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?
