Answer to Question #232730 in Macroeconomics for Laudenarh

Question

The Ghana Statistical Services in 2019 fiscal year estimated that Ghanaians saved 20 percent of their disposable income; however, due to overconsumption in the previous year, autonomous saving for 2019 was negative 100 million Ghana cedis. The government of Ghana imposed a lump sum tax of Gh ₡ 20 million. In addition to the lump sum tax the government also took 20 percent of all incomes earned in the economy in the form of proportional tax. The total government expenditure was GH ₡50 million in 2019. Total investment recorded for 2019 was 66 million. 

 1.Derive the consumption function based on the above information.

2. Write out the aggregate demand function.

3. Calculate equilibrium national income for the economy.

4. Determine the equilibrium consumption.

5. Calculate the value of the government expenditure multiplier for this economy and interpret your result.

6. Calculate the total tax revenue to the government.

Answer 1

Economy is in equilibrium where Aggregate Expenditure = Aggregate Income .

$AE = C + I + (G-T)$

therefore ,

$Y = C + I + (G-T)$

Given :

S = 20% Yd  , where Yd = disposable income 

Yd = Y - tY  ( where t is proportional tax )

S_a= - 100 million , (Autonomous Saving ) in 2019 

T = 20 million , (Lump sum taxes)

t = 20%Y  (Proportional taxes )

I = 66 million 

G = 50 million (Government Expenditure )

1)

Marginal Propensity to save = Change in savings w.r.t change in Income 

= 0.2 

Marginal propensity to save = 1 - Marginal propensity to consume 

$MPC = 1 - 0.2 = 0.8$

Autonomous Consumption = 100 million (As savings were negative of 100 million )

Consumption function = Autonomous Consumption + MPC (Yd) 

$= 100 million + 0.8( Y - tY )$

$= 100 million + 0.8(1 - 0.2)Y \frac{1} {0.36} ×196$

Consumption function = 100 million + 0.64Y 

2)

Y = C + I + G - T (Aggregate demand Equation )

Where , C = consumption , I = investment , G = Government Expenditure , T = Lump sum taxes 

Y = 100 million + 0.64Y + 66million + 50 million - 20 million

Y = 196 million + 0.64Y ----(i)

3)

$y=C+I+G\\=100+66+50\\=216$

4)

From equation (i)

$Y - 0.64Y = 196million$

$Y =\frac{ 1} {0.36} ×196 million$

$Y^*= 576.47 million$ -----(Equilibrium Level of Income )

Putting this into consumption function :

Consumption function $= 100 million + 0.64Y^*$

$C^* = 100 + 368.94 million\\ C^* = 468.94 million$

5)

Multiplier is given by :

$Multiplier = \frac{1}{0.36} = 2.77$

6)

$Tax => Tax \space function = 20 million + 0.2Y^*\\ = 20 million + 0.2(576.47 ) million\\ = 20 + 115.294\\ = 135.294$