Macroeconomics

HW #5 – Transition Dynamics
Answers

Problem 1

Suppose that an economy was initially in steady state when many of its workers are killed by an infectious disease. Assume that none of its capital stock is destroyed by the disease. Use the Solow Model without technological progress to answer the following questions.

  1. What is the immediate impact on total output?

ANSWER: Because total output is a function of capital and labor:

Y=Kα·L(1-α)

the decrease in the labor force would reduce total output.

  1. What is the immediate impact on output per worker?

ANSWER: Because output per worker is a function of capital per worker:

YL=(KL)α

the decrease in the labor force would increase capital per worker, thus increasing output per worker.

  1. Assuming that the country's saving rate remains unchanged, what happens to:
    • output per worker in the post-disease economy?
    • investment per worker in the post-disease economy?
    • consumption per worker in the post-disease economy?
    Illustrate your answers with a diagram.

ANSWER: Because capital per worker has risen above its steady-state level, it will slowly converge back down to its steady-state level.

And as capital per worker falls, so too will output per worker, investment per worker and consumption per worker.

  1. Is the growth rate of output per worker in the post-disease economy greater or smaller than it was before the disease?

ANSWER: Before the disease, the economy was in steady-state and output per worker was constant over time. So the growth rate of output per worker was zero percent per year.

After the disease, output per worker falls back down to its steady-state level. So the growth rate of output per worker will be negative.

By definition, a negative number is less than zero, so the growth rate of output per worker will be lower after the disease than it was before.

Problem 2

Suppose that an economy was initially in steady state when part of its capital stock is destroyed by an earthquake. Assume that none of its workers are killed by the earthquake. Use the Solow Model without technological progress to answer the following questions.

  1. What is the immediate impact on total output?

ANSWER: Because total output is a function of capital and labor:

Y=Kα·L(1-α)

the decrease in the capital stock would reduce total output.

  1. What is the immediate impact on output per worker?

ANSWER: Because output per worker is a function of capital per worker:

YL=(KL)α

the decrease in the capital stock would decrease capital per worker, thus decreasing output per worker.

  1. Assuming that the country's saving rate remains unchanged, what happens to:
    • output per worker in the post-quake economy?
    • investment per worker in the post-quake economy?
    • consumption per worker in the post-quake economy?
    Illustrate your answers with a diagram.

ANSWER: Because capital per worker has fallen below its steady-state level, it will slowly converge back up to its steady-state level.

And as capital per worker rises, so too will output per worker, investment per worker and consumption per worker.

  1. Is the growth rate of output per worker in the post-quake economy greater or smaller than it was before the earthquake?

ANSWER: Before the earthquake, the economy was in steady-state and output per worker was constant over time. So the growth rate of output per worker was zero percent per year.

After the earthquake, output per worker rises back up to its steady-state level. So the growth rate of output per worker will be positive.

By definition, a positive number is greater than zero, so the growth rate of output per worker will be higher after the earthquake than it was before.

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