Or, you could begin with S + T = I + G, derive the savings function
from C = 104.8 + .6Yd, substitute and come up with the same answer. i.e.,
S + T = I + G
-104.8 + (1 - .6)(Y - 599) + 599 = 450 + 657
.4Y - .4(599) = 450 + 657 + 104.8 - 599
.4Y = 450 + 657 + 104.8 - 599 + 239.6
Y = 852.4/.4 = 2131
And of course, after having done this one way, you should do it the other way to check/verify your answer.
Or, you could do the same thing with S + T = I + G,
Or, you could use the tax multiplier, dY/dT which is easy in this simple model, it will be -b/(1 - b) = -.6/(1 - .6) = 1.5, so that the drop in T of 59.9 would result in an increase in Y of 89.85, so that 2131 + 89.85 = 2220.85 or 2221
If MPC were .75 instead of .6 then there are two ways of answering the question: 1. You could go back to the beginning and recalculate all the values up to this last one of C (which would of course make all the figures in the scenario wrong), or 2. You could just sub .75 for .6 in the consumption function and calculate accordingly.
You know:
Y = 2922
I = 5.6
Ms = 234
I = 456
Ia = 322
G = 790
X = 285
M = 95
X-M = 190
t = .5
h = .1
n = .05
p = .08
C = 104.8 + .6Yd or C = 104.8 + .6(Y - T)
Putting the value of the parameters and variables that you know together, you see:
T = To + .5Y, or
T = To + .5(2922)
C = 104.8 + .06(Y - To -tY), or
C = 104.8 + .06[2922 - To - .5(2922)]
M = m + .05Y, or
M = m + .05(2922), or
95 = m + .05(2922)
I = g + hY - ji
456 = 322 + .1(2922) - j(5.6)
i = k - pMd
5.6 = k - .08Md
5.6 = k - .08(234) (234 because Ms must = Md, and we know Ms = 234)
So, the first thing to do is find the obvious: m in the import function, j in the investment function, and k in the money demand function:
95 = m + .05(2922)
95 = m + 146.1
-51.1 = m
so the import function is:
M = -51.1 + .05Y
456 = 322 + .1(2922) - j(5.6)
456 = 322 + 292.2 - j(5.6)
-158.2 = - j(5.6)
-158.2/5.6 = -j
28.25 = j
so the investment function is:
I = 322 + .1Y - 28.25i
5.6 = k - .08(234)
5.6 = k - 18.72
5.6 + 18.72 = k
24.32 = k
so the money demand function is:
i = 24.32 - .08Md
So now, the only thing we don't know is the value of To. To find this we can substitute all our known values into the equation:
Y = C + I + G + X - M
And solve for the only remaining unknown, To
2922 = 104.8 + .06(2922) - .06To - .06[.5(2922)] + 456 + 790 - 95
2922 = 104.8 + 175.32 - .06To - 87.66 + 456 + 790 - 95
1293.54 = -.06To
-21559 = To
So, T = -21559 + .5Y
Therefore your model consists of the following:
C = 104.8 + .6Yd, where Yd = Y - T
T = -21559 + .5Y
I = 322 + .1Y - 28.25i
i = 24.32 - .08Md
M = -51.1 + .05Y
You can, and should, check your math, by combining all the equations, the current parameter values and solving for equilibrium Y:
Y = C + I + G + X - M
Y = 104.8 + .06[Y - (-21559 + .5Y)] + 322 + .1Y - 28.25(5.6) + 790 + 285 - (-51.1 + .05Y)
Y = 104.8 + .06Y + .06(-21559) - .06(.5Y) + 322 + .1Y - 158.2 + 790 + 285 + 51.1 - .05Y
Y - .06Y + .03Y - .1Y + .03Y = 104.8 - 1293.54 + 322 - 158.2 + 790 + 285 + 51.1
Y(1 - .06 + .03 - .1 + .05) = 2688.24
.92Y = 2688.24
Y = 2922
It all checks, so you could now use this model to solve for the kind of policies you are asked about in the first question.