Consider a closed economy to which the Keynesian-cross analysis applies. Consump
ID: 1214354 • Letter: C
Question
Consider a closed economy to which the Keynesian-cross analysis applies. Consumption is given by the equation C= 200 + 2/3(K- T). Planned investment is 300, as are government spending and taxes. a. If K is 1,500, what is planned spending? What is inventory accumulation or Should equilibrium Kbe higher or lower than 1,500? b. What is equilibrium Y? c. What are equilibrium consumption, private saving, public saving, and national saving d. How much does equilibrium income decrease when G is reduced to 200? What is the multiplier for government spending?Explanation / Answer
The Keynesian cross is a fundamental model of determination of income. The Keynesian Cross articulates the relationship between Planned Expenditure and Actual Expenditure. Planned Expenditure is the amount households (in the form of Consumption, C) firms (in the form of Investment, I) and government (in the form of government spending, G) would like to spend on goods and services. This is expressed as:
PE = C + I + G
a) This suggests that C = 200 + 2/3 (1500 - 300) = 1000, I = 300, G = 300
So that PE = 1000 + 300 + 300 = 1600. Hence planned spending is 1600. This shows that PE>AE which implies there is an unplanned inventory accumulation amounting to PE - AE or 1600 - 1500 = 100.
b) Compute equilibrium income as:
Y = PE
Y = 200 + 2/3(Y - 300) + 300 + 300
Y = 800 + 2/3Y - 200
1/3Y = 600
Y = 1800
Hence equilibrium level of GDP or where PE = AE , is Y = 1800
c) Consumtion is C = 200 + 2/3(1800 - 300) = 1200.
Public saving is the excess of tax revenue over and above the government spending. Given that the amount of taxes and government spending both are $300, public saving is zero.
Private saving is the part of disposable income of households that is not consumed. This suggests that the amount of private saving is S = Y - T - C . Substitute the values in the relationship
private saving = 1800 - 300 - 1200 = 300.
National saving is the sum of private saving and public saving. Since public saving is $0 and private saving is $300, national saving amounts to $300.
d) Fiscal policy is the policy of the government to influence the aggregate demand AD. Government, through its spending, affects planned expenditure. Keeping all the other factors constant, when government spending is changed, it affects the income level which can be described by the new Keynesian cross equation
Y/G = 1/1- MPC
The ratio 1/1- MPC is called the government purchases multiplier. This suggests how much the income would change for $1 change in the government purchases (or spending).
When government decreases its expenditure by 200, income decreases multiple times, precisely by G/1 – MPC. Here MPC = 2/3 so income falls by 200*(1/1-2/3) = 600. So income decreases by 600. The size of the multiplier is 1/1-2/3 or 1/1/3 or precisely 3.
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