# Workshop #1

## 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.