Use the Keynesian Model to answer this set of questions.
Suppose that in the economy under consideration the consumption function can be written as C = 200 + .8(Y – T). Furthermore, you know that taxes are autonomous and equal to $10.
Now, suppose that investment spending is equal to $50 at every level of disposable income and government spending is constant and equal to $100 at every level of disposable income, suppose that (X – M) is constant and equal to $20 at every level of disposable income.
(a)Draw a graph of the consumption function with respect to disposable income. Measure/show consumption spending on the vertical axis and disposable income on the horizontal axis
(b) Calculate equilibrium national income Ye from the information given.
(c) From the information given above is the government running a deficit or surplus budget? Explain why.
(d) Full employment output in this economy (Yf) is equal to $2000 what do you predict is happening to inventories if the full employment level of output is produced? Hint: to answer this question you will need to compare this full employment level of output with the level of output.
(e) Show Ye from (b) and Yf from (d) on one Keynesian 45o diagram. What gap is present in the economy?
(f) If the government wants to attain full employment income (Ye) by how much would government spending have to increase given the information from beginning?
The Keynesian economic model provides valuable insights into how changes in various components of an economy can affect its equilibrium and overall stability. In this context, let’s delve into the given scenario and utilize the Keynesian model to answer a set of questions related to the economy’s equilibrium, government budget, full employment output, and potential policy measures.
Graphing the Consumption Function
The consumption function is given by C = 200 + 0.8(Y – T), where C represents consumption spending, Y denotes disposable income, and T stands for taxes. With autonomous taxes set at $10, the consumption function can be simplified as C = 190 + 0.8Y. To graph this consumption function, we plot consumption spending on the vertical axis and disposable income on the horizontal axis. The slope of the consumption function is 0.8, reflecting the marginal propensity to consume.
Calculating Equilibrium National Income (Ye)
In the Keynesian framework, equilibrium occurs when aggregate demand equals aggregate output. The components of aggregate demand are consumption (C), investment (I), government spending (G), and net exports (X – M). Given that investment spending is $50, government spending is $100, and net exports (X – M) is $20 at every level of disposable income, the aggregate demand equation becomes: AD = C + I + G + (X – M) = 190 + 0.8Y + 50 + 100 + 20.
Setting aggregate demand equal to output (Y), we have Y = 190 + 0.8Y + 170. Solving for Y, we find Y = Ye = $700.
Government Budget Deficit or Surplus
The government’s budget situation can be determined by comparing government spending (G) and taxes (T). Given that taxes are autonomous and equal to $10, and government spending is $100, the government’s budget deficit (surplus) is calculated as G – T = $100 – $10 = $90. Therefore, the government is running a budget deficit.
Impact on Inventories at Full Employment Output (Yf)
Full employment output (Yf) is provided as $2000. If the economy produces at this level of output, it is in equilibrium. However, the equilibrium level (Ye) calculated earlier is $700, which is significantly lower than full employment output. This implies that the economy is operating well below its full potential. Given that production is far below the full employment level, inventories are likely to accumulate as goods are not being sold at the expected rate.
Keynesian Diagram and Output Gap
Plotting Ye and Yf on a Keynesian 45-degree diagram, we observe a substantial gap between the two points. This gap represents the output gap, highlighting the difference between the economy’s current output (Ye) and its potential output (Yf). The existence of this gap signifies that there is unused productive capacity within the economy due to insufficient demand.
Government Intervention for Full Employment
To achieve full employment income (Ye), the government can employ expansionary fiscal policy. Since the equilibrium output is $700, and the desired full employment output is $2000, the economy needs to close the output gap of $2000 – $700 = $1300. This can be achieved by increasing aggregate demand. Given that the marginal propensity to consume is 0.8, an increase in government spending (ΔG) can be calculated as follows:
ΔG = (Output Gap) / (Marginal Propensity to Consume) = $1300 / 0.8 = $1625
Therefore, the government would need to increase spending by $1625 to attain full employment income (Ye) and close the output gap.
In conclusion, the Keynesian model provides a framework for understanding the dynamics of an economy’s equilibrium, government budget, and full employment potential. The given scenario illustrates the importance of government intervention to bridge the gap between actual and potential output, and it highlights the role of fiscal policy in stabilizing an economy.
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