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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Outlines1.Definition…………………………………………….32.Objectives…………………………………………...43. Ramsey–Cass–Koopmans
growth model………………………....5
4. Application of Ramsey–Cass –
Koopmans growth model…………….11
5.Conclusion……………………………....18
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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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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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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Budget constraint
,where Bt is assets, wt is wage rate and rt is interest rate.
In per capita terms:
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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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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. 8
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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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
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4.Application of Ramsey –Cass Koopmans growth model in Ethiopia
1.On Risk modeling:
2.On Hydropower and Irrigation Modeling:
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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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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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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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A* Lt α *Kt
β *Etγ + 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
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.17
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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