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EMEA6: Growth Models
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Title: EMEA6: Growth Models
1
EMEA6 Growth Models
- The Ramsey-Cass-Koopmans model of economic growth
- The DICE model of optimal greenhouse gas emission
reduction
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The Ramsey-Cass-Koopmans Model
- This model goes back to the 1928 paper of Frank
Ramsey, which was long neglected - Cass (1965) and Koopmans (1965) developed a model
that looks the same but it is much better founded - The crucial difference between Ramsey and Solow
is that savings are derived from welfare
maximisation - An essential assumption in Ramsey models is that
consumers live forever (or rather paternalistic
dynasties)
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Firms
- There are a large number of identical firms. Each
has a production function - The firms hire workers and rent capital in
competitive markets, and pay them their marginal
products. Firms sell their output in competitive
markets. Firms take A as given. Because the
production function has constant returns to
scale, and the economy is competitive, firms earn
zero profits.
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Firms -2
- In a competitive market, capital earns its
marginal product. Ignoring depreciation, the real
rate of return on capital equals its earnings per
unit of time. Thus, the real rate of interest is - The real wage of effective labour equals its
marginal product
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Households
- There are a large number of identical households.
The size of each household grows at rate n. Each
household member supplies one unit of labour at
every point in time. The household rents its
capital to the firms. Households use their wage,
interests and profits for consumption and saving,
so as to maximise life time utility
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Households -2
- Because the interest rate varies over time,
define compounded interest as - The budget constraint is that the net present
value of consumption may not exceed the net
present value of initial capital and wages earned
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Households -3
- The budget constraint states that total
consumption cannot exceed total earnings,
considering that earnings can be shifted back and
forth in time, accounting for the return on
investment
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Households -4
- As w-c is investment, this essentially says that
the present value of the households assets
cannot be negative in the limit
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Households -5
- We maximise this, under the budget constraint
derived earlier - Note that ßgt0
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Households -6
- The first order condition is
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Households -7
- Eulers equation
- essentially says that if the rate of return on
capital exceeds the time preference, consumption
per worker grows over time - What are the dynamics of the system?
- It is saddle-point stable, until one imposes the
budget constraint - Convergence is faster, as there is an extra
control variable
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The DICE Model
- The Dynamic Integrated Climate Economy model of
Bill Nordhaus, dating back to 1990, is the
prototype of most coupled climate-economy models - DICE combines the simplest of economic growth
models with the simplest of carbon cycle and
climate models - Indeed, the only interesting part of DICE is the
interaction between the natural and the
socio-economic system - Let us go through the equations ...
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DICE Objective
- Maximise total welfare
- Total welfare equals average welfare times the
number of people - Since the number of people is exogenous, total
welfare equals average welfare - Or, total welfare is the sum of individual
welfare distribution does not matter - Future welfare is worth less than current welfare
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DICE Economy
- Production is a combination of labour and capital
- Technology progresses exogenously
- Income is spread over consumption and investment
- Wages and working hours vary freely with labour
demand and supply - Labourers own the stocks of the companies they
work for - There are a large number of firms, none of which
has market power - All products are substitutable, and can be
divided into small units
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DICE Carbon and Climate
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DICE Impact
- Climate change damages are a power function of
temperature - Emission reduction costs are a power function of
emission reduction - Both climate change damages and emission
reduction costs lower income, hence consumption
and investment, hence welfare and growth
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Costs of Emission Reduction
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Marginal cost estimates
- 0 1 3
- Nordhaus 1994 BG 5
- EV 12
- Fankhauser 1994 EV 20 (6-45)
- Tol 1999 BG 73 23 9
- EW 171 60 23
- EVW 244 82 35
- (143) (51) (22)
- Downing 2000 BG 75 46 16
- Tol 2000 BG 20 4 -7
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DICE Overview
- 10 equations that can be solved in a matter of
minutes on a PC - Balances the costs of emission reduction with the
costs of climate change - Thus yields optimal abatement, that is, emission
reduction that maximises social welfare - If the world were ruled by a benevolent dictator,
what would she do?
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DICE Outcomes
- If the world were ruled by a benevolent dictator,
what would she do? - A little emission reduction in the beginning,
more later, but not enough to stabilise
concentrations - The first part is robust, the second part is very
sensitive to assumptions - The last part is robust, unless there is a cheap
alternative to fossil fuels - If we consider many countries, optimal emission
reduction goes down!
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