International macroe.. - Free

4.3. THE TWO-MONEY MONETARY ECONOMY 119products that individuals desire are claims to future dollar and eurotransfers. 5 So to develop this idea, let r t be the price of a claim toall future dollar transfers in terms of x and rt∗ be the price to all futureeuro transfers in terms of x. Let there be one perfectly divisibleclaim outstanding for each of these monetary transfer streams. Let thedomestic agent hold ψ Mt claims on the dollar streams and ψ Nt claimson the euro streams whereas the foreign agent holds ψMt ∗ claims onthe dollar stream and ψNt ∗ claims on the euro stream. Initially, thehome agent is endowed with ψ M =1, ψ N = 0 and the foreign agent hasψN ∗ =1, ψM ∗ = 0 which they are free to trade.Now to develop the problem confronting the domestic household,note that current-period wealth consists of nominal dividends paid fromequity ownership carried over from last period, current period monetarytransfers the market value of equity and monetary transfer claimsW t = P t−1ω xt−1 x t−1 + S tPt−1∗ω yt−1 y t−1P tP| {z t}Dividends+ ψ Mt−1∆M t+ ψ Nt−1S t ∆N tP tP| {z t}Monetary Transfers+ ω xt−1 e t + ω yt−1 e ∗ t + ψ Mt−1r t + ψ Nt−1 rt∗ . (4.40)| {z }Market value of securitiesThis wealth is then allocated to stocks, claims to future monetary transfers,dollars and euros for shopping in securities market trading accordingtoW t = ω xt e t + ω yt e ∗ t + ψ Mt r t + ψ Nt rt ∗ + m t+ n tS t. (4.41)P t P tThe current values of x t ,y t ,M t , and N t are revealed before trading occursso domestic households acquire the exact amount of dollars andeuros required to Þnance current period consumption plans. In equilibrium,we have the binding cash-in-advance constraintsm t = P t c xt , (4.42)5 In the real world, this type of hedge might be constructed by taking appropriatepositions in futures contracts for foreign currencies.