Homework #4
1. Suppose you are using the Keynesian Model to model an economy. Suppose the MPS with respect to disposable income is .2 and that taxes are given by the equation T = 5 + .25Y (i.e., taxes are now a function of income and will vary as the level of income in the economy varies).
a. Suppose you want equilibrium aggregate output to increase by $500. How much would taxes need to change by in order for aggregate income to increase by this amount?
b. In (a), what was the value of the tax expenditure multiplier that you used?
c. Suppose instead of a tax increase the leaders of this economy decide to increase output by $500 through a change in government spending. What must the change in government spending equal in order to change aggregate output by $500.
d. What was the value of the government expenditure multiplier you used in part (c)?
2. Suppose you are told that when disposable income is $100, consumption is $80 and when disposable income is $250, consumption is $200. Furthermore, suppose that taxes are autonomous and equal to $10.
a. What is the MPC with respect to disposable income?
b. What is autonomous consumption with respect to disposable income?
c. What is autonomous consumption with respect to aggregate income?
d. Suppose government spending is autonomous and equal to $20, investment spending is autonomous and equal to $30, and net exports are autonomous and equal to $10. What is the equilibrium level of aggregate output?
e. In equilibrium, what is the relationship between leakages and injections. (Provide numerical support for your answer.)
f. Suppose for every $10 worth of aggregate output produced, two people are employed in this economy. What number of people are employed when this economy is in equilibrium?
g. Suppose you would like to increase employment by 50% by changing the level of government spending. What must the total level of government spending equal in order for this economy to reach this employment goal?
3. Suppose you are told that the MPS is equal to .2 for this economy and that taxes, investment spending, government spending, and net export spending are all autonomously determined in this economy.
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Y
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T
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Y - T
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C
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S
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I
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G
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X - M
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AE
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Direction of change in Y
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1000
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900
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820
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100
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100
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1220
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1900
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3000
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3900
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4820
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a. Fill in the above table.
b. What is the consumption function with respect to aggregate income?
c. What is the equilibrium level of output for this economy?
d. Suppose employment (E), measured in people, is equal to
E = (1/10)(aggregate production)
What is the level of employment in this economy when this economy is in equilibrium?
e. At the equilibrium level of output compute labor productivity. Make sure your answer gives the appropriate units of measurement.
Suppose the government increases government spending by $100. Answer the rest of these questions using this new information.
f. What is the government expenditure multiplier for this economy?
g. What is the new equilibrium level of output for this economy?
h. Suppose employment (E), measured in people, is now equal to E = (1/8)(aggregate production)
What is the change in employment equal to with this increase in government spending?
i. Calculate labor productivity. Make sure your answer gives the appropriate units of measurement.
j. Sketch a graph using the Keynesian Cross to illustrate the initial equilibrium and the new equilibrium. In addition, connect this graph to one using an aggregate production function to illustrate the labor productivity effect of these two equilibrium situations. Label your graphs clearly.
4. Answer the following question using the data for a financial system given in the table below (data are in millions of dollars).
Bank Reserves 10
Demand Deposits 100
Cash in the Hands of the Public 100
Savings-type accounts 200
Large Denomination Time Deposits 100
Small Denomination Time Deposits 50
Noninstitutional MMMF Balances 400
Other Checkable Deposits 150
Travelers Checks 10
a. What is the value of M1?
b. What is the value of M2?
c. Suppose the required reserve ratio for this economy is calculated with respect to all checkable deposits. Furthermore, suppose there are no excess reserves being held by the financial system. What is the required reserve ratio in this case?
d. Suppose the Fed purchases $10 million worth of T-bills from the public. What is the effect of this purchase on M1? Assume all funds stay in the banking system and that there are no excess reserves.