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4.2. THE ONE-MONEY MONETARY ECONOMY 113you did in (3.9) for the monetary model, the equity price—dividend ratiocan be expressed as the present discounted value of future consumptiongrowth raised to the power 1 − γ. You can then get an explicit solutiononce you make an assumption about the stochastic process governingoutput. This will be covered in section 4.5 below.An important point to note is that there is no actual asset tradingin the Lucas model. Agents hold their investments forever and neverrebalance their portfolios. The asset prices produced by the model areshadow prices that must be respected in order for agents to willingly tohold the outstanding equity shares according to (4.21).4.2 The One-Money Monetary EconomyIn this section we introduce a single world currency. The economicenvironment can be thought of as a two-sector closed economy. Theidea is to introduce money without changing the real equilibrium thatwe characterized above. One of the difficulties in getting money intothe model is that the people in the barter economy get along just Þnewithout it. An unbacked currency in the Arrow—Debreu world that generatesno consumption payoffs will not have any value in equilibrium.To get around this problem, Lucas prohibits barter in the monetaryeconomy and imposes a ‘cash-in-advance’ constraint that requires peopleto use money to buy goods. As we enter period t the followingspeciÞc cash-in-advance transactions technology must be adhered to.1. x t and y t are revealed.2. λ t , the exogenous stochastic gross rate of change in money is revealed.The total money supply M t , evolves according toM t = λ t M t−1 . The economy-wide increment ∆M t =(λ t −1)M t−1 ,is distributed evenly to the home and foreign individuals whereeach agent receives the lump-sum transfer ∆Mt =(λ2 t − 1) M t−1.23. A centralized securities market opens where agents allocate theirwealth towards stock purchases and the cash that they will need topurchase goods for consumption. To distinguish between the aggregatemoney stock M t and the cash holdings selected by agents,