Workshop #1
(Answers)
Problem #1:
What do you do?
Y = 6,000 +.75(Y - 16,000) + 11,000 + 20,000
Y = 6,000 + .75Y - .75(16,000) + 11,000 + 20,000
Y = 6,000 + .75Y - 12,000 + 11,000 + 20,000
Y - .75Y = 6,000 - 12,000 + 11,000 + 20,000
(1 - .75)Y = 25,000
.25Y = 25,000
Y = 25,000/.25
Y = 100,000
If Y = 100,000 then C = 6,000 + .75(100,000 - 16,000) = 6,000 + 75,000
- 12,000 = 69,000
You can check yourself by substituting 65,000 for C in Y = 69,000 +
11,000 + 20,000 = 100,000
You can also find equilibrium Y by S + T = I + G
If C = 6,000 +.75(Y -T), Then S = -6,000 + .25(Y - T)
So S + T = I + G
Will be: [-6000 +.25Y - .25T] + T = I + G
or
[-6,000 +.25Y -.25(16,000)] + 16,000 = 11,000 + 20,000
.25Y = 11,000 + 20,000 + 6,000 + 4,000 - 16,000
.25Y = 25,000
Y = 100,000
Evaluate proposal #1:
In a balanced budget G = T, so if G = 20,000 then
T must rise to 20,000. What will be the impact on the economy? Substitute
20,000 for T and G and solve for Y
Y = 6,000 +.75(Y - 20,000) + 11,000 + 20,000
Y = 6,000 + .75Y - .75(20,000) + 11,000 + 20,000
Y = 6,000 + .75Y - 15,000 + 11,000 + 20,000
Y - .75Y = 6,000 - 15,000 + 11,000 + 20,000
(1 - .75)Y = 22,000
.25Y = 22,000
Y = 22,000/.25
Y = 88,000
The total level of output, or economic activity, or Y will drop from
100,000 to 88,000!
Or, you could solve this more quickly using the tax multiplier. The
multiplier in this simple model is dY/dT = -.75/(1 - .75) = -3, so if you
raise taxes from 16,000 to 20,000, or 4,000, you know Y will drop by 3(4,000)
or 12,000 which will give a new equilibrium of 88,000 (as before). This
is a drop of 12%.
Evaluate Proposal #2:
In a balanced budget G = T, so if T = 16,000 then
G must be reduced from 20,000 to 16,000. What will be the impact on the
economy? Substitute 16,000 for T and G and solve for Y
Y = 6,000 +.75(Y - 16,000) + 11,000 + 16,000
Y = 6,000 + .75Y - .75(16,000) + 11,000 + 16,000
Y = 6,000 + .75Y - 12,000 + 11,000 + 16,000
Y - .75Y = 6,000 - 12,000 + 11,000 + 16,000
(1 - .75)Y = 21,000
.25Y = 21,000
Y = 21,000/.25
Y = 84,000
The total level of output, or economic activity, or Y will drop from
100,000 to 8,000, even further than under the previous proposal.
Or, you could solve this more quickly using the government expenditure
multiplier. The multiplier in this simple model is dY/dG = 1/(1 - .75)
= 4, so if you reduce G from 20,000 to 16,000, or 4,000, you know Y will
drop by 4(4,000) or 16,000 which will give a new equilibrium of 84,000
(as before). This is a drop of 16%.
So: Proposal #1 will balance the budget but cut the overall level of
economic activity by 12%. Proposal #2 will balance the budget but cut the
overall level of economic activity by 16%. Both will clearly raise unemployment
substantially.
Conclusion:
You recommend to the president that she eliminate the deficit
by cutting taxes rather than by cutting government expenditures.
Problem #2:
Evaluate Proposal #1:
Using the multiplier you see immediately that
an increase in G of 8,000 would raise Y by 4(8,000) or 32,000 which means
Y would rise from 88,000 to 120,000. Unfortunately this would recreate
the budget deficit that she was unhappy with to start with since T remains
at 20,000 while G rises to 28,000. A deficit of 8,000. Moreover, because
120,000 is also well above you estimated full employment level of income
of 112,000 this policy will also be inflationary.
Evaluate Proposal #2:
The proposed increase in unemployment
compensation of 8,000 will amount to a reduction in net taxes by the same
amount. Given a tax multiplier of -3, the cut in net taxes of 8,000 will
mean an increase in Y of -3(-8,000) or 24,000! This would bring Y up from
88,000 to 112,000 which is the full employment level of income --which
would, of course, have the additional beneficial effect of raising employment,
reducing unemployment and undercutting the movement of the unemployed.
It would, however, also recreate a budget deficit because while G remains
at 20,000, net taxes will have fallen to 12,000. A deficit of 8,000. Moreover, it would do nothing to mollify the taxpayers.
Evaluate Proposal #3:
To pacify the tax payers as well as the unemployed a variation on this theme would be to redistribute
the 8,000 between the unemployed and the taxpayers. The stimulus to the
economy would be the same (Y would rise to 112,000) but the political effects
will be broader. The third proposal does just this by giving 6,000 to the
unemployed and cutting taxes by 2,000. It would, however, once again recreate
the budget deficit because G = 20,000 but T would be reduced to 12,000 producing, once again, a deficit of 8,000.
Results:
Proposal #1 would raise output and cut unemployment (which
will undercut the movement of the unemployed) but would be inflationary
and would fail to pacify the taxpayers and recreate a budget deficit.
Proposal #2 would raise output and cut unemployment while keeping unemployed happy but leave the taxpayers unsatisfied and recreate a budget deficit.
Proposal #3 would raise output, cut unemployment, keep the unemployed happy and
pacify the taxpayers but recreate a budget deficit.
Conclusion:
The third proposal is the best because it boosts the economy
and undercuts two unhappy protesting groups. It does leave Madame President
worse off than a year earlier with a larger budget deficit but so
do all the other proposals.
Problem #3:
You can answer this by letting G = T, substituting 112,000
for Y and solving for the amount of T and G:
112,000 = [6,000 + .75(112,000) - .75T (=G)] + 11,000 + T (= G)
112,000 = 6,000 + 84,000 - .75T + 11,000 + T
112,000 - 6,000 - 84,000 - 11,000 = - .75T + T
112,000 - 6,000 - 84,000 - 11,000 = .25T
11,000 = .25T
44,000 = T ( = G)
The result is likely to be an even wilder taxpayer revolt as taxes more
than double from 20,000 to 44,000.