Answer to Question #239603 in Macroeconomics for tweety

Question

Consider the following Keynesian model for an economy: С C=C + CY C=C+cYd = C + c(1 – t) Y Consumption spending c(1 - 1) С Y Total income where C = 85 million + 0.5Yd ī = 75 million G = 70 million T = 0,25Y Y = R450 million Equilibrium income: Y = C + + G Disposable income: Yd = (1 – t)Y NOTE: A proportional income tax reduces the disposable income of households and therefore also their consumption spending, which forms part of aggregate spending in the economy. The introduction of a proportional income tax thus reduces aggregate spending, ceteris paribus. Question 4 [20] 4.1. Answer the following questions: 4.1.1. What is the value of the marginal propensity to consume in this model? 4.1.2. Calculate the multiplier. (1) (3)

4.1.3. Calculate the equilibrium level of income using the calculated value of the multiplier in 4.1.2. (3) 4.1.4. How much does the government collect in taxes when the economy is in equilibrium? (2) 4.1.5. Is the government currently running at a surplus or a deficit? (2)

Answer 1

Solution:

4.1.1). The value of the marginal propensity to consume is 0.5

4.1.2). The multiplier =$\frac{1}{1 - MPC} = \frac{1}{1 - 0.5} = \frac{1}{0.5}= 2$

The multiplier = 2

4.1.3). The equilibrium level of income using the multiplier:

Y = $(\frac{1}{1 - MPC} )(C + I+ G - cT)$

Y = 450

T = 0.25Y = 0.25 x 450 = 112.5

C = 85 + 0.5(Y – T) = 85 + 0.5(450 – 112.5) = 85 + 168.75 = 253.75

I = 75

G = 70

Multiplier = 2

Y = 2 $\times$ (253.75 + 75 + 70 – (2 $\times$ 112.5))

Y = 2 $\times$ (398.75 – 225)

Y = 2 $\times$ 173.75 = 347.50

Y = 347.50

The equilibrium level of income using the multiplier = 347.50

 

4.1.4). How much does the government collect in taxes when the economy is in equilibrium?

At equilibrium (Y) = 347.5      

Tax = 0.25Y = 0.25(347.5) = 86.875

The government will 86.875 in taxes.

 

4.1.5). The government is running a surplus:

Budget = T – G = 86.875 – 70 = 16.875

The government is running a surplus of 16.875