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114 CHAPTER 4. THE LUCAS MODELdenote individual’s choice variables by lower case letters, m t andm ∗ t . Securities market closes.4. Decentralized goods trading now takes place in the ‘shoppingmall.’ Each household is split into ‘worker—shopper’ pairs. Theshopper takes the cash from security markets trading and buysx and y−goods from other stores in the mall (shoppers are notallowed to buy from their own stores). The home-country workercollects the x− endowment and offers it for sale in an x−goodstore in the ‘mall.’ The y−goods come from the foreign country‘worker’ in the foreign country who collects and sells they−endowment in the mall. The goods market closes.5. The cash value of goods sales are distributed to stockholders asdividends. Stockholders carry these nominal dividend paymentsinto the next period.The state of the world is the gross growth rate of home output, foreignoutput, and money (g t ,g ∗ t , λ t ), and is revealed prior to trading.Because the within-period uncertainty is revealed before any tradingtakes place, the household can determine the precise amount of moneyit needs to Þnance the current period consumption plan. As a result,it is not necessary to carry extra cash from one period to the next. Ifthe (shadow) nominal interest rate is always positive, households willmake sure that all the cash is spent each period. 4To formally derive the domestic agent’s problem, let P t be the nominalprice of x t . Current-period wealth is comprised of dividends fromlast period’s goods sales, the market value of ex-dividend equity shares4 It may seem strange to talk about the interest rate and bonds since individualsdo not hold nor trade bonds. That is because bonds are redundant assets in thecurrent environment and consequently are in zero net supply. But we can computethe shadow interest rate to keep the bonds in zero net supply. The equilibriuminterest rate is such that individuals have no incentive either to issue or to buynominal debt contracts. We will use the model to price nominal bonds at the endof this section.