Final answer:
For the small open economy described by the given equations, the Investment is 320, National savings are -500, indicating dissavings, and the Trade balance (Net exports) is 550. The Equilibrium exchange rate cannot be determined with the given information.
Step-by-step explanation:
The student's question relates to determining several economic variables for a small open economy given certain classical equations.
Investment
Investment (I) can be found by using the equation I = 420 - 25r. Since the domestic interest rate (r) is equal to the world interest rate (r*) and is given as 4, we can calculate investment as I = 420 - 25(4) = 420 - 100 = 320.
National Savings
National savings (S) is the sum of private savings plus government savings, where government savings is the difference between taxes (T) and government spending (G). We have S = (Y - T - C) + (T - G). Using the consumption function C = 250 + 2/3(Y - T), national savings can be calculated as:
Private Savings
Private savings = Y - T - C = 4000 - 1000 - (250 + 2/3(4000 - 1000))
Government Savings
Government savings = T - G = 1000 - 1250
Therefore, national savings = (4000 - 1000 - 250 - 2/3(3000)) + (-250) = 1000 - (250 + 2000) - 250 = -500, which indicates that the economy is dissaving at the national level.
Equilibrium Exchange Rate and Trade Balance
To determine the equilibrium exchange rate, we need more information than what is provided. However, the trade balance, which is the net exports (NX), can be calculated using the given equation NX = 1250 - 175εr, and since r = 4, NX = 1250 - 175ε4 = 1250 - 700 = 550.