Question

a. Consider a household living for two periods. The intertemporal budget constraint is given by:

?₁ + _/?_2/1+r = ?₁ + /y_2/1+r ,

where ? is consumption, ? is income and ? is the interest rate. The household’s preferences are characterised by the utility function.

?(?₁, ?₂ ) = ln ?₁ + ? ln ?₂,

where ? < 1 is the discount factor. Derive the Euler equation.

b. Consider the bathtub model of unemployment. Let ? denote the constant labour force, let ? denote employment and let ? denote unemployment. The job-finding rate is denoted ? and that the job-separation rate is denoted ?. Derive an expression for the unemployment rate.

c. In recent years, many inflation targeting central banks have been struggling with inflation being too low, and some even with deflation. Explain why deflation may be a problem.

e. In the Pissarides search and matching model, the equilibrium is characterised by the following three equations:

? = ? /? + ??(?) ,

? − ? = (? + ?)?? /?(?) ,

? = (1 − ?)? + ??(1 + ??),

where ? is unemployment, ? is labour market tightness and ? is the wage.

Analyse the effect of a decrease in unemployment benefits, Z.

Answer 1

c)

This leads to an overall decline in asset prices as producers are forced to liquidateinventories that people no longer want to buy. Consumers and investors alike begin holding onto liquid money reserves to cushion against further financial loss. As more money is saved, less money is spent, further decreasing aggregate demand.

At this point, people's expectations about future inflation are lowered, and they begin to hoard money. Why would you spend a dollar today when the expectation is that it could buy effectively more stuff tomorrow? And why spend tomorrow when things may be even cheaper in a week's time?