Overview
Introduction
The basic Solow model assumes the following:
 Constant returns to scale production function
 Constant population growth $n$
 Constant technological progress $g$
 Fixed savings rate $s$
Although it is a useful model, the choice of $s$ is arbitrary and does not obey any microeconomic foundation. In particular, microeconomic theory relates present and future consumption decisions through the interest rate. The Ramsey model amends these shortcomings and the decisions of all agents are microeconomically founded. In particular, we assume:
Ramsey assumptions:
 A large number of identical firms operating with the same technology:
 Rent capital and hire labour
 A large number of households:
 Consume, supply labour, own and lend capital
 Constant returns to scale production function
Agents (households) optimally decide consumption and savings, depending on the interest rate. Hence, the saving rate is definitely no longer exogenous and need not be constant.
In this course we focus on the discretetime version of the Ramsey model. In particular, time takes values $t=0,1,\ldots,+\infty.$
References
Ramsey (1928)
Cass (1965)
Koopmans (1965)
Romer, Advanced Macroeconomics: Chapter 2^{1}

Romer derives all the results in continuous time, we use discrete time. ↩︎