The Ramsey Model with a Perfectly Competitive Market

In the previous chapter, we cover the Ramsey model, in which the representative household carries out the production of goods. However, this setting is unrealistic because goods are often produced by firms in the real world. In this chapter, we introduce a market economy to the Ramsey model, in which the representative household supplies labour and capital to a representative firm, which then uses these factor inputs to produce output and sells the output back to the household. As you can see, this familiar setting is basically the neoclassical growth model of Chapter 2. After deriving the equilibrium allocation of resources in the decentralised market economy, we can then compare it to the allocation in the centralised economy that is optimally chosen by the representative household as in Chapter 10. In summary, we find that the two sets of allocations are the same, implying that the market economy is efficient. In other words, the first fundamental theorem of welfare economics holds in this setting due to the absence of distortion in the market economy.