Question

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?