The first constraint implies that the agent takes the money earned in youth and allocates it to the holdings of domestic currency (m£) and foreign currency (m(). Here et is the period t exchange rate: the amount of domestic currency per unit of foreign currency add comment.
The second and third constraints imply that old agents take their money holdings and spend them on home and foreign goods. These constraints reflect two important aspects of our environment. First, within a period, exchange markets open after goods markets. Hence old agents cannot adjust their portfolio holdings before going to goods markets: this is a basic friction in our model.7 Second, agents are required to make purchases using local currency. This is an assumption of our model at this point, though in Section IV we show that this type of constraint will arise endogenously in the game between governments. Given these constraints, old agents have no choice: they will optimally spend all of their money holdings.
The process of money creation is reflected in the evolution of domestic money holdings. In particular, each young agent in generation £, regardless of his money holdings, receives a transfer of rt+1 at the start of old age. This transfer is perfectly anticipated. Note that an agent does not receive transfers of foreign currency: this is the basis of the inflation tax on foreign currency holders which, as we shall see, redistributes real wealth to domestic citizens.
It is critical that в is realized after the choices of employment and currency holdings. If, for example, в was known in youth, then the portfolio choice of the young agents would reflect this variable and there would be no ex post misallocations. In our model, in contrast, because of the local currency in advance constraints, ex post consumption profiles must be financed out of ex ante portfolio choices. Given the nature of the preferences we have assumed, it is clear that agents will generally want to adjust their expenditures after the realization of the taste shock but are prevented from doing so by the local currency constraints and the assumed timing of the markets.
The first order conditions for the agent’s optimization problem is summarized by two conditions:
The first of these conditions relates the marginal disutility of work to the marginal utility from the consumption of the foreign good. The second condition is essentially the expenditure share condition that emerges in optimization problems with Cobb-Douglas preferences, though here the expectation of в rather than the realization of this variable determines expenditure shares since portfolio decisions are made ex ante. Note that given the specification of utility, the future price of foreign goods is not present in these conditions. That is, labor supply and the budget shares depend on the current return to work as well as the transfer but not period t + 1 prices.