Problem set 3 (due Friday, Oct. 9, 23:55pm on Moodle, or earlier in hard copy)
I think you should find this problem set somewhat easier than the last two.
Recent problem sets have asked what effect a particular change in investment will have on equilibrium GDP: âˆ†I à âˆ†Y*. In lecture we have also answered the question: What effect (how large a change in equilibrium GDP, or âˆ†Y*) would a particular change in government spending (âˆ†G) or taxation (âˆ†Tx) produce? (Assume there are no transfers in this economy.)
In this problem set (as the text does in Chapter 15) we turn the question around and ask: How large a change in government spending or taxation (or both) would it take to increase (equilibrium) GDP, or Y*, by a given dollar amount? Here we want Y* to rise by $1 trillion.
You are asked to propose three alternative policies:
Policy #1 is a change in government spending, with no change in taxes or other policies.
Policy #2 is a negative change in taxes (i.e., a tax cut), with no change in government spending.
Policy #3 is an equal change in government spending and taxation (âˆ†G = âˆ†Tx), with no change in transfers. (Such a policy would avoid increasing (or decreasing) the government budget deficit, that is, the part of the government budget for which there are no tax revenues to cover it, so in order to spend the money it has to be borrowed from the public by, for example, selling Treasury bills. We’ll discuss this in lecture this week.)
For all four problems, assume that initially:
C = 2 + 0.6DPI
DPI = Y – Tx
I = 2
G = 4
Tx = 2
àIn these problems, ALWAYS SHOW THE SIGN OF YOUR ANSWER (is it + or – ?).
#1a. Calculate equilibrium GDP (or Y*) in this economy, using the method Y = AE. You must show your work to get credit. Be sure to use the equations for the three-sector model, including government. These equations are in Ch. 15. Substitute the DPI equation into the consumption function and replace Tx with its value. (There should not be Tr in any equation, because we’re assuming it is zero.)
1b. Now find DPI in equilibrium (you couldn’t do this until you calculated Y*), simply by plugging in the value you found in 1a.
1c. What is the government spending multiplier âˆ†Y*/âˆ†G?
1d. To produce a $1 trillion increase in GDP (that is, if âˆ†Y* needs to be $1 trillion), by how much would the government need to increase spending (that is, how large would âˆ†G have to be)? Use your results above.
2a. Go back to the original assumptions and forget the increase âˆ†G.
Now figure out, as an alternative policy proposal, how large a tax cut would be needed to increase equilibrium GDP by $1 trillion. First, what is the tax multiplier âˆ†Y*/âˆ†Tx in this model?
2b. To produce a $1 trillion increase in GDP, by how much would the government need to change total tax revenue (that is, how large would âˆ†Tx have to be)? Use your result from 2a.
3a. As another alternative policy proposal, find how large an EQUAL increase in government spending and taxation (that is, âˆ†G = âˆ†T) would be needed to increase equilibrium GDP by $1 trillion. (Assume that there are many in Congress who will insist that the budget deficit not be increased – or decreased – so that to satisfy them you are proposing this alternative policy.)
To do this problem, notice that the overall effect will have to be the sum of two effects (using the notation in Chapter 15):
âˆ†Y* = âˆ†G kG + âˆ†Tx kTx …BUT since âˆ†G = âˆ†Tx, this can be simplified to:
âˆ†Y* = âˆ†G kG + âˆ†G kTx = âˆ†G (kG + kTx) = $1 trillion
So you just need to add the two multipliers together to get the multiplier for this problem, which in most textbooks is called the balanced budget multiplier. [By the way, calling it the “balanced budget multiplier” does NOT imply that the budget is balanced before or after the change. It does imply that the change in government spending is the same size – and sign – as the change in taxes collected.)]
4. Some of those who become unemployed can collect unemployment benefits equal, in the US, to up to about half their previous weekly wages. Normally they cannot collect unemployment benefits for more than 6 months, however. In many European countries, unemployment benefits are more generous, replacing a higher percent of income and lasting for a longer time. Unemployment benefits are a government transfer and a built-in stabilizer. Based on the discussion in the text and in lecture, explain in a sentence or two why they tend to make recessions less deep than they would otherwise be. Then discuss whether you think a more generous system of unemployment benefits would help the economy recover more quickly from a recession.
5. In “Myths and Realities of Government Spending” (Real World Macro 4.4), Gerald Friedman discusses how growth in federal spending and growth in federal (tax) revenue collected have varied under different presidents. Remembering that spending and taxation have to be voted on by Congress as well as signed by the President (unless Congress passes something by 2/3 or more), summarize Friedman’s conclusions and discuss the extent to which the evidence he offers supports his claims. You will get points for stating the data to which you are referring, which will make your argument much clearer to the reader. If you quote data, you need to cite it clearly to its source. You can do this by writing, for example, “Figure 2 shows that in the Johnson administration….[blah blah blah]…while in the Obama administration…[blah blah blah].” Also, at the bottom, put this:
Work Cited [“Works” if you cite anything else in addition]
Rosero, Luis, Bryan Snyder, Chris Sturr, and the Dollars & Sense collective. 2015. Real World Macro. 32nd edition. Boston, MA: Dollar & Sense.
|Due By (Pacific Time)||10/09/2015 11:50 pm|
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