Ramsey–Cass–Koopmans model

and its application in Ethiopia

By Molla Deribie ID.No.MAEC/0182/2005

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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Cont..

The household faces both capital income (shocks sy) and asset risk (shocks sk).

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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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