Answer to Question #270200 in Macroeconomics for Vickie

Question

In a keynesian model it is assumed that the consumption function is given by C= 2000 + 0.75 (Y-T) and the planned investment is 1,000 government purchases and taxes are both of those and formulate and draw a graph of planned expenditure as a function of income

What is the equilibrium level in the part above

If the government purchases increased by 1250 what is the equilibrium income

With the aid of a algebra prove that a balanced budget multiplier is always equals to 1

Answer 1

Consumption function

The consumption function, alternatively referred to as the Keynesian consumption function, is an economic formula that expresses the functional relationship between total consumption and gross national income. John Maynard Keynes, a British economist, introduced the function, arguing that it might be used to track and forecast total aggregate consumer expenditures.

Recognize the Consumption Process

According to the conventional consumption function, consumer spending is entirely determined by income and its fluctuations. If this is true, aggregate savings should increase proportionately to gross domestic product growth (GDP). The objective is to establish a mathematical relationship between disposable income and consumer expenditure on an aggregate basis.

The stability of the consumption function, based in part on Keynes' Psychological Law of Consumption, is a cornerstone of Keynesian macroeconomic theory, particularly when contrasted with the volatility of the investment. Most post-Keynesians acknowledge that the consumption function is not constant over time, as spending patterns vary as income increases.

Given

C= 2000 + 0.75 (Y-T)

Planned investment = 1,000

Government purchases and taxes = 1000

PART a)

Planned expenditure = C + I + G 

= 2000 + 0.75(Y-T)+1000 +1000

= 4000 + 0.75(Y-1000)

= 3250 + 0.75Y

PART b)

 

Calculate the equilibrium level of income as follows:

G = T = 1000

I = 1000

c = 2000+ 0.75 (Y-T)

= 2000+ 0.75Y - 750

= 1250 - 0.75Y

 

Y = C +I + G

Y = 1250+0.75Y+1000 +1000

Y = 3250 + 0.75Y

 

0.25Y = 3250

 

Y$= \frac{3250}{0.25}$

Y = 13000

 

Thus. the equilibrium level of income is- 13000

 

 

PART C)

Calculate the new equilibrium income as follows:

Change Y =$\frac{(3250 + 250)}{0.25}$

$=\frac{3500}{0.25}$

=14000

Thus. the new equilibrium is -14000

 

Assuming G = 1250

 

AE = 1250 + 0.75Y + 1250 + 1000 = 350 + 0.75Y

 

At equilibrium, aggregate expenditure is equal to total output.

Therefore,

 

Y = AE

Y = 3500 +0.75Y

0.25Y = 3500

Y = 1400

 

The multiplier is the change in income due to change in autonomous expenditure, like in this government purchase. Here for change of 25 in G the Y changes by 100. Therefore, the multiplier is

 

Multiplier $=\frac{ 100}{25} = 4$