178.200 06-12

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178.200 Intermediate Macroeconomics

Tutorial (12) Economic Growth

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Short Answer Questions from Textbook

1. Question 4 of Questions for Review on P205.

In the Solow model, how does the rate of population growth affect the steady-state level of income? How does it affect the steady-state rate of growth?

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Hint:

The higher the population growth rate is, the lower the steady-state level of capital per worker is, and therefore there is a lower level of steady-state income.

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(continued)

The higher population growth n2 means that the line representing population growth and depreciation is higher, so the steady-state level of capital per worker is lower.

(δ+n2)k(δ+n2)k & sf(k)

(δ+n1)k

sf(k)

k2* k1* k

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(continued)

The steady-state growth rate of total income is n+g: the higher the population growth rate n is , the higher the growth rate of total income is. Income per worker, however, grows at rate g in steady-state and, thus, is not affected by population growth.

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2. Question 6 of Questions for Review on P227.

How does endogenous growth theory explain persistent growth without the assumption of exogenous technological progress? How does this differ from the Solow model?

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Hint: Endogenous growth theories attempt to explain the

rate of technological progress by explaining the decisions that determine the creation of knowledge through research and development. By contrast, the Solow model simply took this rate as exogenous. In the Solow model, the saving rate affects growth temporarily, but diminishing returns to capital eventually force the economy to approach a steady-state in which growth depends only on exogenous technological progress.

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(continued)

However, many endogenous growth models in essence assume that there are constant (rather than diminishing) returns to capital, interpreted to include knowledge. Hence, changes in the saving rate can lead to persistent growth.

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Numerical Questions

1. Suppose that the production function is

and 2% of capital wears out every year. Assume that the rate of growth of population equals 0. If the saving rate s is 0.128, calculate the steady state level of capital per worker, output per worker, consumption per worker, saving and investment per worker, and depreciation per worker.

4/34/1 )()(10 LKY

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Numerical Questions

Answer:

Meanwhile, δ = 0.02, s = 0.128, and

Δk = i – δk = sf(k) – δk = sy - δk.

In the steady state, Δk = 0.

4/1

4/14/14/1

4/34/1

10

)/(10)()(10/

)()(10

ky

LKLKLY

LKY

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Numerical Questions

(continued)

Then

k = 256.

c = (1-s)y = 0.872y = 34.88.

i = δk = y - c = 5.12

δk = 5.12

406400010)101( 3

43

44

ys

ys

y

y

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Numerical Questions

2. Suppose the production function is

and capital lasts an average of 10 years. Assume that the rate of growth of population is 4% and the rate of technological growth is 2%. The MPK can be expressed as where k is the level of capital per effective worker.

4/34/1 )()(10 ELKY

4/3)(5.2 kMPK

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Numerical Questions

a. Derive the equation for output per effective worker y = Y/EL = f(k).

Answer:

4/1

4/14/14/1

4/34/1

10

)/(10)()(10/

)()(10

ky

ELKELKELY

ELKY

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Numerical Questions

b. Calculate the Golden Rule level of capital per effective worker and the output per effective worker associated with the steady state.

Answer:

δ = 1/10 = 0.1, n = 0.04, g = 0.02, and

. In the meantime,

subject to the Golden Rule, MPK = δ + n + g.

Then k* = 39.0625,

4/3)(5.2 kMPK

25*)(10 4/1 ky

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Numerical Questions

c. Calculate all of the following at the Golden Rule level: saving rate, saving and investment per effective worker, and consumption per effective worker.

Answer:

Δk = sf(k) – (δ+n+g)k = sy – (δ+n+g)k.

In the steady state, Δk = 0. Then

y

kgns

*)(

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Numerical Questions

(continued)

s = 39.0625 (0.16/25) = 0.25

saving per effective worker = i = 6.25

c = f(k) – (δ+n+g)k = 25 - 6.25 = 18.75.

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Multiple-Choice Questions(2005 Exam Question)

(1) In a steady state with no population growth:a. The amount of capital per worker remains

constant over time.b. Investment per worker equals depreciation per

worker.c. Saving per worker equals depreciation per

worker.d. All of the above.Answer: d.Hint: P185.

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(2) With no population growth, the steady state level of capital per worker will increase whenever:

a. The amount of investment per worker decreases.

b. The depreciation rate increases.

c. The saving rate increases.

d. All of the above.

Answer: c.

Hint: PP189-190.

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(3) If , s = 0.4, and the depreciation rate δ = 20 percent, the steady state level of the capital stock per worker is:

a. 4.b. 8.c. 2.d. 16.Answer: a.Hint:

2/1ky

.4*

.22.0/4.0*

**),(2/1

k

s

k

kkfky

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(4) The Golden Rule level of capital denotes the steady state with the highest:

a. Level of consumption per worker.

b. Level of output per worker.

c. Growth rate of consumption per worker.

d. Growth rate of output per worker.

Answer: a.

Hint: P193.

*goldk

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(5) Excluding population growth, at the Golden Rule level of capital :

a.

b. MPK = δ.

c. f(k) reaches a maximum.


Answer: b.

Hint: P194.

*goldk.)( **

goldgold kkf

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Multiple-Choice Questions(2005 Exam Question)(6) Suppose that a country in a steady state

implements policies to increase its saving rate. After the new steady state is reached:

a. Output per worker will grow more rapidly than before.

b. The level of output per worker will be higher than before.

c. The amount of capital per worker will be the same as before.

d. All of the above.Answer: b. Hint: P190.

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(7) If , δ = 5%, and the Golden Rule level of capital = 100, then the saving rate associated with the Golden Rule level of capital is:

a. 5%.b. 10%.c. 20%.d. 50%.Answer: d.Hint:

2/1ky *goldk

%505.010

100

05.0*

* s

ss

k

k

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(8) In the Solow growth model with population growth n, the change in capital per worker is equal to:

a. sf(k) + (δ + n)k.b. sf(k) + (δ - n)k.c. sf(k) - (δ + n)k.d. sf(k) - (δ - n)k.Answer: c.Hint: P200.

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(9) An increase in the rate of population growth n will:a. Increase the steady state level of capital per

worker.b. Decrease the steady state level of capital per

worker.c. Have no effect on the steady state level of capital

per worker.d. Decrease the steady state level of capital per

worker if δ < n and increase the steady state level if δ > n.

Answer: b Hint: P202.

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(10) The Solow growth model predicts that countries with higher population growth rates will have:

a. Lower steady state level of output per worker.b. Lower steady state growth rates of output per

worker.c. Both a and b.d. Higher steady state growth rates of output per

worker.Answer: a.Hint: P202.

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(11) In the Solow growth model with population growth n and labor augmenting technological progress g, the change in capital per effective worker is equal to:

a. sf(k) + (δ + n + g)k.b. sf(k) + (δ – n - g)k.c. sf(k) - (δ + n + g)k.d. sf(k) - (δ – n - g)k.Answer: c.Hint: P209.

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Multiple-Choice Questions(2005 Exam Question)(12) In the Solow growth model with population

growth and technological progress, the steady state growth rate in output per effective worker is equal to:

a. zero.b. The rate of technological progress g.c. The growth rate of population n plus the rate of

technological progress g.d. The saving rate s.Answer: a. Hint: P210.

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Multiple-Choice Questions(2005 Exam Question)(13) In the Solow growth model with population

growth and technological progress, the steady state growth rate in output per worker is equal to:

a. zero.b. The rate of technological progress g.c. The growth rate of population n plus the rate of

technological progress g.d. The saving rate s.Answer: b. Hint: P210.

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(14) If the capital stock in a country is initially below the Golden Rule level of capital, the country can move toward the Golden Rule steady state by:

a. Increasing the rate of saving.b. Reducing government expenditures on

noninvestment items.c. Providing tax incentives that reward new

investment.d. All of the above.Answer: d. Hint: P212.

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(15) Technological progress is encouraged by:

a. The patent system.

b. Tax incentives for research and development.

c. Government subsidies for research.


Answer: d.

Hint: PP215-216.

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(16) When the steady state has been reached:a. Real wages grow at the rate of technological

progress.b. The real rental cost of capital grows at the rate of

technological progress.c. The number of effective workers grows at the

rate of technological progress.d. All of the above.Answer: a.Hint: P220.

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(17) In the Solow growth model, the rate of technological progress is:

a. exogenous.

b. endogenous.

c. 3%.

d. 0%.

Answer: a.

Hint: P222.

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Multiple-Choice Questions(2005 Exam Question)(18) Acceptance of endogenous growth theory

implies:a. Additional saving and investment can lead to

persistent growth.b. Capital may not be subject to diminishing

returns if knowledge is viewed as a type of capital.

c. The rate of technical change is endogenous.d. All of the above.Answer: d Hint: PP223-224.

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