Consider a two-period model of consumption and exchange of a non-storable good. Assume for simplicity that everyone has zero rate of time preference. In Country A, each person is endowed with 5 at t=1 and 10 at t=2. In equally-sized Country B, each person is endowed with 10 at t=1 and 5 at t=2. The real interest rate in Country A is rA and in Country B it is rB. “W/out trade” means the countries are closed to trade. “W/trade” means the countries are open to trade with each other, as if one large economy.

Question

Consider a two-period model of consumption and exchange of a non-storable good. Assume for simplicity that everyone has zero rate of time preference. In Country A, each person is endowed with 5 at t=1 and 10 at t=2. In equally-sized Country B, each person is endowed with 10 at t=1 and 5 at t=2. The real interest rate in Country A is rA and in Country B it is rB. “W/out trade” means the countries are closed to trade. “W/trade” means the countries are open to trade with each other, as if one large economy.

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We start by restating the setup in our own words to frame the reasoning. We have a two-period model with a non-storable good and zero time preference. Country A endowments: 5 at t=1 and 10 at t=2. Country B endowments: 10 at t=1 and 5 at t=2. Real interest rates: rA in A and rB in B. "W/out trade" means each country consumes from its own endowment; "W/trade" means the economies are integrated and can trade, effectively behaving like one larger economy.: Option 1: W/out trade: rA < 0, rB > 0; W/trade: rA = rB < 0 In a closed economy with zero time preference and non-storable goods, a country with a higher early-endowment relative to late-endowment tends to have a lower (or even negative) interest rate to balance intertemporal consumption, while the country with the larger late-endowment tends to have a higher rate. Here A has more in period 2 (10) than in period 1 (5), while B has more in period 1 (10) than in period 2 (5). This would generally imply rA > 0 and rB < 0 in the no-trade setting, not the reverse. The W/trade clause claiming rA = rB < 0 is also inconsistent with standard intertemporal trade implications where, upon opening, the equalized rate would reflect balanced trade and zero net interest if preferences are identical and endowments are balanced. Therefore this option misstates both signs and the trade outcome. Option 2: W/out trade: rA > 0, rB < 0; W/trade: rA = rB > 0 The sign pattern rA > 0 and rB < 0 in the closed economy aligns with A being relatively heavier in the later period, which could require positive rA to entice consumption today versus future, while B with higher early-endowment could need negative rB. However, the literature on equal access and zero time preference with symmetric conditions would not typically yield rA = rB > 0 under trade; instead, if trade occurs and preferences are identical, rates would equalize and reflect the common intertemporal price, which under zero time preference would be zero, not strictly positive. This makes both the closed-economy sign claim and the positive synchronized rate under trade questionable. Option 3: W/out trade: rA > 0, rB < 0; W/trade: rA = rB = 0 This option has the closed-economy relation rA > 0 and rB < 0, which is plausible given A’s larger late-endowment and B’s larger early-endowment. Under trade, the economies merge into a single larger economy with arbitrage opportunities across countries and periods; with zero time preference and freely tradable non-storable goods, the intertemporal price equals zero in equilibrium, meaning rA = rB = 0. This is consistent with the idea that when trade is allowed and there is zero rate of time preference, the net return to saving or borrowing across the two periods cancels out, yielding a zero real interest rate in the integrated economy. This option thus presents a coherent narrative for both w/o trade and w/trade scenarios. Option 4: W/out trade: rA < 0, rB > 0; W/trade: rA = rB = 0 This choice reverses the plausible signs compared to the endowment structure: it claims A would have a negative rate while B has a positive rate in the closed economy, which contradicts the intuitive interpretation that A’s greater late-endowment tends to push its rate higher, not lower. The W/trade part, rA = rB = 0, is consistent with zero intertemporal price under trade, but since the closed-economy signs are already inconsistent with the endowment pattern, this option is unlikely to capture the correct equilibrium. Summarizing the reasoning across options, the coherent, internally consistent combination is that in the closed economy A’s rate is positive while B’s is negative, and once trade is introduced the two economies share a common intertemporal price, which is zero under zero time preference. This aligns with option 3’s specification: W/out trade: rA > 0, rB < 0; W/trade: rA = rB = 0.

IFEPIA7022_001_2025_3 - Economics of Finance EOF Midterm

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