Question

4. Suppose an individual is offered a choice between two subsidy schemes. Scheme A is composed of $1000 subsidy in the first period and $3600 in the second period. Scheme B is comprised of $3000 subsidy in the first period and $1200 in the second period. The market rate of interest is 20%.

(a) Is it possible to say, whether individual would prefer A to B or B to A or be indifferent between the two schemes? Compare the individual’s intertemporal allocation of consumption under schemes A and B. Illustrate graphically.

(b) Is it possible to say, whether individual would prefer A to B or B to A or be indifferent between the two schemes if this individual can lend at 15%, but borrow only at interest rate, equal to 20%?

Answer 1

	First Year	Second Year	Total Subsidy
Scheme A	1,000.00	3,600.00	4,600.00
Scheme B	3,000.00	1,200.00	4,200.00
Market Rate of Interest is 20%

Present Value of Scheme A = 1,000*(1/1+0.2)+3,600*(1/1+0.2)*(1/1+0.2) = 3,333.33

Present Value of Scheme B = 3,000*(1/1+0.2)+1,200*(1/1+0.2)*(1/1+0.2) = 3,333.33

The Present value of Both Schemes is same. So there will be no difference in the two schemes.

If Rate of Interest of Borrowings is 15%

Present Value of Scheme A = 1,000*(1/1+0.15)+3,600*(1/1+0.15)*(1/1+0.15) = 3,591.68

Present Value of Scheme B = 3,000*(1/1+0.15)+1,200*(1/1+0.15)*(1/1+0.15) = 3,516.07

Scheme A is better than Scheme B. As Present value of Scheme A is greater than Scheme B.

Alternative Method :-

Future Value of Subsidy Received = 3,333.33 * (1.15) * (1.15) = 4,408.39

We are Receiving 4,600 under Scheme A whish is better than this borrowing amount. So Scheme A is to be prefered.