Question

1. Consider a model of unemployment where the changes in the unemployment rate (u) is given by ?u=(b+s)-(b+s+f)u, where b is the rate of entry in the labor force, s is the seperation rate and f is the job findings rate. a. Derive an expression for the steady-state unemployment rate u*.

Answer #1

Consider how unemployment would affect the Solow growth model.
Suppose that output is produced according to the production
function Y = Kα [(1 – u)L]1-α where K is
capital, L is the labor force, and u is the natural rate of
unemployment. The national saving rate is s, the labor force grows
at rate n, and capital depreciates at rate δ.
a. Write a condition that describes the golden rule
steady state of this economy.
b. Express the golden rule...

3.
Assume that
the unemployment dynamics in the U.S. are represented by the
following equations:
LF = U +
E
ΔU =
s(E) – f(U),
Where LF
stands for Labor Force, s is the separation rate (the rate at which
those employed separate from their jobs), and f is the finding rate
(the rate at which those unemployed find a new job). Assume that LF
= 1,000. Separation rate (s) = 5%, and finding rate (f) = 4%. Solve
the...

a. Consider a household living for two periods. The
intertemporal budget constraint is given by:
?1 + /?2/1+r =
?1 + /y2/1+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...

Consider a version of the Solow model where population grows at
the constant rate ? > 0 and labour efficiency grows at rate ?.
Capital depreciates at rate ? each period and a fraction ? of
income is invested in physical capital every period. Assume that
the production function is given by:
?t =
?ta(?t?t
)1-a
Where ??(0,1), ?t is output, ?t is
capital, ?t is labour and ?t is labour
efficiency.
a. Show that the production function exhibits constant...

This question refers to the job search model of the natural rate
of unemployment that we covered in the additional material to
chapter 15. Suppose the economy is in a long-term equilibrium (at a
steady-state unemployment rate), with a separation rate of 0.03 per
month and a job finding rate of 0.12 per month. Assume the labor
force is 200 million people. In equilibrium, how many individuals
lose their jobs each month?

Consider the production function Y = F (K, L) = Ka *
L1-a, where 0 < α < 1. The national saving rate is
s, the labor force grows at a rate n, and capital depreciates at
rate δ.
(a) Show that F has constant returns to scale.
(b) What is the per-worker production function, y = f(k)?
(c) Solve for the steady-state level of capital per worker (in
terms of the parameters of the model).
(d) Solve for the...

Explain why a policy aimed at lowering the natural rate of
unemployment given by the steady state model must either reduce the
rate of job separation or increase the rate of jobs finding

Suppose output is given by
Y = K 1/2 (AN) 1/2
As in the basic model, the workforce grows at rate n, capital
depreciates at rate d and the savings rate is s. In addition,
suppose that TFP grows at a constant rate g. That is:
∆A/A = g
We will refer to the product AN as the “effective workforce”. It
follows that the effective workforce grows at rate n + g.
a. Express the production in per “effective worker”...

If the economy were at a steady-state unemployment rate with a
separation rate of .02 per month and a job-?nding rate of .10 per
month and the labor force was 100 million.
PART A. What is the natural unemployment rate? How many
individuals would lose their jobs
each month?
PART B. Suppose the job separation rate is still .02 per month
and the rate of job ?nding is
now .13 per month. What is the natural unemployment rate? How
many...

Consider a simple economy with search unemployment. The matching
function is given by
M =
eQ^(1/2)A^(1/2)
There were initially Q = 1000 unemployed workers
looking for a job. Let b = 0.5, z = 1,
k = 0.1, e = 3/5 and a
= 0.5, where k is the cost of creating a
vacancy.
Provide the expression for the Beveridge curve.
Calculate and interpret the slope of the Beveridge curve for
the current state of the economy.
How does a...

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