(A Two-Period Sticky-Price Model). Consider a two-period, sticky-price economy like the one studied in lectures 11-13. Suppose that the household’s intertemporal optimality condition is of the form C2 C1 = β P1 P2 (1 + i), where C1 and C2 denote consumption in periods 1 and 2, P1 = P2 = 1 denote the price levels in periods 1 and 2, β = 0.9 denotes the subjective discount factor, and i denotes the nominal interest rate, which must satisfy the zero lower bound (ZLB). Suppose further that the full employment levels of output in periods 1 and 2 are given by Y¯ 1 = Y¯ 2 = 1, and that the economy is always at full employment in period 2 (the long run). Part 1: Suppose the central bank sets the nominal interest rate at the level i ∗ that minimizes unemployment without overheating. Calculate i ∗ . Part 2: Suppose that due to bad expected meteorological conditions, the full-employment level of output in period 2 is revised down to 0.8. Suppose that in response to this news, in period 1 the central bank keeps the interest rate at i ∗ , the value you calculated in the previous question. The fiscal authority, however, steps in and increases government spending from 0 to G∗ in period 1, to ensure full employment and no overheating. Calculate G∗
(A Two-Period Sticky-Price Model). Consider a two-period, sticky-price economy like the one studied in lectures 11-13. Suppose that the household’s intertemporal optimality condition is of the form C2 C1 = β P1 P2 (1 + i), where C1 and C2 denote consumption in periods 1 and 2, P1 = P2 = 1 denote the price levels in periods 1 and 2, β = 0.9 denotes the subjective discount factor, and i denotes the nominal interest rate, which must satisfy the zero lower bound (ZLB). Suppose further that the full employment levels of output in periods 1 and 2 are given by Y¯ 1 = Y¯ 2 = 1, and that the economy is always at full employment in period 2 (the long run).
Part 1: Suppose the central bank sets the nominal interest rate at the level i ∗ that minimizes
Part 2: Suppose that due to bad expected meteorological conditions, the full-employment level of output in period 2 is revised down to 0.8. Suppose that in response to this news, in period 1 the central bank keeps the interest rate at i ∗ , the value you calculated in the previous question. The fiscal authority, however, steps in and increases government spending from 0 to G∗ in period 1, to ensure full employment and no overheating. Calculate G∗
Step by step
Solved in 4 steps with 3 images
