Question

Consider our medium-run model of the economy:

Y =C(Y −T)+I(Y,r+x)+G (IS)

r=r(bar) (LM)

πt − πt − 1 = −α(u_t − u_n) (PC)

Suppose the economy starts at a point such that u_t = u_n and r=r_n Graph the effects of a financial shock that increases the risk premium, x. What happens to output, the interest rate, and inflation in the short-run? What happens in the medium-run? What mechanism causes the transition from the short-run equilibrium to the medium-run equilibrium?

Answer 1

A needed relation is Y - Yn = -L•(u - un);

where Y = current output (dropping t index)

Yn -= natural level of output at the natural rate of unemployment

L = labor force u = current unemployment rate

π - π(-1) = (α/L) (Y - Yn); where π(-1) = π(t-1),

Inflation rate for previous period relative to current rate π = πt and πt e = πt−1 i.e, that future expected inflation is equal to inflation in the past period.

The IS-LM-PC model tells us that when output is above potential, the real interest rate r rises and the change in inflation rate decreases toward zero. When output is below potential, the change in inflation rate increases toward zero. The Phillips curve thus increases with increasing output, and crosses the horizontal axis where Y = Yn, the value of output which stabilizes inflation. In the medium run, output is equal to potential output. In the left diagrams in equilibrium at point A, Y > Yn, output is above potential, and inflation is increasing.

This is a short-run equilibrium. If r does not change over time, inflation continues to increase.

In the medium run, real policy interest r will be raised in response to inflation and “overheating” of the economy. In the right diagrams, the new medium run equilibrium is shown at A′, at which r′ = rn , where rn = the natural rate of interest. This adjustment is difficult to make precisely by the central bank, because potential output Yn is not well known, the signal is noisy, and there is a lag in economic response, consumer response, demand response, etc. Thus to attain a stable inflation over the medium run, the initial boom may in the short run be followed by an overcorrection and a recession. If we assume that inflation will be constant = (π�), termed a so-called anchored inflation expectation,