Question Ten: Nominal Rigidity Assume that the Bank of Zambia has the ability to control real interest rate. And suppose the economy is described by two equations. The IS equation given as Yt=rt/ while the money-market equilibrium condition: mp=L(r+e;Y). Where Lr+e< 0;LY>0;m and p denote logM and logP. a. Suppose prices respond partially to increases in money. Specifically, assume that dp= dm is exogenous, with 0<dp=dm<1. Also assume e=0. i. Find an expression for d r=dm. ii. Does an increase in the money supply lower the real interest rate? b. Suppose increases in money also affect expected inflation. Specifically, assume that de= dm is exogenous, with de=d m>0. Continue to assume 0<dp=dm<1. i. Find an expression for dr=dm. ii. Does an increase in the money supply lower the real interest rate? iii. Does achieving a given change in r require a change in m smaller, larger, or the same size as in part (a)? c. Consider Keynes's model of nominal rigidity where nominal wages are completely unresponsive to current developments, there is labour market imperfection, and firms are competitive with flexible prices. If there is an increase demand brought about by an increase in money stock, what would be the impact of this increase in demand on the real wage and output? You may use graphs to illustrate your answer. d. In your own words, explain the Lucas Critique and its implications for policy decisions based on statistical/econometric relationships..

1. Question Ten: Nominal Rigidity Assume that the Bank of Zambia has the ability to control real
interest rate. And suppose the economy is described by two equations. The IS equation given as
Yt=rt/ while the money-market equilibrium condition: mp=L(r+e;Y). Where Lr+e< 0;LY>0;m and p
denote logM and logP. a. Suppose prices respond partially to increases in money. Specifically,
assume that dp= dm is exogenous, with 0<dp=dm<1. Also assume e=0. i. Find an expression for d
r=dm. ii. Does an increase in the money supply lower the real interest rate? b. Suppose increases
in money also affect expected inflation. Specifically, assume that de= dm is exogenous, with de=d
m>0. Continue to assume 0<dp=dm<1. i. Find an expression for dr=dm. ii. Does an increase in the
money supply lower the real interest rate? iii. Does achieving a given change in r require a change
in m smaller, larger, or the same size as in part (a)? c. Consider Keynes's model of nominal rigidity
where nominal wages are completely unresponsive to current developments, there is labour
market imperfection, and firms are competitive with flexible prices. If there is an increase demand
brought about by an increase in money stock, what would be the impact of this increase in
demand on the real wage and output? You may use graphs to illustrate your answer. d. In your
own words, explain the Lucas Critique and its implications for policy decisions based on
statistical/econometric relationships.