion:
Based on the analysis of the historical pricing data, it is most beneficial to wait before buying the game system and the smartphone due to the significant changes in their future value.
Therefore, the answer is:
- Game System
- Smartphone
