Introduction to Modern Economic Growth of the representative household at time t by A (t) Then we have the following law of motion for the total assets of the household A˙ (t) = r (t) A (t) + w (t) L (t) − c (t) L (t) where c (t) is consumption per capita of the household, r (t) is the risk-free market flow rate of return on assets, and w (t) L (t) is the flow of labor income earnings of the household Defining per capita assets as a (t) ≡ A (t) , L (t) we obtain: (8.7) a˙ (t) = (r (t) − n) a (t) + w (t) − c (t) In practice, household assets can consist of capital stock, K (t), which they rent to firms and government bonds, B (t) In models with uncertainty, households would have a portfolio choice between the capital stock of the corporate sector and riskless bonds Government bonds play an important role in models with incomplete markets, allowing households to smooth idiosyncratic shocks But in representative household models without government, their only use is in pricing assets (for example riskless bonds versus equity), since they have to be in zero net supply, i.e., total supply of bonds has to be B (t) = Consequently, assets per capita will be equal to the capital stock per capita (or the capital-labor ratio in the economy), that is, a (t) = k (t) Moreover, since there is no uncertainty here and a depreciation rate of δ, the market rate of return on assets will be given by (8.8) r (t) = R (t) − δ The equation (8.7) is only a flow constraint As already noted above, it is not sufficient as a proper budget constraint on the individual (unless we impose a lower bound on assets, such as a (t) ≥ for all t) To see this, let us write the single 376