SEM 1 - LEC 6 - ENDOGENOUS GROWTH PART 2 Flashcards
what are the 5 unknowns in the combined model and 5 equations and what do they tell us
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.
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
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.
what does this equation tell us
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.
how do we solve or the growth rate of output
we need to know the growth rate of the three terms on the right-hand side of equation (6).
how do we workout the growth rate of knowledge, gA,
how do we workout the growth rate of capital
how do we workout the growth rate of the number of workers
what’s the growth rate of output in the long run
why In the combined model growth in the long run is even faster: 3/2g ̄.
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.
how do we find the level of output per person along the balanced growth path
how do we express the Level of output per person along the BGP in per capita terms
what’s the principle of transition dynamics and an example
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.
graphically show Output over time after a permanent increase in s ̄.
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.
what can induce differences in the growth rates over long periods of time.
Changes in policies that change the parameters of the model (such as s ̄)
what’s the “Schumpeterian” growth theory.
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.
what may an innovation include
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.
what are the two main elements of the technological process in the Schumpeterian model
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.
what’s The aggregate production function for the Schumpeterian model given by:
what’s the growth rate of A, from innovation to innovation,
what’s the equation for any individual doing research, his or her probability of discovering the next innovation at any moment in time:
The parameter φ is between zero and one and captures a positive knowledge spillover in research.
what’s the equation For the economy as a whole, the probability of an innovation occurring at any moment in time
equal to the individual probability of innovation, μ ̄, times the number of individuals doing research:
what’s the dot notation fir
for the derivatives with respect to time.
what does the capital accumulation equation show
According to equation (20), the change in the capital stock, K ̇ , is equal to the amount of gross investment, s ̄Y , less the amount of depreciation that occurs during the production process, d ̄K.
what does The growth rate of the labour force tell us and what is it
how is the labour force divided
We assume that initially, the economy has some capital stock K0, and
total labour force L0.
We also assume that the initial technology level is A0, meaning that the initial technology level is indexed to zero, and growth will consist of advancing to the next “step” in the ladder of technology.
what’s the expected growth rate of A over time given by
what does this equation show
tells us that the growth rate of output per capita is governed by the growth rate of technology, or more precisely, the expected value of the growth rate of technology.
what is the expected rate of technological progress along the balanced growth path?
might need to know process before idk…. 20 mins in to schumpeitan model part 1.
graphically show the Output per person along the balanced growth in the Schumpeterian model.
The figure shows the distinction between the average growth rate along the BGP and the actual growth in income per capita.
The bold line shows how income per capita actually changes over time.
At any given point in time, no one may have innovated, so growth is zero → flat sections.
When someone does innovate, Ai jumps by γ, so growth is very rapid in that moment.
On average, income per capita grows along the dashed line: growth over long period is smooth.
what’s The production function for a typical final good firm
what’s the Final good firms profit maximization problem
what does the FOC for Ly show
shows that firms hire labour until their marginal product is equal to the wage.
what does the FOC for Xi tell us
tells us that capital goods are purchased until their marginal product is equal to the price charged by the intermediate good firm.
what’s The profit-maximization problem for the typical intermediate good firm
what does this equation tell us….. long steps to get to it 13min part schemputrian
tells us that the intermediate good firm charges a constant markup over the cost of producing the intermediate good.
This result, in turn, generates the profits that will motivate innovation.
the price that intermediate good firms charge does not depend on the version of the intermediate good that they produce.
Since each intermediate good firm charges the same for a unit of the capital good, buying an old version of the capital good is as expensive as buying the latest version.
Because the productivity is highest with the latest version, final good firms will always want to buy it over any others.
This set-up ensures the creative destruction
in the economy.
Once a new innovation occurs (a new xi+1) with a higher productivity, the old intermediate good (xi ) firm goes out of business and the new firm takes over completely.
what’s the equation for the total profits of the intermediate good firm
what’s the equation related to the use the idea of arbitrage to describe the value of the patent, PA, to the intermediate good firm
what’s the the price of a patent along the balanced growth path equation
If the probability of a new innovation, μ, increases, the value of a patent declines.
If the size of innovations, γ, increases the value of a patent increases.
what’s the equation for Workers in the final good sector earn a wage that is equal to the marginal product of labour in that sector
whats the equation for expected wage from research
what equation tells us the share of the population that is engaged in research.
If the term r − n goes up, the value of patents goes down and, in turn, we have a lower sR.
There are two effects of μ.
First effect of μ: from μ(1 − γ) captures the fact that as the probability of innovation goes up, the value of patents declines due to replacement effects.
Second effect of μ: from μa captures the fact that as the probability of innovation goes up, you are more likely to get a patent in the first place.
On net, the second effect “wins”. You get a patent now, and will only be replace later, so if μ goes up, sR goes up.
