Problems and Answers

the aggregate savings function is S = -15 + .2Yd, where Yd = Y - T,

the money demand function is i = 25 + .007Y - .08Md,

government expenditures are 450,

the Treasury is operating an income tax which can be characterized as T = 186.1 + .05Y, and

Greenspan and the Fed have the money supply at Ms = 500.

To derive the IS curve set I + G = S + T and substitute in values from above:

550 - 10i + 450 = -15 + .2(Y - 186.1 - .05Y) + 186.1 + .05Y

550 - 10i + 450 = -15 + .2Y - 37.22 - .01Y + 186.1 + .05Y

550 + 450 + 15 + 37.22 - 186.1 = .2Y - .01Y +.05Y

866.12 - 10i = .24Y

3609 - 41.7i = Y

To derive the LM curve substitute the level of Ms for Md in the money demand equation.

i = 25 + .007Y - .08(500)

i = -15 + .007Y

To find equilibrium Y and i, first substitute

the value of Y in the IS for the Y in LM:

i = -15 + .007(3609 - 41.7i)

i = -15 + 25.263 - .292i

1.292i = 10.263

i = 7.94

then substitute this value of i into the equation

for the IS curve:

Y = 3609 - 41.7 (7.94)

Y = 3609 - 331.098

Y = 3277.9

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You can check (or do) the problem inversely:

Y = 3609 - 41.7 (-15 + .007Y)

Y = 3609 + 625.5 - .2919Y

1.2919Y = 4234.5

Y = 3277.7 then plug Y into the other equation:

i = -15 + .007 (3277.7)

i = -15 + 22.9439 = 7.9439

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In either case the budget = G-T, T = 186.1 + .05 (3277.7) = 349.995,

so, G - T = 450 - 349.995 = 100.005 = deficit

b) Then, suppose you have reason to think that full employment Y = 3400. By how much would you have to expand the money supply to attain this level of Y? What interest rate would this give? What would happen to the government budget?

To find Ms you need only set IS = LM and sub value of Y and solve for Md (which = Ms)

3400 = 3609 - 41.7 (25 + .007{3400} - .08Md)

3400 = 3609 - 1042.5 - 992.46 + 3.336Md

1825.96 = 3.336Md

547.35 = Md = Ms

so, Ms must increase by 47.35.

We can find the interest rate by substituting 3400 into the IS curve:

3400 = 3609 - 41.7 i

i = 5.01

At Y = 3400, T = 186.1 + .05(3400) = 356.1, so G - T = 93.9, so we see that the deficit would shrink by 100.005 - 93.9 = 6.105

c) Finally, suppose you are dependent on foreign money to finance your deficit (as with the US today) and are affraid that a drop in interest rates of this magnitude would result in foreign capital going home. How else might you raise Y to 3400?

The most obvious answer is to shift the IS curve by increasing G or by cutting T which will tend to raise i and the deficit. More imaginative answers might involve doing things to raise MEC via raising business profit expectations to raise I and thus shift IS to the right. Or, do something to influence savings and consumption.