Question

1. Nadia earns $2000 this month and will earn $2500 the next month. The interest rate between each month is 10%. She wants to consume the same quantity each month.

(each question is separate and do not build on each other)

1. How much would Nadia save? How much would she consume?
2. If the interest rate is now 20%, how much would she save? How much would she consume?
3. If she asks her boss to switch her paycheck (she earns $2500 the first month and $2000 the second), how much would she save? How much would she consume?
4. If she asks her parent for a little extra in the second month, raising her income to $3000, how much would she save? How much would she consume?
5. If she knows she will be fired at the end of the first month and receive not benefit, how much would she save? How much would she consume?

Answer 1

Solution :-

(a) :-

Nadia earns = $2000 this month and

will earn = $2500 the next month.

The interest rate between each month is 10%.

C1 + C2/( 1 + r)   Y1 + Y2/( 1+ r)..... intertemporal choice

Where

C1 - consumtion in period 1( this month)

C2 - consumtion in period 2 ( next month)

r - interest rate on savings made during period 1

Y1 - current month's income

Y2 - Next month's income

Now, we have

C1 = C2, Y1 = $2000 , Y2 = $2500 , r = 10%

C1 + C2/( 1 + r)   Y1 + Y2/( 1+ r)

C1 + C2/( 1+ 10)   2000 + 2500/(1 + 10)

C1 + C1/ 11   2000 + 2500/11.......( C1 = C2)

(11C1 + C1)/11   2000 + 227.27

12C1/11   2227.27

C1    2227.27 x 11/12

C1   2041.664

And also C2,

C2    2041.664

Since, C1 + S = Y1

Where S = savings

2041.664 + S = 2000.....( Y1 = 2000)

S = 2000 - 2041.664

S = - 41.664

So, in current month there is no savings.

( b) :-

If the interest rate is now 20%,

r = 20% , C1=C2, Y1 = $2000 , Y2 = $2500

Then,

C1 + C2/( 1 + r)   Y1 + Y2/( 1+ r)

C1 + C2/( 1+ 20)   2000 + 2500/(1 + 20)

C1 + C1/ 21    2000 + 2500/21.......( C1 = C2)

(21C1 + C1)/21   2000 + 119.047

22C1/21   2119.047

C1    2119.047 x 21/22

C1   2022.73

And also C2,

C2   2022.73

Since, C1 + S = Y1

2022.73 + S = 2000.....( Y1 = 2000)

S = 2000 - 2022.73

S = - 22.73

So, there is no savings in current month.

(c) :-

If she asks her boss to switch her paycheck (she earns $2500 the first month and $2000 the second),

Now,

C1 = C2 , Y1 = 2500 , Y2 = 2000 , r = 10%

C1 + C2/( 1 + r)   Y1 + Y2/( 1+ r)

C1 + C2/( 1+ 10)    2500 + 2000/(1 + 10)

C1 + C1/ 11    2500 + 2000/11......( C1 = C2)

(11C1 + C1)/11   2500 + 181.82

12C1/11   2681.82

C1   2681.82 x 11/12

C1   2458.33

Now,

C2   2458.33

Since, C1 + S Y1

2458.33 + S   2500.....( Y1 = 2500)

S   2500 - 2458.33

S   41.67

(d) :-

If she asks her parent for a little extra in the second month, raising her income to $3000,

Now,

C1 = C2 , Y1 = 2000 , Y2 = 3000 , r = 10%

C1 + C2/( 1 + r)   Y1 + Y2/( 1+ r)

C1 + C2/( 1+ 10)   2000 + 3000/(1 + 10)

C1 + C1/ 11 2000 + 3000/11.....( C1 = C2)

(11C1 + C1)/11   2000 + 272.73

12C1/11   2272.73

C1   2272.73 x 11/12

C1   2083.33

Now,

C2    2083.33

Since, C1 + S   Y1

2083.33 + S   2000.....( Y1 = 2000)

S   2000 - 2083.33

S   - 83.33

So, there is no savings in current month.

(e) :-

If she knows she will be fired at the end of the first month and receive not benefit.

Now,

C1 = C2 , Y1 = 2000 , Y2 = 0 , r = 10%

C1 + C2/( 1 + r)   Y1 + Y2/( 1+ r)

C1 + C2/( 1+ 10)    2000 + 0/(1 + 10)

C1 + C1/ 11   2000 .......( C1 = C2)

(11C1 + C1)/11    2000

12C1/11   2000

C1   2000 x 11/12

C1   1833.33

Now, also C2

C2   1833.33

Since, C1 + S   Y1

1833.33 + S   2000.....( Y1 = 2000)

S   2000 - 1833.33

S   166.67