Ramsey–Cass–Koopmans growth model is a neo-classical model of economic growth. It explicitly models the choice of consumption at a point in time. And it has made the savings rate endogenous.

1. Ramsey–Cass–Koopmans model
and its application in Ethiopia
By
Molla Deribie
ID.No.MAEC/0182/2005
Department: Agricultural Economics
St.Mary’s University College
School of Graduate Studies
Jan 2012,Addis Ababa
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2. 2
Outlines
1.Definition…………………………………………….3
2.Objectives…………………………………………...4
3. Ramsey–Cass–Koopmans
growth model………………………....5
4. Application of Ramsey–Cass –
Koopmans growth model…………….11
5.Conclusion……………………………....18

3. 1.Definition of Ramsey–Cass–
Koopmans growth model
It is a neo-classical model of economic
growth
It explicitly models the choice of
consumption at a point in time.
It has made the savings rate
endogenous.
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4. 2.Objectives of the paper
To understand what the Ramsey –
Cass–Koopmans growth model says
about;
To see application of the model in
Ethiopia and
To draw a relevant conclusion on
wards the results and scientific findings
of the model.
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5. 3. Ramsey–Cass–Koopmans model
Households
 there is a social planners problem.
 whose goal is maximization of the
sum of intertemporal utility.
Objective function:
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6. Budget constraint

,whereBtis assets, wt is wage rate and rt is
interest rate.
 In per capita terms:
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7. Problem of the representative households:
• L= u (c)e-(ρ-n)t
+λ[ wt+(r-n)bt-ct] ,where λ is
Lagrangian multiplier or marginal utility
of income.
FOC
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8. Transversality condition:
The value of the representative
household’s assets must approach zero
as time approaches infinity.
The higher r, the more willing
households are to save and shift
consumption in the future.
The higher the rate of return to
consumption is, the more willing
households are to sacrifice future
consumption for more current
consumption and thereby less current
saving.
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9. Firms
Problem of the representative firm i:
choose the amount of capital Κi and
labor input Li to maximize its profit πi
 πi = F(Ki , Li ) − (r +δ )Ki – wLi
FOC


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10. Cont..
The marginal product of each input
equals its associated cost. This is an
optimal point of profit maximization.
To maximize profit, the firm hires up
to the point at which the marginal
product of each input equals its
associated cost.
All firms and factor owners being paid
their marginal product
10

11. 4.Application of Ramsey –Cass
Koopmans growth model in
Ethiopia
1.On Risk modeling:
2.On Hydropower and Irrigation Modeling:
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12. Risk modeling:
This model can identify the aggregate
effect of risk on resource accumulation,
economic growth and savings and the
nature of the risk faced on the rural
peoples of Ethiopia.
Agents maximize expected utility over an
infinite horizon. Each household solves
for the optimal investment function.
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13. Cont..
The household faces both capital
income (shocks sy) and asset risk
(shocks sk).
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14. Hydropower and Irrigation Modeling:
Empirical evidence from the International
Food Policy Research Institute (IFPRI)
The objective is to evaluate if Ethiopia’s
economy is better off with or without the
implementation of the hydropower project.
This model is applied on energy
development, identification of suitable
hydropower and irrigation projects,
assessing hydropower and irrigation
optimization.
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15. Cont..
The basic premise of the model is to
balance capital, labor, and the energy
sector (collectively constituting gross
domestic product) with consumption
and investment
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16. A* Lt
α
*Kt
β
*Et
γ
+ ETt = ct + it + IEt
• A is a calibration
• E the consumed energy in
domestic=4,643 GWh
• ET is energy trade
• L=37.5 million
• K=US$ 16.5 billion
• α, β, and γ are set to 0.446, 0.48, and
0.074, respectively.
• IE energy investment 16

17. Objective function
A multiplier greater than 1.0 indicates
economic growth if the project is
realized.
less than 1.0 implies that the project
may not be economically wise.
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18. 5.Conclusion
In general the Ramsey–Cass–Koopmans
model is applicable on economic
optimization problems in Ethiopia.
It is also valid on utility and profit
maximization problems and project
worthiness.
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