Many economists have argued on macroeconomics words for several years in their school of thoughts. Ramsey, the neoclassical economist, has not believed in the Solow model with some terms. What makes his model differs from the Solow model is that it explicitly models the choice of consumption at a point in time and so has made the savings rate endogenous. The Twentieth first research in Ethiopia (Seid Nuru, 2012, p.6-7) found that the outcome of the optimization of the dynamic model is that growth in the long-run depends on the rate of technological change and rate of change of rainfall variability in terms of both amplitude and frequency.

1. 1
1.Introduction
Many economists have argued on macroeconomics words for several years in their school of
thoughts. Ramsey, the neoclassical economist, has not believed in the Solow model with some
terms. What makes his model differs from the Solow model is that it explicitly models the choice
of consumption at a point in time and so has made the savings rate endogenous. The Twentieth
first research in Ethiopia (Seid Nuru, 2012, p.6-7) found that the outcome of the optimization of
the dynamic model is that growth in the long-run depends on the rate of technological change
and rate of change of rainfall variability in terms of both amplitude and frequency.
Further recent research (B. J. Heijdra & F. van der Ploeg, 2004, p.71) has suggested that the
model is attractive because it features intertemporal optimization by households rather than ad
hoc consumption-saving rules. As a result, unlike in the Solow model, the saving rate may not be
constant along the transition to the long run steady state. This result is due not just to the
endogeneity of the saving rate but also because of the infinite nature of the planning horizon of
the agents in the model; it does not hold in other models with endogenous saving rates. In the
absence of technological progress the Ramsey model predicts zero growth as in the simple
Solow-Swan model (Sarantis Kalyvitis, n.d, p.7).
1.1. Definition
The Ramsey–Cass–Koopmans model or the Ramsey growth model is a neo-classical model of
economic growth that makes the savings rate endogenous. It focuses on the decentralized
economy development.

2. 2
2.Objectives of the paper
In line with the give title this task has the following specific objectives;
• To understand what the Ramsey growth model says about;
• To analyze the Ramsey growth model;
• To see the application of the Ramsey growth model in Ethiopia and
• To draw a relevant conclusion on wards the results and scientific findings of the model;
3.The Ramsey–Cass–Koopmans model
As long as a Ramsey model has considered, there is a social planner and firms’ behavior in the
decentralized economy problem whose goal is maximization of the discounted sum of
intertemporal utility and profit respectively.
Household in the Ramsey Growth Model
Assumptions:
• One infinitely-lived household that maximizes intertemporal utility
• Households are identical.
• Closed economy is there⇒there are no loans among households since all households are
identical.
• The household receives wage income in exchange for its labor services and interest income
for its accumulated assets
• The income acquired is directed in purchasing goods for consumption and in savings through
the accumulation of additional assets
• Population growth rate is constant (equal to n) and at time t=0 there is only one individual in
the economy (i.e. L0 = 1), so that the total population at any time t is given by Lt = ent
Objective function:
∞
dt ,
Budget constraint (the change in assets equals the sum of labor and interest income less
consumption):
B = wt Lt + rtBt − Ct, where Bt is assets, wt is wage rate and rt is interest rate. In per capita terms:
= + − − , where b = !
"
, c =
$!
"

3. 3
Problem of the household: Maximize intertemporal utility subject to the budget constraint
(the Hamiltonian approach)
L= u e '
+ λt[wt +(r – n) bt-ct], where ) is Lagrangian multiplier or marginal utility of
income.
FOC
*L
*C
= 0 ⇒ ′
e '
= )
-L
-.
= −) ⇒ ) = − r − n )
Transversality condition:
lim
→∞
λ5 = 0
The value of the representative household’s assets must approach zero as time approaches
infinity ⇒ individuals do not prefer to hold assets perpetually or –if they do- these assets should
have no value in terms of the objective function.
Households choose consumption so to equate the rate of return to savings, r, to the ‘rate of
return’ to consumption. Or return on future consumption = return on current consumption.
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.
Households are indifferent between consumption and saving if the associated rates of
return are equal.
Firms’ behavior in the decentralized economy
Assumptions:
• The economy consists of a large number of identical firms producing a homogeneous
consumption good Υ. If there are a large number of firms, no single firm holds any market
power.
• Each firm uses a production technology Υ = F(K,L) that satisfies the neoclassical properties, and
pays wages and interest in exchange for labor and capital services respectively

4. 4
• R is the rental price for a unit of capital ⇒The net rate of return to capital equals then R-δ=r,
with δ denoting the capital depreciation rate, because r is the interest rate on loans to other
households, which are perfect substitutes with capital.
Problem of the representative firm i: choose the amount of capital Κi and labor input Li to
maximize its profit πi (static problem)
πi = F(Ki , Li ) − (r +δ )Ki – wLi
FOC
67
68
= 0 ⇒ 9′ : = + ; (Marginal product of capital)
67
6<
= 0 ⇒ 9′
= (Marginal product of labor)
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
4.1 On Risk modeling:
This model applies in Ethiopia in such a way that on growing out of poverty under risk. It can
identify the aggregate effect of risk on resource accumulation, economic growth and savings, the
nature of the risk faced.
Based on a research has done in 2009 on evidence from rural Ethiopia assumes that there is a
single good, used for consumption, as a store of value and also as a productive asset. Agents
maximize expected utility over an infinite horizon. Each household solves for the optimal
investment function.
The household faces two types of risk: capital income risk (shocks sy) and asset risk (shocks
sk). We assume rational expectations: the household knows the distributions of these shocks.
4.2 On Hydropower and Irrigation Modeling:
Discussion on Ramsey model application in Ethiopia is now focusing on a recent research has
done by et al,Paul J. Block on Integrated Management of the Blue Nile Basin in Ethiopia. The
researchers have applied the Ramsey model on their task.
This model is applied on energy development, identification of suitable hydropower and
irrigation projects, assessing hydropower and irrigation optimization.
Project Multipliers
A Ramsey growth model for energy development specifies project multipliers on total GDP over
the 100-year simulation ranging from 1.7-5.2, for various climatologic conditions.
To assess the influence of the proposed hydropower project on the Ethiopian economy as a
whole, a series of Ramsey economic growth models are developed. The basic premise of the
model is to balance capital, labor, and the energy sector (collectively constituting gross domestic
product) with consumption and investment; irrigation has not been included.
A* Lt
α
*Kt
β
*Et
γ
+ ETt = ct + it + IEt

6. 6
A is a calibration parameter to rectify units, and t is the time step, in months. L represents the
labor force, initially equal to 37.5 million, growing at a rate consistent to the population growth
rate of 2.9 percent per year (CIA 2006).K is the capital within the country, initially set at US$
16.5 billion (UNECA 2000), growing with investment. E symbolizes the domestic energy sector,
set to 4,643 GWh in the base year, and represents energy that is consumed by Ethiopia, while ET
represents energy generated beyond the country’s ability to absorb, available for trade to
neighboring countries. The exponents represent the value share, and follow a Cobb-Douglas
approach summing to 1.0 (Mansfield and Yohe 2004). For this model, α, β, and γ are set to
0.446, 0.48, and 0.074, respectively. c stands for the country-wide consumption, and i the
investment. IE represents specific investment in the energy sector (infrastructure and associated
costs.)
Objective function
U = >[dt ∗ log Ct ]
U symbolizes the country-wide utility, and d the discount factor.
The project multipliers derived here represent a multiplier on gross domestic product (GDP) over
the 100-year simulation, and provide an indication of the potential benefits of the project,
including associated benefits through economic feedbacks. They result from a combination of
the total gross domestic product from these Ramsey growth models utilizing energy from
IMPEND or prescribed energy growth.
CDEFGHEGIJ =
KLKMN OPQRSQTP − KLKNM OPQUVWXYVZ[W
U]RSQTP
The numerator represents the difference between the total GDP from the Ramsey model using
energy from the Investment Model for Planning Ethiopian Nile Development (IMPEND) (first
term) and prescribed energy (second term.), PW represents the present worth of the hydropower
project, discounting benefits and costs. The Ramsey model utilizing prescribed energy includes
ET and IE values set to zero (no excess energy produced and no massive energy investment
costs.). The objective is to evaluate if Ethiopia’s economy is better off with or without the
implementation of the hydropower project. A multiplier greater than 1.0 indicates economic

7. 7
growth if the project is realized; less than 1.0 implies that the project may not be economically
wise. To reiterate, the multiplier is not simply a benefit-cost ratio of the hydropower project, but
reflects the potential impact of significantly increasing the size of the energy sector on the total
GDP.
Empirical evidence from the International Food Policy Research Institute (IFPRI)
The followings table present expected multipliers for the three climatic conditions under the two
flow policies. Table 6 assumes a prescribed growth rate in energy demand of zero percent; Table
7 assumes a 3 percent prescribed energy growth rate.
Table 1: Multipliers on total GDP utilizing IMPEND and zero percent prescribed energy
models
Scenario: Historic 2 x La 2 x El Nino
Flow Policy
5% Policy 4.3 4.2 5.0
50% Policy 4.3 3.8 5.2
Table 2: Multipliers on total GDP utilizing IMPEND and 3 percent prescribed energy
models
Scenario: Historic 2 x La 2 x El Nino
Flow Policy
5% Policy 1.9 1.9 2.2
50% Policy 1.9 1.7 2.3
Clearly all ranges of multipliers are well above 1.0, indicating the potential positive impact of the
hydropower project on the economy as a whole. The values for the El Niño condition are slightly
higher based on lower overall net present values, but may indicate a greater overall risk. An
evaluation of energy traded (ET) to neighboring countries indicates a strong potential for
boosting the Ethiopian economy, and reinforces the need for significant economic planning
including the necessity of securing energy trade contracts prior to extensive development.

8. 8
5. Conclusion
The overall study aims to assess Ramsey–Cass–Koopmans model and its application in Ethiopia.
This model mainly focuses on both households and firms in the decentralized economy.
Households have a problem of maximizing its intertemporal utility via consuming goods and
services with a constraint of budget allocation on purchasing of goods and services they render.
In general, from the Ramsey model the study of this theme can conclude a given household
intertemporal utility which is constrained by its budget availability. This will be true if and only
if the consumer is a rational being. As households’ budget level become high, the households’
tendency towards consuming a commodity will increase. Thereby therefore, intertemporal utility
of a representative household become maximize. As households consume more and more,
interetemporal utility become diminish and we call it the law of diminishing marginal utility.
Firms have a problem of maximizing its profit via producing goods and services with a
constraint of factors of production (capital rental rate and wage rate).
In general the Ramsey–Cass–Koopmans model is applied in Ethiopia in such a way that on risk
modeling (checking the aggregate effect of risk on accumulation, the effect of risk on economic
growth, the nature of the risk faced on the economy, the effect of risk on savings depends, the
welfare cost of risk) and on Hydropower and Irrigation Modeling (for energy development,
identification of suitable hydropower and irrigation projects, assessing hydropower and irrigation
optimization).

9. 9
References
• Paul J. Block, Kenneth Strzepek, Balaji Rajagopalan, 2009, Integrated Management of
the Blue Nile Basin in Ethiopia;Hydropower and Irrigation Modeling,University of
Colorado
• (Sarantis Kalyvitis, n.d).
• Christopher D. Carroll August 11, 2012, handout of The Ramsey/Cass-Koopmans (RCK)
Model
• A hand out on The Ramsey/Cass-Koopmans (RCK) Model
• B. J. Heijdra & F. van der Ploeg May 2004 Foundations of Modern Macroeconomics
• Temesgen Tadesse Deressa, 2007, Measuring the Economic Impact of Climate Change
on Ethiopian Agriculture:Ricardian Approach
• Kenza Benhima, 13th October 2008, A Reappraisal of the Allocation Puzzle through the
Portfolio Approach ,Crest (Paris)
• Seid Nuru Ali, 2012,Climate Change and Economic Growth in a Rain-fed Economy:
How Much Does Rainfall Variability Cost Ethiopia?, Addis Ababa, Ethiopia
• Pengfei Wang, 2010,Notes on the Ramse,Hong Kong University of Science and
Technology,on the Ramsey Model
• Vahagn Galstyan, 2012, MSc Macroeconomics Topic 2: The Ramsey Model of Growth,
Trinity College Dublin
• Chris Elbers, Jan Willem Gunning and Lei Pan, 2009, growing out of Poverty under
Risk: Evidence from Rural Ethiopia, the Netherlands