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Finance and Monetary Policy: Use our standard Keynesian macroeconomic model:

Y = E = C + I + NX + G: GDP equals the sum of consumption, investment, net exports, and government purchases.

C = c0 + cy x Y: consumption equals the consumer-confidence term plus the mpc times GDP or income

I = I0 - Ir x r: Business investment spending equals the business animal-spirits term minus the interest sensitivity of investment times the long-run real risky interest rate.


μ = 1/(1 - cy): The multiplier is the inverse of one minus the mic.


Y = μ(c0 + I0 + NX) - (μ Ir) x r + μG: Our summing-up equation, telling us how the level of annual GDP depends on the multiplier μ, on the private spending flows c0 + I0 + NX, on the interest-sensitivity parameter Ir, on the interest rate r, and on government purchases G

 

a) Suppose that the short-term safe nominal interest rate on government securities the Federal Reserve controls, i = 5%, the expected inflation rate = 2.5%, the term premium = -1%, and the risk premium = 3%. What is the real risky interest rate r at which banks lend to companies the rate that matters for investment spending?

b) Suppose that the expected inflation rate stays the same, but a financial crisis causes the risk premium to spike from 3% to 8%. What happens to the long-term risky real interest rate r if the term premium and the short-term safe interest rate on government securities 'i' remain constant?

c) Suppose that for each one-percentage-point the Federal Reserve reduces the interest rate it controls 'i', the term premium moves by 1/2 percentage point in the opposite direction. What happens to the long-term risky real interest rate r if the risk premium spikes from 3% to 8% and the Federal Reserve responds by lowering the short-term safe nominal interest rate 'i' it controls by as much as possible?

d) Suppose that the interest sensitivity of investment 'Ir' is $0.2T that a 1% point change in r moves annual investment spending I by $0.2T in the opposite direction. By how much downward pressure would the shift from the situation in (a) to the situation in (c) have put on investment spending?

e) With a multiplier μ of 3, and holding other things constant, how much downward pressure on annual GDP Y would have been generated by the downward pressure on investment spending in (d)?

f) Suppose that the Federal Reserve had kept the 'i' it controls the same. How much downward pressure would the financial crisis and its interest rate spike have put on annual GDP Y?

g) Suppose the Federal Reserve took active, aggressive, and successful policy steps to convince people that it would keep the interest rate 'i' it controlled at zero for a long time into the future, and so had nailed the term premium to the value of 0. What would your answer to (f) have
been?

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Darryn D'Souza
Darryn D'SouzaLv10
28 Sep 2019

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Related questions

Monetary Policy and Inflation: Use our standard Keynesian macroeconomic model:

• Y = E = C + I + NX + G — GDP equals the sum of consumption, investment, net exports, and government purchases
• C = c0 + cy x Y — consumption equals the consumer-confidence term plus the mpc times GDP or income
• I = I0 - Ir x r — business investment spending equals the business animal-spirits term minus the interest sensitivity of investment times the long-run real risky interest rate
• μ = 1/(1 - cy) — the multiplier is the inverse of one minus the mic
• Y = μ(c0 + I0 + NX) - (μ Ir) x r + μG — our summing-up equation, telling us how the level of annual GDP depends on the multiplier μ, on the private spending flows c0 + I0 + NX, on the
interest-sensitivity parameter Ir, on the interest rate r, and on government purchases G


For this problem, assume a value of the Keynesian multiplier of μ = 2, and with Ir, the sensitivity of investment spending I to the interest rate r, such that Ir = $0.15T. And let’s use the Greek letter Δ—capital delta—as a shorthand symbol for changes from the previous equilibrium situation.


The Federal Reserve controls the short-term safe interest rate on government securities—it can nail that value to whatever it wants by buying and selling bonds for cash. We call this interest rate i. But the interest rate that matters for determining investment spending is the long-term real risky interest rate at which banks lend to companies. We call this interest rate r.


a) Suppose that the interest rate r that matters for investment spending falls by 1.5%-pts:
Δr = -1.5
By how much would you expect investment spending to fall given the parameter values of our model? How large is ΔI?

b) Continue your analysis from (a): given the parameter values of our model and the boosting of investment spending you calculated in (a), by how much would you expect GDP Y to grow?


c) Annual real GDP in the mid-2000s was about $15T. How large is this boost to GDP ΔY you calculated in (b) as a percentage of the then-level of real GDP?


d) On average, a 1% extra boost to GDP is associated with a 1.5% extra decrease in the unemployment rate. By how much extra would you expect the unemployment rate to fall as a
result of the boost to GDP you calculated in (b) and (c)?


e) Suppose that with the interest rate decline the unemployment rate falls from 6% to 4.5%. What would the unemployment rate have been without this interest-rate decline?

f) Suppose that real GDP had been lower for each of three years by the amount you calculated in (b). How much poorer would Americans have been in terms of reduced income over those three years had the interest rate r not fallen?


g) In an America with about 135 million workers, how much is this lost income per worker?

Suppose the basic consumption level of Primaland is $10,000 million and that people save only 10% of their income. Government spending there is $5,000 million and the budget deficit is balanced while exports are $700 but Trade is balanced as well. The investment level is $6000 million; however, investment is independent of income and interest rate.

Aggregate Demand Z is defined as Z = C+I+G+(X-M) and the equilibrium condition is Y=Z.

The disposable income is YD=(Y-T).

Consumption is C=C0+c1YD and Investment is: I=I0.

a. Set up the model for this economy.

b. Calculate and graph the equilibrium level of income for this economy.

c. What is the multiplier of this Economy?

d. What is the level of consumption at equilibrium?

e. What is the saving level if S= -C0+0.1YD? What is it equal to?

Consumer confidence drops and people decide to "save" more or "consume" less by lowering their basic consumption to $8,000

f. What happens to the equilibrium Y = income and what happens to save, EXPLAIN.

In the country of Utopia, the structure of the economy is described as the following:

Y = C + I + G + (X – M)

C = C0 + (mpc)(DI)

I = I0 + (mpi)(Y)

M = M0 + (mpm)(DI)

DI = Y – T

T = (t)(Y)

Where Y is the level of real GDP in the economy, DI denotes the disposable income in the economy, C represents the level of consumption in the economy, C0 is the autonomous consumption level, mpc denotes the marginal propensity to consume, I is the level of investment in the economy, I0 characterizes the autonomous investment, mpi is the marginal propensity to invest, G characterizes the level of government expenditure, X is the level of export from the country, M represents the amount of import in the country, M0 is the level of autonomous import, mpm denotes the marginal propensity to import, T is the amount of tax imposed in the country, and t represents the average tax rate in the economy.

After extensive research, the economists in Utopia believe that the following values (all the dollar values are in number of millions) can be assigned to the structure of the economy, C0 = $500; mpc = 0.8; I0 = $200; mpi = 0.2; G = $400; X = $300; M0 = $100; mpm = 0.1; and t = 0.25. The Utopian economists further believe that the level of potential GDP in the country is $4,000.

Questions:

1. What is the demand side equilibrium level of real GDP in the country? Please show your calculations.

2. Is the overall Utopian economy in equilibrium? Elaborate your answer.

3. If the economy is not in equilibrium, what will happen eventually? Explain your answer.

4. What is the value of the overall multiplier? Please show your calculations and explain the value.

The country of Utopia is probably experiencing a recessionary pressure in its economy now. The economists are suspecting that, since the latest estimates of mpc, mpi, and mpm indicate that their estimated values have gone down to 0.65, 0.15, and 0.05 respectively.

5. What is the demand side equilibrium level of real GDP in the country now? Please show your calculations.

6. Is the overall Utopian economy now in equilibrium? Elaborate your answer.

7. If the economy is not in equilibrium now, what will happen eventually? Explain your answer.

8. What is the adjusted value of the overall multiplier? Please show your calculations and explain the value.

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