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    Week4 Thursday Slides

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    Siham Buule
    The Romer model introduces increasing returns from ideas and knowledge in the production function. It exhibits balanced growth with constant growth rates of output, capital, and ideas. The combined Solow-Romer model adds capital to the Romer model. It has transition dynamics as the economy adjusts to its balanced growth path. Along the balanced growth path, the growth rate of output depends on investment and productivity parameters. Changes in parameters like population or investment rate cause the balanced growth path to shift.

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    Week4 Thursday Slides

    Uploaded by

    Siham Buule
    21 views35 pages
    The Romer model introduces increasing returns from ideas and knowledge in the production function. It exhibits balanced growth with constant growth rates of output, capital, and ideas. The combined Solow-Romer model adds capital to the Romer model. It has transition dynamics as the economy adjusts to its balanced growth path. Along the balanced growth path, the growth rate of output depends on investment and productivity parameters. Changes in parameters like population or investment rate cause the balanced growth path to shift.

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    The Romer model introduces increasing returns from ideas and knowledge in the production function. It exhibits balanced growth with constant growth rates of output, capital, and ideas. The combined Solow-Romer model adds capital to the Romer model. It has transition dynamics as the economy adjusts to its balanced growth path. Along the balanced growth path, the growth rate of output depends on investment and productivity parameters. Changes in parameters like population or investment rate cause the balanced growth path to shift.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    21 views35 pages

    Week4 Thursday Slides

    Uploaded by

    Siham Buule
    The Romer model introduces increasing returns from ideas and knowledge in the production function. It exhibits balanced growth with constant growth rates of output, capital, and ideas. The combined Solow-Romer model adds capital to the Romer model. It has transition dynamics as the economy adjusts to its balanced growth path. Along the balanced growth path, the growth rate of output depends on investment and productivity parameters. Changes in parameters like population or investment rate cause the balanced growth path to shift.

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    EC1B3

    Macroeconomics I
    Lent Term
    The Romer Model
    The Romer model
    • Distinction between ideas and objects
    • Output requires knowledge and labor
    The production function of the Romer model
    • Constant returns to scale in objects alone
    • Increasing returns to scale in objects and ideas

    𝑌! = 𝐴! 𝐿"!
    The Romer Model
    New ideas depend on
    • The existence of ideas in the previous period
    • The number of workers producing ideas
    • Worker productivity
    Δ𝐴!#$ = 𝑧𝐴 ̅ ! 𝐿%!

    The population
    • Workers producing ideas
    • Workers producing output
    Solving the Romer Model
    Express the endogenous variables in terms of the
    parameters: 𝐿!" = ℓ# 𝐿#

    • Where ℓ,( 𝑎𝑛𝑑 𝐿( are parameters


    • 𝐿𝑎𝑡 and 𝐿𝑦𝑡 are endogenous variables

    𝐿#" = (1 − ℓ# )𝐿#
    Solving the Romer Model
    Romer model:
    • Output per person depends on the stock of knowledge.
    𝑌"
    #
    𝑦" ≡ = 𝐴" (1 − ℓ)
    𝐿#
    • The growth rate of knowledge is constant.
    ∆%!"#
    %!
    = 𝑧𝐿!" = 𝑧ℓ# 𝐿#

    Solow model:
    • Output per person depends on capital per person.
    Solving the Romer Model
    % 𝐿%
    The growth rate of technology: 𝑔̅ = 𝑧ℓ

    The stock of knowledge depends on its initial value


    and its growth rate.

    Initial amount Growth rate


    Stock of of knowledge of knowledge
    knowledge
    Solving the Romer Model
    • Combining:

    and

    yields:

    • Output per person is a function of the parameters


    of the model.
    Output per Person—1
    Why Is There Growth in the Romer Model?
    The Romer model produces long-run growth.
    • Does not have diminishing returns to ideas because
    they are nonrivalrous

    • Labor and ideas have increasing returns together.


    • Returns to ideas are unrestricted.
    In the Solow model, capital has diminishing returns.
    • Eventually, capital and income stop growing.
    Balanced Growth
    The Solow model
    • Transition dynamics
    The Romer model
    • Does not exhibit transition dynamics
    • Instead, has balanced growth path
    • Constant growth rates of all endogenous variables
    Case Study: A Model of World Knowledge
    The United States has more researchers than
    Luxembourg has people.
    Growth rates 1960–2017
    • United States:
    • 2.0 percent per year increase in per capita GDP
    • Luxembourg:
    • 2.7 percent per year increase in per capita GDP
    All countries can benefit from all ideas, no matter
    where the ideas were discovered.
    Experiment #1: Changing the PopulaJon

    Changes in the population


    → Changes in the growth rate of knowledge
    An increase in population
    → Immediately and permanently raises the growth
    rate of per capita output
    An Increase in 𝐿! —1
    Experiment #2: Changing the Research Share
    ̅
    An Increase in 𝑙—2
    Growth Effects versus Level Effects
    Growth effects:
    • Changes to the rate of growth of per capita output
    Level effects:
    • Changes in the level of per capita GDP
    The degree of increasing returns matters for growth
    effects.
    • If the exponent on ideas is not equal to 1,
    • there will still be sustained growth.
    • growth effects are eliminated.
    Case Study: On the Possibility of Progress
    Can economic growth be sustained given that we live
    on a planet with Vinite resources?
    • Prices of industrial commodities have been falling.
    • We can see that the
    industrialization of China and
    India has made an impact around
    the year 2000.
    Combining Solow and Romer: Overview
    The combined Solow–Romer model
    • Nonrivalry of ideas results in long-run growth along
    a balanced growth path.
    • The model exhibits transition dynamics if economy
    is not on its balanced growth path.
    • For short periods of time, countries can grow at
    different rates.
    • In the long run, countries grow at the same rate.
    Combining Solow and Romer (Algebraically)
    The combined model is set up by adding capital into
    the Romer model production function.
    The combined model features Vive equations and Vive
    unknowns.
    The Vive unknowns: The Vive equations:
    • Output Yt
    • Capital Kt
    • Knowledge At
    • Workers Lyt
    • Researchers Lat
    SeQng Up the Combined Model—1
    The production function for output

    The accumulation of capital over time

    Ideas
    Setting Up the Combined Model—2
    The numbers of workers and researchers sum to equal
    the total population.

    Our assumption is that a constant fraction of the


    population works as researchers.
    Setting Up the Combined Model—3
    The production function:
    • Constant returns to scale in objects
    • Increasing returns in ideas and objects together:

    The change in the capital stock is investment minus


    depreciation:

    Researchers are used to produce new ideas.


    SeQng Up the Combined Model—4
    The combined model will result in:
    • A balanced growth path
    • Since 𝐴! increases continually over time
    • Transition dynamics
    • Long-run growth:
    • To be on a balanced growth path, output, capital,
    and stock of ideas all must grow at constant rates
    SeQng Up the Combined Model—5
    Start with the production function for output and
    apply the rules for computing growth rates:

    Growth Growth Growth Growth


    rate of rate of contribution contribution
    output knowledge from capital from
    workers
    SeQng Up the Combined Model—6
    To solve for the growth rate of knowledge, divide the
    production function for new ideas by 𝐴𝑡

    To solve for the growth rate of capital, divide the


    capital accumulation equation by 𝐾𝑡
    SeQng Up the Combined Model—7
    Constant along a
    Therefore: balanced growth
    path

    Must be constant as well

    The asterisk (*) means these variables are evaluated


    along a balanced growth path.
    Setting Up the Combined Model—8
    The growth rate in the number of workers is zero.
    • The number of workers is a constant fraction of the
    population.
    • The population itself is constant.
    Therefore:
    SeQng Up the Combined Model—9
    Plug the results into:
    SeQng Up the Combined Model—10
    Solve for the growth rate of output

    For the long-run combined model, this equation pins


    down
    • the growth rate of output.
    • the growth rate of output per person.
    Setting Up the Combined Model—11
    The growth rate of output is even larger in the
    combined model than in the Romer model.
    Output is higher in this model because
    • ideas have a direct and an indirect effect.
    • Increasing productivity raises output because
    productivity has increased.
    • Higher productivity results in a higher capital
    stock.
    Output per Person—2
    The capital-to-output ratio is proportional to the
    investment rate along a balanced growth path.

    This solution can be substituted back into the


    production function and solved to get:
    SeQng Up the Combined Model—12

    •Growth in At leads to sustained growth in output per


    person along a balanced growth path.
    •Output yt depends on the square root of the
    investment rate.
    •A higher investment rate raises the level of output per
    person along the balanced growth path.
    TransiJon Dynamics
    The Solow model and the combined model both have
    diminishing returns to capital.
    Transition dynamics applies in both models.
    In the combined model,
    • the further below its balanced growth path an
    economy is, the faster the economy will grow.
    • the further above its balanced growth path an
    economy is, the slower the economy will grow.
    Setting Up the Combined Model—13
    A permanent increase in the investment rate in the
    combined model implies that
    • the balanced growth path of income is higher
    (parallel shift).
    • current income is unchanged.
    • The economy is now below the new balanced
    growth path.
    • the growth rate of income per capita is immediately
    higher.
    • The slope of the output path is steeper than the
    balanced growth path.
    Setting Up the Combined Model—14
    Changes in any parameter result in transition
    dynamics.
    • Long-run growth through ideas
    • Explains differences in growth
    rates across countries

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