Universitat Pompeu Fabra
Introduction to Macroeconomics 2023-24
Teresa Garcia-Milà, María Gundín, Alberto Martín, Luigi Pascali
Problem set 5
Question 1
Consider the price-setting relation (in the simple case when productivity is constant and equal to
one):
𝑊𝑊
1
=
𝑃𝑃
1 + 𝑚𝑚
where m is the mark-up over the marginal cost that firms can charge when they have market power
in the goods markets.
a. Explain why an increase in the mark-up m implies that the real wage is lower.
b. Draw this price-setting relation on the (u, W/P) graph, where u is the unemployment rate and
W/P is the real wage. Graphically show how the real wage changes when there is an increase in the
markup.
c. Now draw the wage-setting relation and explain this relationship.
d. Assume that, due to stricter antitrust regulation, there is a decline in market power. What will
happen to the natural rate of unemployment?
e. Suppose that the parliament approves a rise in the minimum wage to further help workers. Show
graphically the new equilibrium.
f. What happens to the real wage and the natural rate of unemployment?
Question 2
Consider the following wage- and price-setting equations in the country of Mediterranea:
- wage-setting relation (WS):
𝑊𝑊
- price-setting relation (PS):
𝑊𝑊
𝑃𝑃
𝑃𝑃
= 0.2 + 𝑧𝑧– 𝑢𝑢
𝐴𝐴
= (1+𝑚𝑚)
a. Suppose that, due to technological change, workers in Mediterranea become more productive.
What is the effect on equilibrium wages and unemployment? Explain.
b. Suppose that the new technology makes workers more productive, but also easier to substitute
for machines. This decreases the bargaining power of workers, which we can capture by a decline
in z. What is the effect on equilibrium wages and unemployment? Explain.
c. Given your previous answers, are workers in Mediterranea in favor of the new technology or not?
Explain your reasoning.
Question 3
Consider a labor market that works according to the wage- and price-setting equations as seen in
class. Suppose that the government mandates that employers provide higher benefits to workers,
in a manner proportional to their wage. Specifically, besides paying the wage W, the firm must pay
than additional 𝜌𝜌 × 𝑊𝑊 which is added to the cost of labor.
What happens to unemployment, the real wage, and total worker compensation as a consequence
of this regulation? Show your answer graphically and provide an intuition.
Hint: Take into account that, when bargaining with employers, employees take into account their
entire compensation (i.e., including benefits), and not just the wage.
Question 4
Consider the labor market equations seen in class:
- wage-setting relation (WS):
- price-setting relation (PS):
𝑊𝑊
𝑃𝑃
𝑊𝑊
= 0.55 + 0.5 ∙ 𝑧𝑧– 𝑢𝑢
𝐴𝐴
= (1+𝑚𝑚)
𝑃𝑃
And assume z=0.6, m=0.25, A=1.
a. Calculate the equilibrium natural rate of unemployment 𝑢𝑢𝑛𝑛 (that is, find the equilibrium when
WS=PS).
𝑊𝑊
b. Calculate the corresponding equilibrium real wage � 𝑃𝑃 � .
𝑛𝑛
𝑊𝑊
c. Suppose that z increases to 0.65, what happens to u𝑛𝑛 , and � 𝑃𝑃 � ?
𝑛𝑛
d. Suppose instead that, starting from the original values for z, m, and A, the markup increases to
𝑊𝑊
m=1/3. What happens to u𝑛𝑛 , and � 𝑃𝑃 � ?
𝑛𝑛