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?

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*.

3. Consider Prunella in (1). Let denote w as the wage rate and r
as the rental rate.
(a) Derive her total cost function.
(b) Based on (a), what is the marginal cost?
PS:1. Prunella raises peaches. L is the number of units of
labour she uses and T is the number of
units of land she uses, her output (bushels of peaches), denoted as
Q, is given by
Q =L*T^(1/2)
(a) Consider the short-run decision, in which she has...

Consider the following consumption decision problem. A consumer
lives for two periods and receives income of y in each period. She
chooses to consume c1 units of a good in period 1 and c2 units of
the good in period 2. The price of the good is one. The consumer
can borrow or invest at rate r. The consumer’s utility function is:
U = ln(c1) + δ ln(c2), where δ > 0.
a. Derive the optimal consumption in each period?...

1. Prunella raises peaches. L is the number of units of labour
she uses and T is the number of units of land she uses, her output
(bushels of peaches), denoted as Q, is given by Q = √ LT . (a)
Consider the short-run decision, in which she has a fixed amount of
land (T = 9). Does this production function exhibit the diminishing
marginal return on the labour input? Explain your answer.
(b) If she uses 4 units...

Consider a consumer with preferences over current and future
consumption given by U (c1, c2) = c1c2 where c1 denotes the amount
consumed in period 1 and c2 the amount consumed in period 2.
Suppose that period 1 income expressed in units of good 1 is m1
= 20000 and period 2 income expressed in units of good 2 is m2 =
30000. Suppose also that p1 = p2 = 1 and let r denote the interest
rate.
1. Find...

Consider a consumer with preferences over current and future
consumption given by U (c1, c2) = c1c2 where c1 denotes the amount
consumed in period 1 and c2 the amount consumed in period 2.
Suppose that period 1 income expressed in units of good 1 is m1
= 20000 and period 2 income expressed in units of good 2 is m2 =
30000. Suppose also that p1 = p2 = 1 and let r denote the interest
rate.
1. Find...

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...

1. In the short-run IS-LM model with income taxation, taxes are
given by ?=? +??. Suppose that MPC = 0.75 and the marginal tax rate
?=0.2. Then, when ? decreases by 1000, then for any given interest
rate, the IS curve shifts:
Select one:
a. to the left by 1000.
b. to the right by 3000.
c. to the right by 3750
d. to the right by 1875.
2.
Suppose that the adult population in an economy is 28 million,...

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