Examen de Introducció a la Macroeconomia UPF 2021 · Final Exam - March 2021

Part I: Questions 1-20 (5 points). Multiple Choice Section

Choose the single correct option for each of the following questions:

a.

Regarding price indices and inflation:

b.

During the late 1990s, Japan experienced a declining GDP deflator. From this information, we know with certainty that:

c. Let private consumption be given by $C = c_0 + c_1(Y - T)$. As vaccination spreads and consumer confidence recovers, assume the marginal propensity to consume $c_1$ increases. Consequently:

.

d.

Identify the correct macroeconomic relationship:

.

g.

Which of the following changes reduces the money multiplier?

.

h.

What constitutes high-powered money (also known as the monetary base or central bank money)?

.

e.

Regarding the dynamics of the labor market:

.

f.

In the short run, monetary policy is more potent at altering real output (GDP) when:

.

Use the following extended IS-LM framework to answer Questions i to l:

$$IS: Y = C(Y - T) + I(Y, r + x) + G$$

$$LM: r = \bar{r}$$

i.

An increase in the risk premium $x$ produces:

.

j.

In equilibrium, an increase in government purchases $G$ leads to:

.

k.

A simultaneous and identical increase in government purchases and taxes ($dG = dT > 0$) leads to:

.

l.

Suppose the central bank conducts an expansionary monetary policy by lowering the policy interest rate. How is this represented in the IS-LM framework?

.

n.

Which of the following events triggers a shift in the Phillips curve?

o.

When inflation expectations are fully anchored:

m.

In the standard IS-LM-PC model, which policy or shock lowers the unemployment rate in the medium run?

p.

For an economy that imports all its oil, a permanent fall in the world price of crude oil causes what medium-run outcome?

q.

In the Solow model with population growth $g_n$ and no technological progress ($g_A = 0$), an increase in $g_n$:

.

r.

A policymaker asserts that the only mechanism to sustain a higher long-run growth rate of output per capita is to increase the rate of technological progress. As an economist, you:

.

s.

Consider a nation initially resting in its Solow steady state. A severe earthquake destroys a significant share of the physical capital stock without causing any loss of human life. In the aftermath of this disaster, the economy will:

.

t.

Two countries are identical in all structural parameters except that Country 1 has a higher saving rate than Country 2. In the Solow steady state, Country 1 will have a level of total output and a rate of growth of output per worker compared to Country 2.

.

Question 1 (2.0 points). Extended IS-LM Model with Pandemic Risk and Policy Responses

Consider the following extended IS-LM framework:

$$\text{IS: } Y = C(Y - T, Q) + I(Y, r + x, Q) + G$$

$$\text{LM: } r = \bar{r}$$

There is a single homogeneous good utilized for private consumption, private investment, or government expenditure. Firms satisfy whatever quantity is demanded at the prevailing price level. This model departs from the benchmark framework through two specific modifications:

$Q$ captures the perceived probability/risk of a systemic economic crisis triggered by an exogenous event (such as a pandemic, conflict, or terrorist attack). Both private consumption and investment depend negatively on $Q$.

$r$ denotes the risk-free real interest rate set by the central bank ($r = i - \bar{\pi}^e$, where expected inflation is anchored and held constant).

$x$ represents the exogenous risk premium demanded by financial intermediaries over the risk-free real rate to fund business investment.

a)

[0.3 points] Draw the standard IS-LM diagram. Label both axes and clarify the slope of each schedule. Identify the point where both goods and financial markets clear simultaneously.

b)

[0.3 points] Assume the economy is hit by COVID-19, causing households and firms to fear economic collapse, which manifests as an increase in $Q$. Illustrate the impact of this exogenous shock on the IS-LM diagram and describe the qualitative adjustments in output and the real interest rate.

c)

[0.3 points] Assuming no macroeconomic policy intervention occurs, summarize the directional effect of the pandemic shock on each of the following variables by indicating ↑ (increase), ↓ (decrease), → (constant), or ? (uncertain):

Variable

Direction of Change

Consumption ($C$)

Investment ($I$)

Production ($Y$)

Income ($Y$)

Real interest rate ($r$)

d)

[0.3 points] In response to the crisis, European and OECD governments rolled out substantial fiscal stabilization packages to preserve productive capacity and support household disposable income. Depict the graphical impact of these expansionary fiscal measures on the IS-LM diagram relative to the post-shock position.

e)

[0.3 points] State the impact of this expansionary fiscal package on consumption, investment, production, income, and the real interest rate using the same directional indicators (↑, ↓, →, ?):

Variable

Direction of Change

Consumption ($C$)

Investment ($I$)

Production ($Y$)

Income ($Y$)

Real interest rate ($r$)

f)

[0.2 points] Consider now the monetary policy environment in the euro area:

Between March and December 2020, key ECB policy rates remained constant (MRO at 0.00%, marginal lending at 0.25%, deposit facility at -0.50%). Why did the ECB decide not to lower its key interest rates further?

g)

[0.3 points] Instead, the ECB deployed unprecedented asset purchase programs (expanding APP and creating PEPP). Assuming these purchase programs directly reduce the risk premium $x$ without altering $G, T, Q$, or $r$, explain and illustrate how this monetary response impacts the IS-LM equilibrium.

Question 2 (1.5 points). Medium-Run Equilibrium and the IS-LM-PC Framework

Consider an economy that in December 2019 (period $t$) was in medium-run equilibrium with actual and expected inflation both equal to 2% ($\bar{\pi} = \bar{\pi}^e = 2\%$). The aggregate production function is linear in labor:

$$Y_t = N_t$$

The central bank sets the nominal policy interest rate such that the real interest rate is fixed at a given value $r$. The nominal rate is at the zero lower bound. Inflation expectations follow an adaptive/anchored pattern given by $\bar{\pi}_t^e = \bar{\pi}_{t-1}$.

In 2020 (period $t+1$), a pandemic forces a mandatory lockdown across key economic sectors. The lockdown causes substantial cost increases, represented in our framework as an increase in the firm markup $m$.

a)

(0.3 points) Using the wage-setting (WS) and price-setting (PS) equations, depict the medium-run labor market equilibrium before and after the shock. State the mathematical equations for both curves and provide an economic interpretation of the changes in the natural unemployment rate and real wages.

b)

(0.3 points) Graphically illustrate the Phillips curve (relating output $Y$ to the change in inflation $\bar{\pi}_t - \bar{\pi}_{t-1}$) before and after the pandemic. Write down the equation of the Phillips curve and explain the shift in potential output from $Y_n$ to $Y'_n$.

c)

(0.3 points) Suppose the crisis not only affects locked-down sectors, but also depresses general consumer and business confidence, such that aggregate demand contracts by an amount greater than the reduction in potential output. Represent the short-run equilibrium in an IS-LM-PC diagram. Is this point a medium-run equilibrium? Describe the behavior of output and inflation.

d)

(0.3 points) Suppose the fiscal authority expands public expenditure $G$ by exactly the amount needed to compensate for the drop in private consumption and investment. Show the new short-run equilibrium on the IS-LM-PC diagram. Is this sustainable as a medium-run equilibrium if the lockdown persists?

e)

(0.3 points) Propose an alternative, more suitable policy mix for this economy instead of the one outlined in part 2.4 (part d). Justify your answer using macroeconomic reasoning and an IS-LM-PC diagram.

Question 3 (1.5 points). Solow Growth Model with Technological Progress

Consider the canonical Solow growth model with labor-augmenting technological progress and population growth. The aggregate production function is Cobb-Douglas:

$$Y = K^{\bar{a}} (AN)^{1 - \bar{a}}$$

where $K$ is physical capital, $N$ is labor input, $A$ is technology, and $\bar{a}$ (with $0 < \bar{a} < 1$) is an exogenous constant. Technology and population grow at constant exogenous rates $g_A$ and $g_n$, respectively:

$$\frac{\Delta A}{A} = g_A, \quad \frac{\Delta N}{N} = g_n$$

A constant fraction $\delta$ (with $0 < \delta < 1$) of physical capital depreciates each period. The aggregate saving rate is constant at $s$.

a.

Define capital per effective worker as $k \equiv \frac{K}{AN}$. Derive the steady-state level of capital per effective worker, $k^*$, as a function of the model parameters. [0.3 points]

b.

Express the steady-state level of output per effective worker, $y^* \equiv \frac{Y}{AN}$, as a function of the parameters. [0.2 points]

c.

Derive the steady-state level of consumption per effective worker, $c^*$, as a function of the parameters. [0.3 points]

Now assume the economy has reached its steady state. Due to the long-term disruptions of the pandemic, investment in basic research and R&D falls permanently, causing a permanent reduction in the rate of technological progress from $g_A$ to $g_A' < g_A$.

d.

Using the Solow steady-state diagram, explain how the growth rate of income per effective worker responds in the initial transition years following this shock. [0.3 points]

e.

Is the long-run growth rate of output per capita (income per worker) affected by this shock? Justify your answer. [0.2 points]

f.

What happens to the steady-state level of capital per effective worker ($k^*$)? [0.1 points]

g.

Will long-run living standards (measured by the level and trajectory of output per worker over time) increase or decrease as a result of this permanent drop in R&D? [0.1 points]