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Answer :
a) i) Assuming that the full-employment level of output is $1000, there is a recessionary gap of $60.
ii) Size of the Gap = $60
b) Consumers are saving $60 at full employment
c) The equilibrium value of a public open economy is $250.
d) The equilibrium for a private open economy is not defined as it is not possible.
e) The value of our multiplier is 5.
a) When Yd = $1000,
C = $100 + 0.8($1000)
C = $900
Real GDP, Y = C + I + G + (X-M)
Where I = $50, G = $60, X = $120, M = $190
Y = $900 + 50 + 60 + (120-190)
Y = $940
There is a recessionary gap of $60.
Size of the Gap = Full Employment Level of output - Current output
Size of the Gap = $1000 - $940
Size of the Gap = $60
b) At full employment, C = $100 + 0.8($1000)
C = $900
Y = C + I + G + (X-M)
Where Y = $1000, I = $50, G = $60, X = $120, M = $190
$1000 = $900 + S + 50 + 60 + (120-190)
S = $60
Consumers are saving $60 at full employment
c) In a public open economy, the equilibrium output is determined by the level of income that equates the savings and investment. Thus, we can obtain the equilibrium output by equating savings with investment, i.e.
S = I
Where S = Y - C - G
Y - C - G = I
GDP = I / (1 - MPC)
where MPC is the marginal propensity to consume= 0.8 / 1 = 0.8
GDP = 50 / (1 - 0.8)
GDP = 50 / 0.2
GDP = $250
The equilibrium value of a public open economy is $250.
d) In a private open economy, investment demand comes from both domestic and foreign sources. Thus, the equilibrium output is determined by the level of income that equates domestic savings, domestic investment, and net foreign investment (NX), i.e. Sd = Id + NX
Where Sd = Y - C - G + NX, Sd is domestic savings, Id is domestic investment, and NX is net exports.
NX = X - M = $120 - $190 = -$70
Sd = Y - C - G + NX
Y - C - G + NX = I
Private Saving = Y - C - G = $1000 - $900 - $60 = $40
Therefore, Sd = $40, Id = $50, and NX = -$70
Equating Sd and Id + NX, we have:
$40 = $50 - $70
$40 = -$20
The equilibrium for a private open economy is not defined as it is not possible.
e) Multiplier is the amount by which an increase in autonomous spending is multiplied to determine the increase in equilibrium spending.
Multiplier = 1 / (1 - MPC) = 1 / (1 - 0.8) = 1 / 0.2 = 5
Therefore, the value of our multiplier is 5.
To know more about recessionary gap, refer to the link below:
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