Question

The wage setting equation is W = P(1 − u) (this means that the workers’ reservation wage z is normalized to 1), and the markup is 20%. (i) Calculate the natural rate of unemployment un. (ii) Calculate the natural rate of unemployment corresponding to a 5% increase in the markup (that is, m = 25%). (iii) Calculate the natural rate of unemployment corresponding to a 5% reduction in the reservation wage (that is z = .95).

Answer 1

(i) The wage setting equation is given by

W=P(1-u) [ where z = 1]

or W/P = 1-u ..... (1)

When m = 20% ( or 0.20) , the price setting equation is given by,

P=(1+0.20) W

or W/P = 1/1.20 .................(2)

From (1) & (2), we get:

1-u = 1/1.20

=> u = 1- 1/1.20 ................(3)

=> natural rate of unemployment = u = 0.16666 or 16,67%

(ii) Since u= 1-W/P (as shown above)

When m is 25% (or 0.25),

u = 1 - 1/ 1+0.25

=> => natural rate of unemployment = u = 1- 1/1.25 = 0.20 or 20%

(iii) With z = 0.95 (ceteris paribus), natural rate of unemployment is given by,

u = 0.95 - 1/1.20 = 0.1166 or 11.67% (when, z=0.95 and m=20%)

u = 0.95 - 1/1.25 = 0.15 or 15% (when, z=0.95 and m=25%)