National defense is a good that is nonexcludable and nonrival in consumption. Suppose that instead of national defense being pai
d for with tax dollars national defense is paid for by voluntary contributions from (potentially) all individuals within Latvia. Cedric, who is a Latvian citizen, must decide whether he wants to contribute to the national-defense budget. Further, suppose that there are a total of 10 citizens, including Cedric. For the optimal amount of safety, each citizen should pay $10$10 . Every $1$1 contributed (by anyone) to the national defense leads to increased security, which each person values at $0.20$0.20 . This means that every dollar spent on defense is worth $2.00$2.00 to Latvia as a whole. How much does Cedric personally value the increase in national defense when he contributes $10$10 to the defense fund? Cedric's personal value: $ If contributions are voluntary, and assuming people rationally maximize their utility, what is the total contributed to national defense? total contributed voluntarily: $ Suppose that instead of relying on voluntary contributions the government simply levies a tax of $10$10 on each person to pay for national defense. How much better or worse off would Cedric be if everyone (including himself) were taxed $10$10 instead of contributing voluntarily? If Cedric is worse off, be sure to put a negative sign in front of the number. Cedric's gain or loss under tax: $
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Solution :
Preferred Common
Non cumulative and non Participative 12,600 67,400
Cumulative and non participative 37800 42200
Cumulative and participative 47876 32124
<u> Current Stock Out Standing </u>
Common stock at the rate 50 5100 shares 255000
Preferred stock 7% at the rate 100 1800 shares 180000
<u> Cumulative the annual dividend on the preferred stock </u>
Preferred stock dividend (180000 x 7%) 12600
Dividend Arrears to preferred stock (12600 x 2) 25200
<u> Non cumulative and non participative </u>
Preferred Common Total
Current year 12600 12600
Arrears 0 0
Common stock 67400 67400
Total dividend 12600 67400 80000
<u> Cumulative and non participative </u>
Preferred Common Total
Current year 12600 12600
Arrears 25200 25200
Common stock 42200 42200
Total dividend 37800 42200 80000
<u> Cumulative and participative</u>
Preferred Common Total
Current year 12600 12600
Arrears 25200 25200
Common stock (255000 x 7%) 17850 17850
Balance dividend pro data 10076 14274 24350
Total dividend 47876 32124 80000
Working notes :
Amount for the participation = 80000-(12600+25200+17850) = 24350
Rate of participation = = 5.5977%
Participating dividend:
Preferred stock = 18000 x 5.5977% = 10076
Common stock = 255000 x 5.5977% = 14274
Total participating dividend = 24350