Ramsey model is an extension of the Solow model in terms of bringing optimization into the growth process. It is one of the basic workhorse models in macroeconomics. The basic point about Ramsey model is that, it is a prescriptive theory and not a predictive. Basically, this kind of model is developed for a closed economy. The only agents included are households and firms. The household supplies labour to the firm and is also shareholder of the firm.
There are two key equations of the Ramsey model.
1. The first equation is the law of motion for capital accumulation.
2. The second equation concerns the savings behavior of households and is less intuitive.
The first equation simply states that investment, or increase in capital per worker is that part of output which is not consumed, minus the rate of depreciation of capital.
In the second equation, If households are maximizing their consumption inter-temporally, at each point in time they equate the marginal benefit of consumption today with that of consumption in the future, or equivalently, the marginal benefit of consumption in the future with its marginal cost.
There are two reasons why households prefer to consume now rather than in the future.
First, they discount future consumption.
Second, because the utility function is concave, households prefer a smooth consumption path. An increasing or a decreasing consumption path lowers the utility of consumption in the future.