Consider a 3-setor economy and its PAE = 50 + 0.7Y, which sets the equilibrium output topotential output.a Determine the equilibrium income and the size of multiplier.b. If the tax rate (1) is 0.1, what is the marginal propensity to consumer? c.Assume there is an exogenous decrease in investment spending by 10 units due to a pessimistic expectation of the economy (a business expectation is called the animal spirits' by Keynes). Determine the new equilibrium output and output gap.d. Suppose that government wants to use a tax cut (i.e., a lower r) to eliminate the output gap in (c). Determine the new tax rate to achieve this goal.
Question
Consider a 3-setor economy and its PAE = 50 + 0.7Y, which sets the equilibrium output topotential output.a Determine the equilibrium income and the size of multiplier.b. If the tax rate (1) is 0.1, what is the marginal propensity to consumer? c.Assume there is an exogenous decrease in investment spending by 10 units due to a pessimistic expectation of the economy (a business expectation is called the animal spirits' by Keynes). Determine the new equilibrium output and output gap.d. Suppose that government wants to use a tax cut (i.e., a lower r) to eliminate the output gap in (c). Determine the new tax rate to achieve this goal.
Solution
a. The equilibrium income is determined by setting Planned Aggregate Expenditure (PAE) equal to output (Y). So, we have:
50 + 0.7Y = Y
Rearranging the equation, we get:
Y - 0.7Y = 50
0.3Y = 50
Y = 50 / 0.3
Y = 166.67
So, the equilibrium income is 166.67.
The size of the multiplier is determined by the formula 1 / (1 - MPC), where MPC is the marginal propensity to consume. In this case, MPC is 0.7, so the multiplier is 1 / (1 - 0.7) = 3.33.
b. The marginal propensity to consume (MPC) is the change in consumption due to a change in income. If the tax rate is 0.1, then the after-tax income is 0.9Y. The MPC is then the change in consumption divided by the change in after-tax income, which is 0.7 / 0.9 = 0.78.
c. If investment spending decreases by 10 units, the new PAE is 40 + 0.7Y. Setting this equal to Y to find the new equilibrium output, we get:
40 + 0.7Y = Y
0.3Y = 40
Y = 40 / 0.3
Y = 133.33
The output gap is the difference between the potential output and the actual output, which is 166.67 - 133.33 = 33.34.
d. To eliminate the output gap, the government needs to increase aggregate demand by 33.34 units. This can be achieved by a tax cut that increases disposable income and hence consumption. The change in consumption due to a change in tax is given by the tax multiplier, which is -MPC / (1 - MPC). In this case, the tax multiplier is -0.78 / (1 - 0.78) = -3.55. So, the required change in tax is 33.34 / 3.55 = 9.4. Therefore, the new tax rate should be 0.1 - 9.4 / 166.67 = 0.044, or 4.4%.
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