An economy is described by the following equations:C = 1600 + 0.8(Y – T)I = 1000G = 1800T = 3000 + tYWhere t denotes the marginal tax rate. Suppose potential GDP is Y* = 10,000. What marginal tax rate t would restore GDP to potential?Group of answer choices00.10.20.3
Question
An economy is described by the following equations:C = 1600 + 0.8(Y – T)I = 1000G = 1800T = 3000 + tYWhere t denotes the marginal tax rate. Suppose potential GDP is Y* = 10,000. What marginal tax rate t would restore GDP to potential?Group of answer choices00.10.20.3
Solution
To find the marginal tax rate (t) that would restore GDP to its potential, we need to set up an equation using the given information and solve for t.
The equation for GDP (Y) is given by the sum of consumption (C), investment (I), and government spending (G).
So, Y = C + I + G
Substituting the given equations into the GDP equation, we get:
Y = [1600 + 0.8(Y - T)] + 1000 + 1800
We know that potential GDP (Y*) is 10,000, so we can substitute that into the equation:
10,000 = [1600 + 0.8(10,000 - T)] + 1000 + 1800
Solving this equation for T will give us the total tax revenue needed to restore GDP to its potential.
10,000 = 1600 + 8000 - 0.8T + 1000 + 1800
10,000 = 6400 + 8000 - 0.8T
10,000 - 6400 = 8000 - 0.8T
3600 = 8000 - 0.8T
0.8T = 8000 - 3600
0.8T = 4400
T = 4400 / 0.8
T = 5500
Now, we know that T = 3000 + tY. Substituting T = 5500 and Y = 10,000 into this equation, we can solve for t:
5500 = 3000 + t(10,000)
5500 - 3000 = t(10,000)
2500 = t(10,000)
t = 2500 / 10,000
t = 0.25
So, the marginal tax rate (t) that would restore GDP to its potential is 0.25, or 25%. This is not one of the provided answer choices, so there may be a mistake in the problem or in my calculations.
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