Consider a money-in-the-utility function model with inelastic supply of labor. Suppose that preferences are given by:
Where and . The household budget constraint is:
Output is produced according to a classical Cob-Douglass production function with constant productivity ( ). Suppose that nominal money supply grows at the rate and it's deviation from steady state ( ) evolve according to:
Where
a) Define and characterize the competitive equilibrium
b) Solve for a steady state of the economy. Is money super-neutral in this model? Why?
c) Derive the money demand function.
d) Explain the propagation mechanisms of the model.