Let the measure of unemployed workers be denoted by u = uL + uH, be useful to

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Question:

Let the measure of unemployed workers be denoted by u = uL + uH, be useful to define the market tightness as θ ≡ ν/u. Once a match has been formed, the wage is determined through Nash bargaining, with β ∈ (0, 1) representing the worker's power. The output of all jobs is p > 0 per unit of time, i.e., p does not depend on the worker's type and p > zi , for all i. Also, while a firm is searching for a worker it has to pay a search (or recruiting) cost, pc > 0, per unit of time. All jobs are exogenously destroyed at rate λ >.

a) Write down the value functions for a firm and a worker of each type in all possible states.

b) Exploiting the free entry condition of firms, derive the analogue of the job creation (JC) curve for this economy.

c) Using the same methodology as in the lectures (adjusted to accommodate the differences in the new environment), derive the wage curve (WC) for this economy.

d) Combine the JC curve and the WC curve determined in the previous parts in order to provide an equation that (implicitly) determines the equilibrium θ. Compare with the analogous equilibrium condition from the lectures. For the remainder of this question, we will make an important change in the environment. We will assume that the total production of a filled job is given by px, where x is the match-specific (idiosyncratic) productivity. (But we will maintain the assumption that there are two types of workers and they enjoy a different unemployment benefit.) As in the theory of "endogenous job destruction", we will assume that existing matches get hit by a productivity shock at rate λ; when that happens the random variable x attains a new value drawn from the cdf G(x). This distribution is iid over time and has support in the interval [0, 1].

2 New jobsworker decide whether it is worth keeping the match alive and, if yes, they renegotiate over the wage. To answer the following questions make a conjecture about the equilibrium form, similar to the one we made in class in the endogenous job destruction theory.

e) In this new environment what is the unemployment rate of workers of type i = L and H? Is it the same? f) Write down the value functions for a firm in all possible states. g) Write down the value functions for a worker of each type in all possible states.

h) Without characterizing equilibrium (just using the economic intuition you have developed by studying these types of models) answer the following question: In the model with exogenous job destruction L-type workers are worse off compared to H-type workers because they get paid a lower wage. How is the well being of L-types compared to that of H-types affected as we switch from the model of exogenous to the model of endogenous job destruction? (Hint: Compare the wage the two types receive but also the length of time for which they get to keep this wage, since now job destruction is endogenous.)

A closed economy can be described by the long-run classical model:

Y = 5000

C = 950 + 0.5(Y - T) - 70r

I(r) = 3000 - 30r

Note: r is measured in percentage points (i.e., if r = 5, then r = 5%).

Initially, the government collects 14% of output as income taxes and it runs a budget surplus of 100.

Part (a) Find the equilibrium levels of real interest rate and investment.

Part (b) Suppose the business confidence index changes from 113 to 115. As a result, autonomous investment changes by 6%. Find the new equilibrium levels of real interest rate, and investment.

Note: you will need to decide whether autonomous investment increases or decreases.

Part (c) (continued from part b) Suppose the government wants to raise its budget surplus by 60 via a change in government spending. Find the level of government spending that could achieve this goal and the new level of investment.

ensure to answer all questions.