Macroeconomics II: Practice Problem Sets

Session 2 - Question 2: Labor market mechanisms and unemployment theories

1 Session 2 - Question 1: Natural rate of unemployment calculation

An economy possesses an active workforce of 20,000,000 individuals, out of which 18,000,000 hold jobs at present. The job-finding probability for any jobless worker is $f = 0.8$ per period, whereas the separation probability for an active worker is $s = 0.2$. Calculate the natural rate of unemployment prevailing in the steady-state equilibrium.

Session 2 - Question 2: Labor market mechanisms and unemployment theories

2 Session 2 - Question 2: Labor market mechanisms and unemployment theories

Identify the statement that is incorrect:

Session 2 - Question 2: Labor market mechanisms and unemployment theories

3 Session 2 - Question 3: Household labor supply decision

A representative consumer has preferences represented by the utility function:

$$U(C, H) = \ln(C) + \ln(H)$$

where $C$ corresponds to final consumption goods and $H$ denotes hours of non-working time (leisure). Total disposable time per day is 24 hours, divided between hours worked ($L$) and leisure ($H$), such that $H + L = 24$. Assuming an hourly real wage rate of $w = 2$, determine the optimal quantity of hours dedicated to work.

Session 2 - Question 2: Labor market mechanisms and unemployment theories

Select the true assertion regarding aggregate curves:

Session 2 - Question 2: Labor market mechanisms and unemployment theories

Session 2 - Question 5: Disinflation and unemployment policy options

As an economic advisor to policymakers, you are asked how the administration could engineer a reduction in the unemployment rate without inducing higher inflation. Which assessment should you deliver?

Session 2 - Question 2: Labor market mechanisms and unemployment theories

Session 2 - Question 6: Money in a frictionless Walrasian economy

Choose the correct statement concerning the role of money:

Session 3 - Question 1: Lucas aggregate supply specification

Consider the short-run aggregate supply formulation:

$$Y = \bar{Y} + \alpha(P - P^e)$$

Which of the following propositions is valid?

Session 3 - Question 2: Transmission mechanism with nominal wage rigidity

In an economy characterized by predetermined nominal contractual wages, suppose the central bank triggers an unforeseen expansion in the monetary base. Which sequence of events unfolds following this shock?

Session 3 - Question 3: Accelerationist Phillips curve with adaptive expectations

Assume economic agents form inflation expectations adaptively according to $\pi^e = \pi_{-1}$, and inflation dynamics are governed by a expectations-augmented Phillips curve. Which proposition is true?

Session 3 - Question 4: Lucas imperfect information framework

Under the Lucas 'islands' imperfect information model, what explains why producers expand production in response to an observed price rise?

Session 3 - Question 5: Derivation and properties of the Phillips curve

Which of the following propositions accurately characterizes the Phillips curve?

Session 3 - Question 6: Equilibrium inflation via Phillips curve and Okun's law

Consider an economy governed by the following structural relations:

Phillips curve:

$$\pi = \pi^e - \beta(u - \bar{u})$$

Okun's law:

$$\frac{1}{\alpha}(Y - \bar{Y}) = -\beta(u - \bar{u})$$

Suppose the structural parameters and state variables are:

$\pi^e = 2\%$

$\bar{u} = 5\%$

$\beta = 0.5$

$\alpha = 2$

The current output gap shows that real GDP exceeds potential GDP by 4%:

$$\frac{Y - \bar{Y}}{\bar{Y}} = 0.04$$

Determine the observed rate of inflation ($\pi$):

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Session 4 - Question 1: Fiscal shock in a small open economy

Take a small open economy where physical capital and labor endowments are held constant in the short run, fixing real output exogenously. Fiscal policy is defined by decisions on income tax revenues and public outlays. If the government implements an expansion in public expenditures, what is the consequence for national savings and the external trade balance?

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Session 4 - Question 2: Fiscal shock in a large open economy

Consider a large open economy in the short run, with domestic productive capacity predetermined. The government enacts a fiscal expansion by boosting public spending. What is the expected impact on the external trade balance?

Session 4 - Question 3: Ricardian model opportunity cost

Assume an international trade framework with two nations (A and B), two goods (automobiles and grain), and labor as the single production input. In Country A, manufacturing one automobile requires 10,000 labor hours, whereas producing one kilogram of grain requires 1 labor hour. What represents the opportunity cost of assembling a car in Country A?

Session 4 - Question 4: Comparative advantage and trade specialization

Continuing with the previous setting, suppose Country B requires 40,000 labor hours to produce an automobile and 2 labor hours to produce one kilogram of grain. If both economies engage in bilateral international trade, which outcome must occur?

Session 4 - Question 5: Absolute prices and real exchange rate comparison

Assume cars are the only traded commodity in the global economy. An automobile sells for $10,000 in the United States and €5,000 in Spain. The nominal exchange rate is pegged at$1 = €0.8. In which location is it cheaper to acquire a vehicle, and what is the relative price?

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