Question

In: Economics

Consider an economy with the following components of aggregate expenditure: Consumption function: C=20 + 0.8YD Investment...

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.

  1. What is the marginal propensity to consume in this economy?
  2. What is the equation of the aggregate expenditure function in this economy?
  3. Determine the size of the autonomous expenditure multiplier.
  4. Determine the size of the tax multiplier.
  5. What is the size of the budget deficit at the equilibrium level of income?
  6. How much in tax cuts is required to increase the equilibrium level of income by 50.

Solutions

Expert Solution

(a) C = 20 + 0.8YD

=> MPC = ΔC / ΔYD

=> MPC = 0.8

Thus, the marginal propensity to consume is 0.8

-----------------

(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

---------------

Note: YD = Y -T

and, T = tY

=> T = 0.2Y

=> YD = Y - 0.2Y

=> YD = 0.8Y

----------------

=> AE = 60 + 0.8(0.8Y) - 0.2Y

=> AE = 60 + 0.64Y - 0.2Y

=> AE = 60 + 0.44Y.

-------------------------------------------------------

(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

---------------------------------------

(d) Tax multiplier = -MPC * (autonomous expenditure multiplier)

=> Tax multiplier = -0.8 *(1.785)

=> Tax multiplier = -1.428

----------------------------

(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.

-----------------------------------

(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.


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