Intermediate Microeconomics · free preview
Cash, Vouchers, and Tax Rebates
The same transfer paid as cash or in kind reshapes budgets differently, cash shifts the line out, a voucher kinks it, and the consumer is worse off under the voucher exactly when the kink binds, while a taxed good with its revenue rebated still shrinks consumption of the taxed good.
1. Two ways to give twelve dollars
Two ways to give twelve dollars
2. A voucher that binds
A voucher that binds
3. Taxing and rebating
Taxing and rebating
4. The design lesson
The design lesson
5. Why cash weakly dominates
Comparing the 12-dollar voucher budget with the 12-dollar cash budget, why is cash always at least as good?
6. When the voucher binds
Under u equal to x1 x2 cubed with the cash income 42, why does the voucher make the consumer worse off?
7. The rebate keeps the old bundle affordable
In the tax-and-rebate example, why is the old bundle (60, 60) exactly affordable after the tax and rebate?
8. The policy geometry matching
Which budget transformation belongs to a tax on good 1 with full per-person rebate?
9. The binding voucher's bundle
Under the voucher with u equal to x1 x2 cubed, the optimum is the kink bundle. Compute its x1, and write the number.
10. Gasoline after tax and rebate
In the tax-and-rebate example with u equal to x1 x2, income 120, prices 2 and 1 after the policy, compute x1 at the new optimum, and write the number.
11. The voucher's utility bill
Under u of x1 times x2 cubed, cash income 42 delivers about 328187 utils, the voucher optimum 324000. What is the loss from the binding kink?
12. Engineering the rebate
In the tax-and-rebate example, income 120, prices 1 and 1, p1 doubles. What rebate makes the old bundle (60, 60) exactly affordable?
13. The new optimum after the pivot
After the tax and rebate, the budget is 2 x1 plus x2 equals 180. Where does u of x1 x2 land?
14. Why utility rises anyway
Utility climbs from 3600 to 4050 under tax-and-rebate. What explains the gain?
15. The pivot's new income
In the tax-and-rebate example, income 120 plus the 60-dollar rebate gives what budget-right-hand-side number, and write it.
16. The kink's utility
Under the voucher, the optimum is the kink bundle (12, 30). Compute its utility for u of x1 times x2 cubed, and write the number.
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