Instructions:

1)  Using Maple, solve for the following ISLM equilibrium by cutting and pasting the following set of code to the command line (after the ">").  The equations and definitions are explained below. 

ISLM Model (Closed Economy):

restart; 
dr:=0.04; MB:=800; GP:=2393; tr:=0.25; EXP:=1317;
islm:={ Y=PC+GPI+GP,
 PC=(225-730.1)+0.80*(Y-NT),
 NT=tr*Y-1320,
 GPI=2600-10000*R,
 MS=0.6*Y-20000*R,
 MS=(12.2-100*dr)*MB,
 Sp=Y-NT-PC,
 Sg=NT-GP };
islmresult:=solve(islm, {Y, PC, NT, GPI, MS, R, Sp, Sg});

2)  For #1 above, explain your answer with an appropriate graph. 

3)  Shifting either the IS or the LM curve on your graph, explain how monetary and fiscal policy affects output and interest rates in the model:

a) dr := 0.05 (a 1% increase in the discount rate)
b) MB := 808 (a 1% increase in the monetary base)
c) GP := 2417 (a 1% increase in government purchases)
d) tr := 0.24 (a 1% cut in the tax rate)

ISLM Model (Simple Open Economy, slightly more realistic and current numbers):

restart; 
dr:=0.04; MB:=800; GP:=2393; tr:=0.25; EXP:=1317;
islm:={ Y=PC+GPI+GP+NX,
 PC=225+0.80*(Y-NT),
 NT=tr*Y-1320,
 GPI=2600-10000*R,
 MS=0.6*Y-20000*R,
 MS=(12.2-100*dr)*MB,
 Sp=Y-NT-PC,
 Sg=NT-GP,
 NX=EXP-IMP,
 IMP=0.19*(Y-NT),
 NX+Sf=0 };
islmresult:=solve(islm, {Y, PC, NT, GPI, MS, R, Sp, Sg, NX, IMP, Sf});

5)  Solve for the above equilibrium, and show that saving still equals investment.

6)  Explain how monetary and fiscal policy affects net exports (i.e., the balance of trade) and foreign savings in this model:

a) dr := 0.05 (a 1% increase in the discount rate)
b) MB := 808 (a 1% increase in the monetary base)
c) GP := 2417 (a 1% increase in government purchases)
d) tr := 0.24 (a 1% cut in the tax rate)
e) EXP:= 1330 (a 1% increase in exports)

Exogenous Variables (Parameters):

 

dr	- Discount Rate set by central bank, which affects commercial bank reserve ratios.
MB	- Monetary Base (equal to central bank reserve assets).
GP	- Government Purchases of Goods and Services.
tr	- Marginal Tax Rate.
EXP	- Exports.

Endogenous Variables:

 

Y	- Gross National Product.
PC	- Private Consumption.
NT	- Net Taxes (less government transfer payments).
GPI	- Gross Private Investment.
MS	- Money Supply.
R	- Interest Rate, not including risk premium.
Sp	- Private Savings (business and household).
Sg	- Government Savings (i.e., the fiscal surplus).
IMP	- Imports.
NX	- Net Exports (the balance of trade).
Sf	- Foreign savings (i.e., inward flows, including unilateral transfers).

Equations:

 

MS = k*Y - h*R	Liquidity demand as a function of income and interest rates.
C + I + G = Y	Aggregate expenditures equation.
PC=a+mpc*(Y-NT)	Consumption as a function of disposable (after net taxes) income.
NT=at+tr*Y	Net taxes as a function of income.
GPI=b-d*R	Investment as a function of the interest rate.
MS = dem*MB,  dem = f(dr)	Money supply as the deposit expansion multiplier (itself a function of the discount rate) times the monetary base.
IMP = mpi*(Y-NT)	Imports as a function of disposable income.