Question : Monetary Neutrality/Non-Neutrality

Suppose that we have a partially sticky price New Keynesian model. Suppose that the consumption and investment demand functions are given by:

Ct= 40 + 0.8Yt- 200rt

It= 250 - 300rt

The resource constraint is Ct+ It+ Gt= Yt

Government spending is exogenous and equal to 20 (Gt= 20).Lastly, suppose the LM function is given by: rt= 0.1 + 0.1Yt- 0.4Mt+ 2Pt

a. Derive an expression for the AD curve.

Hint: Find the IS curve first and use it along with the LM curve to derive an expression for Ptas a function of Ytand other variables (only other variable is Mtin this example).

b. In the partially sticky price model, the AS curve is given by Pt= 2.8 + 0.008Yt. Use this along with AD curve to derive an expression for the equilibrium level of output (derive an expression for Ytas a function of Mt).

c. Suppose that Mt= 100. Use your answer for part (b) to solve for numeric values of Yt,rt,Ct,and It.

d. Suppose that Mtincreases from 100 to 110. Solve for new numeric values of Yt,rt, Ct,and It. How does the equilibrium level of output change when Mtchanges? Does the concept of monetary neutrality hold in this case? Explain!