Question

Y = C + I + G + NX

Y = 18,500; G = 4,000; T = 2,000

C = 750 + 3/4 (Y - T)

I = 1,000 - 50r

CF = 750 - 25r

NX = 1,825 - 150ϵϵ

(a) In this economy solve for consumption, private and public saving, national saving, investment, the trade balance, the net capital outflow (net foreign investment), the real interest rate and the real exchange rate.

(b) The demand of funds for foreign direct investment is in reality a function of the domestic real interest rate, r, and the world real interest rate, r*, given by: CF = 750 - 50r + 25r*. Confirm that if r = r* at the real interest rate you found in (a) you get the same solution as in (a).

(c) The world interest rate increases to r* = 10. Solve for consumption, private and public saving, national saving, investment, the trade balance, the net capital outflow (net foreign investment), the domestic real interest rate, and the real exchange rate. (Hint: To solve you need CF as a function of only r, so use the value of r* in the CF function to leave it like that and solve the model.)

(d) What can you concur that happens in a large open economy in the long run if the world interest rate increases relative to the domestic real interest rate with respect to what you've found in part (c)?

Answer 1

Question:

Solution: The given statement is Y = C + I + G + NX ...............1

Y = 18,500; G = 4,000; T = 2,000

C = 750 + 3/4 (Y - T)

I = 1,000 - 50r

CF = 750 - 25r

NX = 1,825 - 150ϵϵ

Solution: (a) In an economy to find all these values , putting values in respective formula

1. consumption = 750 +3/4 (Y - T)

= 750 + 3/4 (18,500 - 2,000)

= 750 + 3/4 (16,500) = 750 + 12375

= 13,125

2. Private Saving = Y - T - C = 18500 - 2000 - 13125 = 3,375

3. Public saving = T - G = 2000 - 4000 = - 2000

4. National saving = Public + private saving = 3375 - 2000 = 1375

5. Investment = 1000 - 50 r

since sving = investment then investment value is also 1375

1375 = 1000 - 50 r

1375 - 1000 = - 50 r

375 = - 50 r  

or r = - 375 / 50 = - 7.5

now, putting in value

I = 1000 - 50 ( - 7.5 ) = 1000 + 375 = 1375

6. the trade balance or NX = S - I = 1375 -1375 = 0

7.the net capital outflow (net foreign investment),

8. the real interest rate

Investment = 1000 - 50 r

1375 = 1000 - 50 r

1375 - 1000 = - 50 r

375 = - 50 r  

or  r = - 375 / 50 = - 7.5

9. the real exchange rate =NX= 1825 - 150 ee =0

0r    150 ee = 1825

or    ee = 12.16

Solution: (b)

The demand of funds for foreign direct investment is in reality a function of the domestic real interest rate, r, and the world real interest rate, r*, given by:

CF = 750 - 50r + 25r*.

750 - 25 r = 750 - 50 r + 25 r^*

- 25 r + 50 r = 25 r ^*

25 r = 25 r ^*

^{Putting value of real interest rate from part (a)}

25 (- 7.5 ) / 25 = r ^*

- 187.5 /25 = r ^*

or r ^* = - 7.5

Henc, its Confirm that value of domestioc (r) = world ( r*) interest rate  are same in part (a) and (b)

Solution: (c)

The world interest rate increases to r* = 10. Solve for consumption, private and public saving, national saving, investment, the trade balance, the net capital outflow (net foreign investment), the domestic real interest rate, and the real exchange rate. (Hint: To solve you need CF as a function of only r, so use the value of r* in the CF function to leave it like that and solve the model.)

CF = 750 - 25r

= 750 - 25 (10) = 750 - 250 = 500

Solution: (d)

What can you concur that happens in a large open economy in the long run if the world interest rate increases relative to the domestic real interest rate with respect to what you've found in part (c)?

Since with r = - 7.5

CF = 750 - 25 r = 750 - 25 (-7.5) = 750 + 187.5 = 937.5

And with r = 10

CF = 500 from part (c)

Henc, In a large open economy in the long run if the world interest rate increases i.e., 10 relative to the domestic real interest rate i.e. -7.5 then consumption function shows that the consumption pattern will decrease from 937.5 to 500. with the increase in real interst rate , purchasing power will reduce.