Mock Exam
Advanced Macroeconomics I
Christian Manger xx.xx.2025
Winter Semester 2024/25
1. The Solow Model without technological progress
Consider a Solow model without technological progress:
L̇ = nL (1)
K̇ = sY − δK (2)
α 1−α
Y = K L (3)
(a) Explain the economic intuition behind (2).
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(b) Express per-capita output and the real wage as function of the capital labour ratio
k = K/L.
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(c) Compute the steady state level of k.
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(d) Explain how the properties of the Neoclassical production functions make sure that we
have a unique steady state with k∗ > 0 (of course keeping our standard assumptions
for the Solow model).
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(e) Evidence shows a negative correlation between wages and fertility. Name and brie y
explain one economic reason.
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(f ) Assume that population grows at rate n if w < w and it grows at rate n′ < n if
w ≥ w. Illustrate in a diagram why there can be two steady states with k > 0. Specify
parameter restrictions for which there are two such steady states.
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(g) Name and brie y explain one policy measure that could help a country to escape the
low-income steady state.
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2. Consider a Ramsey-Cass-Koopmans model without technological progress and without de-
preciation, described by the following equations
ċt f ′ (kt ) − ρ
= (4)
ct θ
k̇t = f (kt ) − ct − nkt (5)
RT ′
0 = lim e− 0 f (kt )dt+nT kT (6)
T →∞
(a) What is the interpretation of θ? Explain economically the eect of θ on ĉt . What's the
eect of an increase in θ on k and c on the balanced growth path?
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(b) Draw the phase diagram, including arrows describing the dynamics, and the saddle
path.
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(c) Assume the economy is on its balanced growth path. Suddenly and unexpectedly, the
country starts to receive development aid from abroad. The development is d (constant,
exogenous) units of wealth for each person of the Lt people in the economy in every
period, is directly paid from abroad to the households and must never be paid back
(free lunch). Use the phase diagram to illustrate the short-run and the long-run eects
on c and k.
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(d) Is consumption maximised on the balanced growth path? Why (not)?
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(e) Can the government increase (household) consumption on the balanced growth path?
Explain intuitively how or why not! Is such a policy socially bene cial? Explain!
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(f ) Can this RCK-model explain long-run growth if you assume that workers' productivity
grows at the exogenous rate g? Which mechanism gives rise to this result?
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3. Consider a Diamond model with a learning-by-doing externality. Two-period lived households
supply one unit of labour in the rst period, consume only in the second period, and they
transfer wealth between periods by holding shares in capital. Lt is the number of young
households in period t, and the population grows at rate n. There is a continuum i ∈ [0, 1]
of rms, each with technology Yti = Ktiα (At Lti )1−α , and labor e ciency depends on the
aggregate capital-labor-ratio according to At = Kt /Lt .
(a) Compute the real wage. Using the learning-by-doing externality, show how the real
wage depends on the capital-labour-ratio. Solution: wt = (1 − α)Kt /Lt .
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(b) What equation describes the evolution of Lt ?
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(c) What equation describes the evolution of Kt ?
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(d) Use these two equations to derive one equation describing the evolution of
kt = Kt /Lt .
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(e) What is the growth rate of kt on the balanced growth path? How does the growth rate
depend on α? Explain why.
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(f ) Assume that the economy is on its balanced growth path. Suddenly, the swine u kills
a sizable share of the population at t = 0. Illustrate the evolution of y and r over time
in separate diagrams with t on the horizontal axis.
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