a)
The equilibrium values of output, real interest rate,
a)
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Explanation of Solution
An economy with the following equations is presented:
Desired consumption
Desired investment
Real money demand
Full employment output
Expected inflation
Using the equation
Substituting the desired consumption and investment and solving for Y
Setting the real money demand to
The aggregate demand curve is
The equilibrium interest rate is
The equilibrium value of the price level is
The equilibrium value of consumption is
The equilibrium value of investment is
Substituting the given values of T and G into the general IS equation to obtain the IS curve equation
Equation is
Substituting the value of M into the Lm equation to obtain the equation for LM curve,
Thus, the equation for LM curve is
Using the IS and LM equations to find out the aggregate demand equation
Solving the IS equation for 2000r,
Equating the IS and LM equations, following is derived:
Thus, the aggregate demand curve is
Substituting the full employment output into the IS equation to obtain the real interest rate.
Therefore, the equilibrium interest rate is 0.1.
Using the aggregate demand curve to obtain the price level,
Substitute the full employment output value.
The equilibrium price level is 17
To obtain the value of consumption, substitute the given values of output and tax and the calculated value of interest rate into the desired consumption equation
The equilibrium consumption is 600
Substituting the value of real interest rate into the desired investment equation to obtain the equilibrium investment value
Thus, the equilibrium investment is 200
b)
The equilibrium values of output, real interest rate, price level, consumption and investment and the equation of the aggregate demand curve.
b)
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Explanation of Solution
An economy with the following equations is presented:
Desired consumption
Desired investment
Real money demand
Full employment output
Expected inflation
Using the equation
Substituting the desired consumption and investment and solving for Y
Setting the real money demand to
The new aggregate demand curve is
The equilibrium price level is P=20
Now, the money supply has increased to M=9000
Use the IS and LM equations to find the new aggregate demand equation
By substituting, following is derived:
Multiplying the LM equation by 4 and solving it for 2000r
Solving the IS equation for 2000r
Equating the IS and LM equations, following is derived:
Thus, the new aggregate demand curve is
The change in money supply does not affect the equilibrium values of real interest rate consumption or investment
Therefore, using the aggregate demand curve to obtain the value for price level.
The equilibrium price level is 20.
c)
The equilibrium values of output, real interest rate, price level, consumption and investment and the equation of the aggregate demand curve.
c)
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Explanation of Solution
An economy with the following equations is presented:
Desired consumption
Desired investment
Real money demand
Full employment output
Expected inflation
Using the equation
Substituting the desired consumption and investment and solving for Y
Setting the real money demand to
The aggregate demand equation is
The equilibrium value of real interest rate is
The equilibrium value of price level is
The equilibrium value of consumption is
The equilibrium value of investment is
The values for taxes have increased to
Recalculating the IS equation
The equation for LM curve remains the same.
Using the M and IS equations to find the aggregate demand equation,
Multiplying the Lm equation by 4 sand solving for 2000r.
Solving the IS equation for 200r
Equating the IS and LM equations
The aggregate demand equation is
Substituting the given full employment output into the IS equation to obtain the real interest rate
The equilibrium value of real interest rate is therefore 0.15.
Using the aggregate demand curve for obtaining the value of price level,
The equilibrium value of price level is 18.
Substituting the values of output and tax and calculated value of real interest rate into the desired consumption to obtain the value of consumption,
The equilibrium value of consumption is therefore 525
Using the desired investment equation to find the equilibrium value of interest
The equilibrium value of investment is 175.
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