In: Economics
Consider an economy with the following components of aggregate expenditure:
Consumption function: C=20 + 0.8YD
Investment function: I = 30
Government expenditures: G = 8
Export function: X= 4
Import function: M=2 + 0.2Y
Tax rate, t = 0.2 or 20%.
Answer the following question.
(a) C = 20 + 0.8YD
=> MPC = ΔC / ΔYD
=> MPC = 0.8
Thus, the marginal propensity to consume is 0.8
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(b) AE = C + I + G + X -M
=> AE = 20 + 0.8YD + 30 + 8 + 4 - (2 + 0.2Y)
=> AE = 62 + 0.8YD - 2 - 0.2Y
=> AE = 60 + 0.8YD - 0.2Y
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Note: YD = Y -T
and, T = tY
=> T = 0.2Y
=> YD = Y - 0.2Y
=> YD = 0.8Y
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=> AE = 60 + 0.8(0.8Y) - 0.2Y
=> AE = 60 + 0.64Y - 0.2Y
=> AE = 60 + 0.44Y.
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(c) AE = 60 + 0.44Y
=> Slope of AE = ΔAE / ΔY
=> Slope of AE = 0.44
Autonomous expenditure multiplier = 1 / (1 - Slope of AE)
=>Autonomous expenditure multiplier = 1 / (1 - 0.44)
=>Autonomous expenditure multiplier = 1.785
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(d) Tax multiplier = -MPC * (autonomous expenditure multiplier)
=> Tax multiplier = -0.8 *(1.785)
=> Tax multiplier = -1.428
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(e) At equilibrium, Y = AE
=> Y = 60 + 0.44Y
=> Y - 0.44Y = 60
=> 0.56Y = 60
=>Y = (60 / 0.56)
=> Y = 107.14
Equilibrium income is 107.14
T = tY
=> T = 0.2 (107.14)
=> T = 21.43
Budget deficit = G - T
Budget deficit = 8 - 21.43
Budget deficit = -13.43.
there is negative budget deficit of 13.43, it means there is budget surplus of 13.43 at equilibrium.
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(f) Tax multiplier = Change in equilibrium income / Change in tax
=> -1.428 = (50 / Change in tax)
=> Change in tax = (50 / -1.428)
=> Change in tax = -35
Hence, the tax should be cut by 35.