# Intertemporal Choice: Income Shifting ## Problem Summary An employee can **shift \( x \) units of income** from next year to the current year, increasing current income by \( x \) but reducing next year's income by \( x \). --- ## [1].a **Why Would the Employee Take This Option?** ### **Diagram Explanation** - **Axes:** - **X-axis:** Consumption this year (\( C_1 \)) - **Y-axis:** Consumption next year (\( C_2 \)) - **Budget Constraint:** - **Original constraint:** \( C_1 + \frac{C_2}{1+r} = Y_1 + \frac{Y_2}{1+r} \) - **After shifting \( x \):** - Current income increases by \( x \): \( Y_1 + x \) - Future income decreases by \( x \): \( Y_2 - x \) - New constraint: \( C_1 + \frac{C_2}{1+r} = (Y_1 + x) + \frac{(Y_2 - x)}{1+r} \) - **Indifference Curves:** - Employee chooses the point that gives the highest utility (tangent to the budget line). **Why shift?** - If the employee prefers more consumption now (higher marginal utility from current consumption), shifting income forward allows them to better smooth consumption or meet urgent needs. --- ## [1].b **How Does This Affect Consumption and Savings?** ### **Diagram Description** - **Show two budget lines:** - Original budget line. - New budget line after shifting \( x \). - The new line pivots outward for \( C_1 \) (current consumption) and inward for \( C_2 \) (future consumption). #### **Effects:** - **Consumption This Year (\( C_1 \)):** Increases. - **Consumption Next Year (\( C_2 \)):** Decreases. - **Current Savings:** - **Savings = Income - Consumption.** - As current income rises and current consumption rises (potentially by less than \( x \)), **current savings may decrease**. ### **Explanation:** - The shift allows the employee to transfer resources to the period where they value consumption more. - The individual will re-optimize consumption across the two periods, likely increasing current consumption and reducing future consumption. - If the individual consumes all of the increased income, savings drop by \( x \). If they save part of it, the drop in savings is less than \( x \). --- ## **Summary Table** | Period | Income Change | Consumption Change | Savings Change | |--------------------|--------------|-------------------|-----------------------| | Current (Year 1) | +\( x \) | Increase | Likely decreases | | Next (Year 2) | \(-x\) | Decrease | Future savings adjust | --- ## **Key Takeaways** - The employee will opt to shift income if it increases their overall utility. - This raises current consumption and lowers future consumption. - **Current savings are likely to decrease** because more income is being spent now rather than saved for the future. --- ### **Simple Diagram Illustration (Text-based)** ``` C2 | | / (new budget line, after shifting x) | / | / |______/ C1 ``` - The new budget line allows more \( C_1 \) at the expense of \( C_2 \). --- Let me know if you need a more detailed diagram or a specific mathematical example!