What do you do?

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

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%.

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.

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.

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.