Part B. Numerical exercise (32 points). The aggregate demand of one IS-LM-PC economy is characterized by the following set of equations: C₁ = 50+0.6(Yt − T) ; It = 30+0.2Y₁ − 140(rt+x); T = G = 100; it = 0.05; x = 0. On the supply-side, the production function is Y₁ = Nt, the labor force is L= 600, and the Phillips curve is πtπ=0.001 (Yt - Yn) In the current period (year t), the economy is in a medium-run equilibrium with π = π = 0.02 (2%). i) Write down the IS curve and the LM line, and find the equilibrium values for the endogenous variables Yt, rt, Ct, It, ut, and πt. ii) There is a financial crisis in year t +1 and the risk premium rises to 3.25%, x' = 0.0325, while expected inflation is still +1 ==0.02. Such financial turmoil creates a demand contraction in the IS-LM-PC model, and there is no initial reaction by either the government or the central bank (G, T and i remain unchanged). Derive the new IS curve and obtain the equilibrium values for Yt+1, rt+1, C++1, It+1, ut+1, and #++1, comparing them with their values before the financial crisis. iii) In year t +2, risk premium is still high at 3.25%, expected inflation de-anchors and it is revised to the observed value of lagged inflation +2 = +1, and the central bank decides to intervene to restore the medium-run equilibrium. Find the value of the nominal interest rate set by the central bank to (try to) return to medium-run equilibrium. (Hint: You should find that the required nominal interest rate is negative and the zero lower bound on it+2 becomes a constraint that must be satisfied by the central bank). Report the values for Yt+2, Tt+2, Ct+2, It+2, ut+2, and ++2 obtained when monetary policy is constrained by the zero lower bound. Show the evolution of the economy over years t, t+1 and t+2 in a graphical display using the (r,Y) and (π - πe, Y) diagrams.
Part B. Numerical exercise (32 points). The aggregate demand of one IS-LM-PC economy is characterized by the following set of equations: C₁ = 50+0.6(Yt − T) ; It = 30+0.2Y₁ − 140(rt+x); T = G = 100; it = 0.05; x = 0. On the supply-side, the production function is Y₁ = Nt, the labor force is L= 600, and the Phillips curve is πtπ=0.001 (Yt - Yn) In the current period (year t), the economy is in a medium-run equilibrium with π = π = 0.02 (2%). i) Write down the IS curve and the LM line, and find the equilibrium values for the endogenous variables Yt, rt, Ct, It, ut, and πt. ii) There is a financial crisis in year t +1 and the risk premium rises to 3.25%, x' = 0.0325, while expected inflation is still +1 ==0.02. Such financial turmoil creates a demand contraction in the IS-LM-PC model, and there is no initial reaction by either the government or the central bank (G, T and i remain unchanged). Derive the new IS curve and obtain the equilibrium values for Yt+1, rt+1, C++1, It+1, ut+1, and #++1, comparing them with their values before the financial crisis. iii) In year t +2, risk premium is still high at 3.25%, expected inflation de-anchors and it is revised to the observed value of lagged inflation +2 = +1, and the central bank decides to intervene to restore the medium-run equilibrium. Find the value of the nominal interest rate set by the central bank to (try to) return to medium-run equilibrium. (Hint: You should find that the required nominal interest rate is negative and the zero lower bound on it+2 becomes a constraint that must be satisfied by the central bank). Report the values for Yt+2, Tt+2, Ct+2, It+2, ut+2, and ++2 obtained when monetary policy is constrained by the zero lower bound. Show the evolution of the economy over years t, t+1 and t+2 in a graphical display using the (r,Y) and (π - πe, Y) diagrams.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Part B. Numerical exercise (32 points). The aggregate demand of one IS-LM-PC economy is
characterized by the following set of equations: C₁ = 50+0.6(Yt − T) ; It = 30+0.2Y₁ − 140(rt+x); T =
G = 100; it = 0.05; x = 0. On the supply-side, the production function is Y₁ = Nt, the labor force is
L= 600, and the Phillips curve is
πtπ=0.001 (Yt - Yn)
In the current period (year t), the economy is in a medium-run equilibrium with π = π = 0.02 (2%).
i) Write down the IS curve and the LM line, and find the equilibrium values for the endogenous
variables Yt, rt, Ct, It, ut, and πt.
ii) There is a financial crisis in year t +1 and the risk premium rises to 3.25%, x' = 0.0325, while
expected inflation is still +1 ==0.02. Such financial turmoil creates a demand contraction in the
IS-LM-PC model, and there is no initial reaction by either the government or the central bank (G, T and
i remain unchanged). Derive the new IS curve and obtain the equilibrium values for Yt+1, rt+1, C++1,
It+1, ut+1, and #++1, comparing them with their values before the financial crisis.
iii) In year t +2, risk premium is still high at 3.25%, expected inflation de-anchors and it is revised to
the observed value of lagged inflation +2 = +1, and the central bank decides to intervene to restore
the medium-run equilibrium. Find the value of the nominal interest rate set by the central bank to (try
to) return to medium-run equilibrium. (Hint: You should find that the required nominal interest rate
is negative and the zero lower bound on it+2 becomes a constraint that must be satisfied by the central
bank). Report the values for Yt+2, Tt+2, Ct+2, It+2, ut+2, and ++2 obtained when monetary policy is
constrained by the zero lower bound. Show the evolution of the economy over years t, t+1 and t+2 in
a graphical display using the (r,Y) and (π - πe, Y) diagrams.
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