# 延遲折扣

## 數學模型

${\displaystyle g(D)={\frac {1}{1+kD}}\,}$

• 如果折扣因素同延遲之間條式係（本嚟認為係比較合乎直覺嘅）指數函數（exponential function；${\displaystyle g(D)=e^{-kD}}$）嘅話，佢喺兩個情況下實會做同一選擇。
• 但如果折扣因素同延遲之間條式係好似雙曲線折扣噉嘅，佢好有可能喺第一個情況下會揀即刻攞 50 文，但喺第二個情況下會揀六年後攞 100 文。

## 應用

### 引人儲錢

• 佢哋搵咗班打工仔返嚟，問佢哋肯唔肯將佢哋下次加人工嗰陣嘅退休福利計劃劃撥率提升（簡單講就係將多啲錢攞去做退休福利）－而唔係問佢哋肯唔肯而家呢一刻將劃撥率提升；
• 根據雙曲線折扣嘅原理，如果將個選擇由「而家對一年後」變成「五年後對六年後」嘅話，啲人比較有可能會揀長遠有利嘅選擇，所以理論上，呢個操作能夠提高啲人為退休儲錢嘅意慾。
• 結果真係發現，呢個操作有效噉提升班打工仔提高劃撥率嘅意慾，成功噉鼓勵佢哋為退休做好準備[13]

## 攷

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10. Shamosh, N. A., DeYoung, C. G., Green, A. E., Reis, D. L., Johnson, M. R., Conway, A. R., ... & Gray, J. R. (2008). Individual differences in delay discounting: relation to intelligence, working memory, and anterior prefrontal cortex (PDF). Psychological science, 19(9), 904-911.
11. Peters, J., & Büchel, C. (2010). Episodic future thinking reduces reward delay discounting through an enhancement of prefrontal-mediotemporal interactions (PDF). Neuron, 66(1), 138-148.
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13. Thaler, R. H., & Benartzi, S. (2004). Save more tomorrow™: Using behavioral economics to increase employee saving. Journal of political Economy, 112(S1), S164-S187.