ISLM Model

Instructions:

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

1.  Keynesian Cross Model:

This is a simple model with a consumption function, but net taxes, investment, government purchases, and the current account are assumed to be fixed.

restart; 
MPC:=0.80; GOV:=2675; NT:=2275; CA:=-730; GPI:=2130;
islm:={ Y=PC+GPI+GOV+CA,
 PC=503+MPC*(Y-NT),
 Sp=Y-NT-PC,
 Sg=NT-GOV};
islmresult:=solve(islm, {Y, PC, Sp, Sg});

PC is personal consumption expenditures, MPC is the marginal propensity to consume, GPI is gross private investment, GOV is government consumption and investment purchases, CA is the current account balance, NT is net taxes, Sp is private savings (corporate and personal), Sg is government savings, and Y is Gross National Disposable Income.  These variables have been calibrated to approximate the 2007 values for the U.S. economy, in billions of dollars.

a)  Solve for the initial equilibrium.  Round off your numbers to the nearest billion.

b) Solving for each case in turn, use the Keynesian Cross Diagram to explain how the results are affected by the following changes..  In all cases, compare the change against the initial equilibrium in (a).

(1) NT := 2047 (a 10% cut in net taxes).
(2) GOV:= 2943 (a 10% increase in government purchases).
(3) GPI:= 2343 (a 10% increase in investment).
(4) MPC:= 0.75 (an increase of 5% in the marginal propensity to save).
(5) CA := -657 (a 10% decline in the current account deficit).
c)  Show that savings equals investment for the original equilibrium, and for each of the five changes.

2.  ISLM Model:

Now we assume that both investment and money demand depend on the interest rate.

restart;  
MPC:=0.80; GOV:=2675; NT:=2275; CA:=-730; MS:=7168; P:=1.00; 
islm:={ Y=PC+GPI+GOV+CA,
 PC=503+MPC*(Y-NT),
 GPI=2610-6000*IR, 
 (0.6-IR)*Y = MS/P,
 Sp=Y-NT-PC,
 Sg=NT-GOV};
islmresult:=solve(islm, {Y, PC, GPI, IR, Sp, Sg});

GPI is now a decreasing function of the interest rate (IR), and the money market equilibrium is MS/P = L*Y, where MS and P are exogenous and L (normalized money demand) is a decreasing function of IR.

a)  Solve for the initial equilibrium.  Round off your numbers, as appropriate (Y and similar numbers to the nearest billion, the interest rate to the tenth of a percentage point).

b) Solving for each case in turn, use the ISLM Diagram to explain how the results are affected by the following changes..  In all cases, compare the change against the initial equilibrium in (a).

(1) NT := 2047 (a 10% cut in net taxes).
(2) GOV:= 2943 (a 10% increase in government purchases).
(3) MS := 7885 (a 10% increase in the money supply).
(4) MPC:= 0.75 (an increase of 5% in the marginal propensity to save).
(5) CA :=-657 (a 10% decline in the current account deficit).
c)  How are your results above different from those in #1(b) above?

3.  ISLM Model, Redux:

Now we add some more assumptions.  Net taxes are now an increasing function of income (TR is the net marginal tax rate), the current account is a function of disposable private income, foreign income (FY), and the real exchange rate), the money supply is the product of monetary reserves (MR)  and the deposit expansion multiplier, which declines with the federal funds rate (FFR).  The real exchange rate is E*FP/P, where E is the direct exchange rate and FP is the foreign price level.

restart;  
MPC:=0.80; GOV:=2675; TR:= 0.25; MR:=794; FFR:=0.05; P:=1.00; FP:=1.00; FY:=41350; E:=1.02; 
islm:={ Y=PC+GPI+GOV+CA,
 PC=503+MPC*(Y-NT), 
 NT=TR*Y-1171,
 CA=0.04*FY*(E*FP/P)-0.21*(Y-NT),
 MS=MR*(9.5*(1-FFR)),
 GPI=2610-6000*IR, 
 (0.6-IR)*Y = MS/P,
 Sp=Y-NT-PC,
 Sg=NT-GOV};
islmresult:=solve(islm, {Y, PC, NT, CA, MS, GPI, IR, Sp, Sg});

a)  Solve for the initial equilibrium.  

b) Solving for each case in turn, use the ISLM Diagram to explain how the results are affected by the following changes..  In all cases, compare the change against the initial equilibrium in (a).

(1) TR := 0.20 (a 5% cut in the net tax rate).
(2) GOV:= 2943 (a 10% increase in government purchases).
(3) MR := 873 (a 10% increase in monetary reserves).
(4) FFR:= 0.04 (a 1% decrease in the federal funds rate).
(5) E  := 1.12 (a 10% increase in the exchange rate).

c)  How are your results above different from those in #2(b) above?

4.  ISLM-FX Model:

Now we add one more change, by assuming E adjusts to give is interest rate parity (as a result of financial openness), depending on the foreign interest rate (FIR) and the expected future exchange rate (EFE).

restart;  
MPC:=0.80; GOV:=2675; TR:= 0.25; MR:=794; FFR:=0.05; P:=1.00; FP:=1.00; FY:=41350; EFE:=1.00; FIR:=0.06;
islm:={ Y=PC+GPI+GOV+CA,
 PC=503+MPC*(Y-NT), 
 NT=TR*Y-1171,
 CA=0.04*FY*(E*FP/P)-0.21*(Y-NT),
 MS=MR*(9.5*(1-FFR)),
 GPI=2610-6000*IR, 
 (0.6-IR)*Y = MS/P,
 IR=FIR+(EFE/E-1),
 Sp=Y-NT-PC,
 Sg=NT-GOV};
islmresult:=solve(islm, {Y, PC, NT, CA, MS, GPI, IR, E, Sp, Sg});

a)  Solve for the initial equilibrium.  

b) Solving for each case in turn, use the ISLM-FX Diagram to explain how the results are affected by the following changes..  In all cases, compare the change against the initial equilibrium in (a).

(1) TR := 0.20 (a 5% cut in the net tax rate).
(2) GOV:= 2943 (a 10% increase in government purchases).
(3) MR := 873  (a 10% increase in monetary reserves).
(4) FFR:= 0.04 (a 1% decrease in the federal funds rate).
(5) EFE:= 1.10 (a 10% increase in the expected future exchange rate).

c)  How are your results above different from those in #3(b) above?