endog growth 222

Question 1

what are the 5 unknowns in the combined model and 5 equations and what do they tell us

Answer 1

Equation (1) exhibits constant returns to scale to objects (capital and workers), but because of non-rivalry it exhibits increasing returns to scale to objects and ideas together.

Equation (2) tells us that the change in the capital stock is equal to the new investment s ̄Yt less depreciation d ̄Kt.

Equation (3) tells us that ideas are produced using the existing stock of ideas and researchers.

Equation (4) tells us that the number of workers and researchers add to the total population.

Equation (5) captures the assumption that a constant fraction of the population l ̄ works as researchers. This implies that 1 − l ̄ works to produce the output good.

Question 2

in the Solow model, the productivity level, A ̄, was a constant parameter: a one-time increase in this productivity level produced transition dynamics that led the economy to grow for a while before settling down at its new steady state.
Now At increases continuously over time. what implications doe this have

Answer 2

1 Rather than achieving a steady state with a constant level of capital, we will have a balanced growth path where capital grows at a constant rate;

2 The transition dynamics are likely to be important.

Question 3

what does this equation tell us

Answer 3

Equation (6) tells us that the growth rate of output is the sum of the three terms: the growth rate of knowledge, the growth from capital, and the growth contribution from workers.

Question 4

how do we solve or the growth rate of output

Answer 4

we need to know the growth rate of the three terms on the right-hand side of equation (6).

Question 5

how do we workout the growth rate of knowledge, gA,

Answer 5

Question 6

how do we workout the growth rate of capital

Answer 6

Question 7

how do we workout the growth rate of the number of workers

Answer 7

Question 8

what’s the growth rate of output in the long run

Answer 8

Question 9

why In the combined model growth in the long run is even faster: 3/2g ̄.

Answer 9

In the Solow model, when productivity increases, the level of capital increases. Output increases for two reasons:
1 there is an increase in productivity itself → a direct effect;
2 the productivity increase leads to a higher capital stock, which in turn
leads to an even higher level of output → an indirect effect.

Therefore, capital helps to amplify the underlying growth in knowledge: long-run growth in output per person is therefore higher in this model than in the Romer model.

Question 10

how do we find the level of output per person along the balanced growth path

Answer 10

Question 11

how do we express the Level of output per person along the BGP in per capita terms

Answer 11

Question 12

what’s the principle of transition dynamics and an example

Answer 12

the farther below its balanced growth path an economy is (in percentage terms), the faster the economy will grow. Similarly, the farther above its balanced growth path an economy is, the slower it will grow.

Example: assume that the economy starts on its balanced growth path, but then the investment rate s ̄ increases permanently.

According to equation (14), the increase in the investment rate means that the balanced growth path level of income is now higher.
Since the current income is unchanged, the economy is now below its balanced growth path and we should expect it to grow rapidly to “catch” up to this path.

Question 13

graphically show Output over time after a permanent increase in s ̄.

Answer 13

Before the increase in the investment rate, yt is growing at a constant rate: this is represented by the orange straight line.

After the increase in the year 2030, the growth rate increases immediately, the slope of the path increases sharply.

Over time, the growth rate declines until eventually it exhibits the same slope as the original path: this is represented by the dashed green line.

The new level of output is permanently higher as a result of the increase in the investment rate, but the growth is unchanged (g ̄ does not depend on s ̄) → this is called as long-run level effect.

Question 14

what can induce differences in the growth rates over long periods of time.

Answer 14

Changes in policies that change the parameters of the model (such as s ̄)

Question 15

what’s the “Schumpeterian” growth theory.

Answer 15

Growth requires the continual obsolescence of old techniques as new ones are invented, improving the productivity of the economy at each step.

Innovation works through entrepreneurs who implement new discoveries and bring them to the market.

Question 16

what may an innovation include

Answer 16

1 developing a new route by which exiting factors of production are channelled into the production process;
2 improving the quality of an existing product;
3 developing a new production process for an existing product;
4 creating a new market.

Question 17

what are the two main elements of the technological process in the Schumpeterian model

Answer 17

Creation: entrepreneurs introduce new products or processes in the hope that they will enjoy temporary monopoly profits as they capture markets.

Destruction: entrepreneurs make old technologies or products obsolete.

Question 18

what’s the “standing on shoulders effect”. +example

Answer 18

The discovery of ideas in the past makes us more effective researchers today,

Example: the theory of gravity by Isaac Newton created spillover to future researchers.

When φ increases the probability that an individual researcher will produce an innovation increases as well.

Finally, the parameter θ measures the sensitivity of μ with respect to the “stepping on toes” and “standing on shoulders” effects.

Question 19

what are The Schumpeterian model three sectors:

Answer 19

(i) final good sector;
(ii) intermediate good sector;
(iii) research sector.

Question 20

when do innovations raise output

Answer 20

only if final good firms actually purchase the latest version of the capital good.

intermediate goods firms will sell all the versions of the capital goods at the same price.

Therefore, final good firms will purchase only the latest version, as it gives them the highest productivity level.