Question

8) Consider an economy in long-run equilibrium with an inflation rate () of 0.08 per year and a natural unemployment rate of 0.05. Suppose Okun's law holds and a one percentage point unemployment rate reduces real output by 2% of full-employment output. The expectation-augmented Phillips curve is givep by increase in the т . ne . 2.5 (u-005). Consider a two distr maErTTelintyear,π .006 and me . 008. In the second year, π.004 and㎡. (a) In the first year, what is the value of the unemployment rate? Go o,o-25 lu-oo)u. (b) In the first year, by what percentage does output fall short of full-employment output? O.05t-0,oso O.08 (e) In the second year, what is the value of the unemployment rate? a-2os)Oo.t V(d) In the second year, by what percentage does output fall short of full V(e) What is the sacrifice ratio for this disinflation? output? 6) Explain how each of the following events would affect the short-run aggregate supply curv a. A decrease in the price level b. A decrease in what the price level is expected to be in the future c. A price level that is currently lower than expected d. An unexpected decrease in the price of an important raw material e. A decrease in the labor force 6)

Answer 1

You have posted two unrelated questions in one post. I will address all the sub parts of the firs t question only. Please post the second question separately.

Part (a)

Applying the equation for the first year,

0.06 = 0.08 - 2.5 x (u - 0.05) = 0.08 - 2.5u + 0.125 = 0.205 - 2.5u

Hence, u = (0.205 - 0.06) / 2.5 = 0.058 = 5.80% = value of unemployment rate

Part (b)

Cyclical unemployment = u - 0.05 = 0.058 - 0.05 = 0.008 = 0.8%

Hence, the output shortfall = 2% x 0.8% = 1.6%

Part (c)

Applying the equation for the second year,

0.04 = 0.05 - 2.5 x (u - 0.05) = 0.05 - 2.5u + 0.125 = 0.175 - 2.5u

Hence, u = (0.175 - 0.04) / 2.5 = 0.054 = 5.40% = value of unemployment rate

Part (d)

Cyclical unemployment = u - 0.05 = 0.054 - 0.05 = 0.004 = 0.4%

Hence, the output shortfall = 2% x 0.4% = 0.8%

Part (e)

Sacrifice ratio = coefficient of (u - 0.05) = 2.5