# CONCORDIA UNIVERSITY ECON 498F/598F: Sample Exam Questions

November 24, 2016

The midterm exam will cover lectures up to date of the exam, and chapters 1-5.1 in the
textbook.
1. Consider a production technology that takes three inputs: capital (K), labor (N ), and
materials (M ). The production function is given by Y = AK ? N ? M ? , where ?, ?, ? > 0
and ? + ? + ? = 1. For this production function,

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(a) show that it exhibits constant returns to scale;

(b) show that it satis?es the Inada conditions for materials;

(c) derive a corresponding function in per capita terms (per unit of labor);
(d) derive a corresponding growth accounting equation;

(e) assume ? = 2? = 2?. Suppose you observe that over a period of a year output
grew by 5%, capital increased by 4%, labor declined by 2%, and materials grew
by 5%. What fraction of output growth came from the technological change and
what was the growth rate of A?
2. Given the law of motion for the aggregate capital stock in the Solow growth model
?
with technological progress, K = sK Y ? ?K, derive a law of motion for capital per
˜
e?cient worker (k).
3. Explain why a saving rate above the golden rule saving rate creates dynamic ine?ciency.
4. Explain what the notion of “conditional convergence” is supposed to capture.

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5. Consider an in?ow of immigrants (a temporary jump in the population growth rate)
in the Solow growth model without technological change.
(a) What are the e?ects on the steady state capital per worker, output per worker,

(b) How are these variables a?ected in the short run? Draw and explain the transition
paths for
i. the growth rate of capital per worker;
ii. output per worker;
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https://www.coursehero.com/file/11769316/growth-sample-questions/

iii. aggregate savings;

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iv. the growth rate of aggregate output.

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