Week 2

Question 1

What did Malthus argue?

Answer 1

Any technological growth for production food will lead to population growth. Higher population will reduce the average person back to the subsistence level.

Question 2

According to Mathus’ theory, what will happen in the long run?

Answer 2

Population and consumption would grow over time but in the long run there would be no improvement in standard of living unless limits were put on population growth.

Question 3

Write the aggregate production function and what does each variable mean? What are the 3 assumptions put in place.

Answer 3

Question 4

How to write the population for next period?

Answer 4

Question 5

Write an equation that tells how the population evolves over time in equilibrium as it gives the future population as a function of current population.

Answer 5

Question 6

Using the graph below and explain why does population converse to a steady rate if population is below or above

Answer 6

Question 7

What do we get?

Answer 7

Question 8

Sketch these equations and explain how they are related?

Answer 8

In panel (a) c* determines the steady state quantity of land per worker l* as land is fixed. We can determine steady state population as N* = L/l. Standard of living in model is determined by c. Therefore long run standard of living is determined entirely by function g. (Nothing in Panel (a) affects c* so improved tech has no effect on long run living standards)

Question 9

An economy initially in steady state with factor productivity z ‘subscript 1’ increases to z ‘subscript 2’ . Show the steady state effects

Answer 9

Question 10

Show diagrammatically how the economy moves to a new steady state with regards to population and consumption adjusting with regards to consumption per worker and population.

Answer 10

Question 11

Malthus’ proposition for population control would have effect of reducing rate of population growth for each level of consumption per worker. Show diagrammatically how the result of population control will affect function g(c).

Answer 11

Question 12

The malthusian growth model was a good explanation for what 3 facts?

Answer 12

• Constant GDP per capita
• Population growth is higher when living standards rise
• Mainly an agricultural economy

Question 13

What 3 things does malthusian model fail to take into consideration?

Answer 13

• Sustained growth in GDP per capita
• Demographic transition, decline is growth rate of population
• Structural transition from agricultural economy to services

Question 14

What does the Solow model tell us?

Answer 14

• What causes living standards to rise over time
• What happens to the level and growth rate of aggregate income when the savings rate or population growth rate rises.

Question 15

According to the solow model how is the population in the next period modeled and explain each variable along with the assumption for population.

Answer 15

Question 16

How is consumption modeled in the solow model and explain each variable.

Answer 16

Question 17

Write the aggregate production function for the solow model and how it evolved to per worker production function. Draw the per worker production function.

Answer 17

Y = zF(K,N)

Which then becomes to

Y/N = zF(K/N,1)

then

y = zf(k)

Question 18

How is depreciation modeled in solow model and explain each variable.

Answer 18

Question 19

What are the 2 markets that exist in solow economy.

Answer 19

• Current consumption good traded for current labour
• Current consumption good traded for current capital

Question 20

Capital market is in equilibrium when what two variables are equal?

Start from the equilibrium condition and end up to the equation stating stock of capital in future period which is equal to quantity of saving this period plus quantity of capital this period post depreciation.

Answer 20

Question 21

Write the equation for law of motion for capital per capita, and what does it determine?

Answer 21

Question 22

Draw the graph of the equation for law of motion for capital per capita with the steady state.

Answer 22

Question 23

If current stock of capital per worker is less than steady state and capital stock per worker increases from current period to future period. What happens?

Answer 23

Current investment is large relative to depreciation and growth in labour so, per worker quantity of capital increases.

Question 24

If current stock of capital per worker is greater than steady state and capital stock per worker decreases from current period to future period. What happens?

Answer 24

Current investment is small that it cannot keep up with depreciation and labour force growth and per worker quantity of capital declines current period to future period.

Question 25

What is the quantity of output per worker that converses to a constant from the per worker production function?

Answer 25

Question 26

What does Solow model tell us if savings rate, labour growth rate, and factor of productivity are constant.

Answer 26

Then the real income per worker can’t grow in the long run. Since real income per worker is also real income per capita in the model we can use that as a measure of standard of living.

Question 27

How can output per worker grow and what happens to marginal return to investment and why?

Answer 27

It grows as long as capital per worker continues to grow.

Due to, capital per worker growing, it takes more investment per worker in current period to produce one more unit of capital per worker for future period.

Question 28

As the economy grows, what happens to new investment?

Answer 28

New investment eventually keeps up with depreciation and growth of labour force. Then growth per worker output stops.

Question 29

In the long run, when economy converges to steady state quantity of capital, what happens to all aggregate quantities?

Answer 29

They all grow at rate n

Question 30

What is the equation for aggregate quantity of capital in steady state?

Answer 30

K = k*N

Question 31

What is equation for aggregate real output?

Answer 31

Y= yN = zf(k)N

Question 32

Since quantity of investment is equal to savings, what is investment in steady state?

Answer 32

I = sY = szf(k)N since szf(k) is a constant, I also grows at rate n in steady state.

Question 33

What is the equation for aggregate consumption?

Answer 33

C = (1-s)zsf(k*)N

Question 34

If in the long run, savings rate, labour growth rate, factor productivity are constant then what are the growth rates in aggregate quantities determined by?

Answer 34

growth rates in labour force