Question

Suppose that autonomous consumption and planned investment in the economy described in problem 5 change to C_a = 470 − 15r and I_p = 1,700 − 60r. All other aspects of the structure of the commodity and the money markets are as described in problem 5.

(a) Derive the equation for the new IS curve and verify that the equilibrium interest rate and real output are the same as you computed in parts 5g and 5h, respectively.

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(b) Calculate the slope of the new IS curve, Δr/ΔY.

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(c) Compared to problem 5, have autonomous consumption and planned investment become more or less responsive to a change in the interest rate? Is the IS curve steeper or flatter as a result? How does this change in the interest responsiveness of autonomous spending alter the amount by which real output will change following an expansionary change in fiscal or monetary policy?

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(d) Compute the new equilibrium interest rate and real output if government spending increases by 160.

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(e) Compute the new equilibrium interest rate and real output if G equals 1,700 but the real money supply increases by 100.

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(f) How and why do the answers in parts d and e differ from problem 6a and 6b, respectively? Is your prediction in part c confirmed?

Answer 1

Given:

The autonomous consumption is .

The planned investment is .

a.

Autonomous spending equation:

The autonomous spending equation is derived as follows:

Therefore, the equation for the autonomous spending is .

IS curve equation:

The IS curve equation is given as follows:

Hence, in order to get the new equilibrium interest rate set the new IS curve equation equal to LM curve.

New equilibrium interest rate:

The new equilibrium interest rate is calculated as follows:

Thus, the new equilibrium interest rate is 6.9565.

Equilibrium real output:

The equilibrium real output is calculated as follows:

In order to get the equilibrium real output, substitute the interest rate into the IS and LM equations.

Thus, the new equilibrium real output is 9,195.5.

b.

Slope of the new IS curve:

The slope of the new IS curve is. The equation for the IS curve is. So, the slope of the LM curve is calculated as follows.

Hence, the slope of the LM curve is 0.0053.

c.

Changes in autonomous consumption and planned investment:

The autonomous consumption and planned investment is very responsive to the changes in interest rate. So, any one percentage increase in interest rate will result in a 75 billion decrease in the autonomous consumption and planned investment as compared to 40 billion in the previous solution.

Slope of the new IS curve:

The slope of the new IS curve is, that is less in absolute value than, the slope of the IS curve. Thus, the new IS curve is flatter.

Changes in fiscal policy due to autonomous spending:

An increase in income and demand for money results from the fiscal expansion. And it creates an excess demand that increases the interest rate. It is due to the autonomous spending being more responsiveness to the changes in the interest rate, that the importance of the increase in the interest rate that is required to restore the equilibrium in the money market resulted in a larger decrease in the real output and autonomous spending. Hence, due to the effects of it on the income, the fiscal policy is weaker.

Changes in monetary policy due to autonomous spending:

It is due to the autonomous spending being more responsiveness to the decrease in the interest rate, that the importance of the decrease in the interest rate that is required to restore the equilibrium in the money market resulting in an increase in the money supply could result in a larger increase in the real output and autonomous spending. Thus, the monetary policy is stronger.

d.

Autonomous spending equation:

The autonomous spending equation is as follows:

Autonomous spending equation is .

New IS curve:

The new IS curve is as follows:

Hence, in order to get the new equilibrium interest rate set the new IS curve equal to the LM curve.

New equilibrium interest rate:

The new equilibrium interest rate is calculated as follows:

Thus, the new equilibrium interest rate is 8.3478.

Equilibrium real output:

The equilibrium real output is calculated as follows:

In order to get the equilibrium real output, substitute the interest rate into the IS and LM equations.

Thus, the new equilibrium real output is 9,334.78.

e.

New LM equation:

The new LM equation is a as follows:

New equilibrium interest rate:

The new equilibrium interest rate is calculated as follows:

Thus, the new equilibrium interest rate is 5.5652.

Equilibrium real output:

The equilibrium real output is calculated as follows:

In order to get the equilibrium real output, substitute the interest rate into the IS and LM equations.

Thus, the new equilibrium real output is 9,546.52.

f.

Results of fiscal expansion:

Due to the fiscal expansion, there is a smaller increase in income and interest rate. And an increase in the money supply results in a larger increase in the output and smaller decrease in the interest rate.