Consider a two-period small open endowment economy populated by a large number of households with preferences described by the lifetime utility function

An Anticipated Output Shock

Consider a two-period small open endowment economy populated by a large number of households with preferences described by the lifetime utility function: 11 U = C 10 C 11 (1) Suppose that households receive exogenous endowments of goods given by Q1 = Q2 = 10 in periods 1 and 2, respectively. Every household enters period 1 with some debt, denoted B0∗, inherited from the past. Let B0∗ = −5. The interest rate on these liabilities, denoted r0, is 20 percent. Finally, suppose that the country enjoys free capital mobility and that the world interest rate on assets held between periods 1 and 2, denoted r∗, is 10 percent.

a (14 points) Compute the equilibrium levels of consumption, the trade balance, and the current account in periods 1 and 2. Do not forget to show step by step your algebraic calculations. Explain in detail your reasoning. No credit without an explanation.

b (16 points) Assume now that the endowment in period 2 is expected to increase from 10 to 15. Calculate the effect of this anticipated output increase on consumption, the trade balance, and the current account in both periods. Provide intuition. Do not forget to show step by step your algebraic calculations. Explain in detail your reasoning. No credit without an explanation.

Solutions

Expert Solution

a.The lifetime utility function is ln C1+(10 / 11)ln C2. Compute the marginal rate of substitution as MRS = MUC1 / MUC2

MRS = (1/C1)/(10/11C2) = 1.1C2/C1. Now see the intertemporal budget constraint

C1 + C2/(1+r) + B0*(1 + i) = Q1 + Q2/(1+r)................. r is the interest rate on saving and i is the interest rate on debt

C1 + C2/1.1 + 5*(1 + 0.2) = 10 + 10/1.1

C1 + C2/1.1 = 4 + 10/1.1

1.1C1 + C2 = 14.4

Utility maximization requires MRS = slope of the budget constraint

1.1C2/C1 = 1.1/1

C2 = C1

Placing this in the budget equation

1.1C1 + C1 = 14.4

C1* = 6.8571 and C2* = 6.8571

These are the current consumption levels. In period 1 when consumers receive 10, they consume 6.8571, save the remaining and invest the same at 10% so that in period 2 they have (10 - 6.8571)*(1 + 0.1) = 3.4572. In the second period, they consume 6.8571, and add the two-period savings = 3.4572 + (10 - 6.8571) = 6.6 to pay off the liability.

Rahul Sunny answered 1 year ago

Next > < Previous

Related Solutions

Consider a two-period, small, open, endowment economy without investment and government expenditures, but with durable consumption...

Consider a two-period, small, open, endowment economy without investment and government expenditures, but with durable consumption goods. Purchases of durable consumption goods in period 1, denoted C1, continue to provide utility in period 2. The utility of households in period 2 depends on purchases of durable consumption goods in period 2 , denoted C2, and on the un-depreciated stock of durables purchased in period 1. Durable consumption goods are assumed to depreciate at the rate δ ∈ [0, 1]. Household...

Consider a small-open endowment economy described in Topic 4 with free capital mobility, a single traded...

Consider a small-open endowment economy described in Topic 4 with free capital mobility, a single traded good per period, and a government that levies lump-sum taxes to finance government purchases. Assume that there is no physical capital and hence no investment. Assume that the economy exists for an infinite number of periods. Assume a fixed exchange rate and the effects of the once-and-for-all devaluation of the domestic currency. In THREE sentences provide a critic of the assumptions made in seminar...

Consider two assets, A and B, in a competitive market populated by a large number of...

Consider two assets, A and B, in a competitive market populated by a large number of risk-averse agents. ForassetA: pricepA =10attime0;andpaysXA =12attime1. For asset B: price pB = 10 at time 0; and pays, at time 1, XB = 20 with probability 0.5, and XB = 4 with probability 0.5. a. Please calculate the expected return and the standard deviation of return for asset A. b. Please calculate the expected return and the standard deviation of return for asset B....

Two period saving model) Consider an economy populated by identical people who live for two periods....

Two period saving model) Consider an economy populated by identical people who live for two periods. They have preferences over consumption of the following form: U=ln(c1) +βln(c2), where ct denotes the stream of consumption in period t. They also receive an income of 50 dollars in period 1 and an income of 55 dollars in period 2. They can use savings to smooth consumption over time, and if they save, they will earn an interest rate of 10% per period....

Consider a two-period model of a small open economy that cannot commit to repaying its debt....

Consider a two-period model of a small open economy that cannot commit to repaying its debt. The endowments are Q1 and Q2 in periods 1 and 2. The world interest rate is r. In period 1, the country can borrow from or lend to the rest of the world, but it cannot commit to repaying its debts. In period 2, if the economy does not repay, then it loses a fraction F of its endowment. The representative consumer has preferences...

Consider a classical model of large-open economy described by the following equations: Y = C +...

Consider a classical model of large-open economy described by the following equations: Y = C + I + G + NX Y = 8,000 G = 2,500 T = 2,000 C = 500 + 2/3 (Y − T) I = 1,000 − 50r CF = 500 − 50r NX = 1,000 − 250ε where Y is output, C is consumption, I is investment, G is government purchases, NX is net exports, T is taxes, r is the real interest rate,...

Question 1. One period macroeconomic model We consider an economy closed to a period populated by...

Question 1. One period macroeconomic model We consider an economy closed to a period populated by consumers and produce. The representative consumer chooses the quantity of leisure, let of consumption, as its utility under budget constraint. The representative producer chooses the labor factor that maximizes his profile Preferences satisfy the same properties as in the standard consumer model Similarly, the production function, Y = F(K.N), where k is the capital stock and the quantum labor factor obeys the properties than...

1. How does a small open economy differ from a large open economy? A. A small...

1. How does a small open economy differ from a large open economy? A. A small open economy has no effect on the world real interest rate. B. A small open economy is only open to trade with similar economies. C.A small open economy is able to influence the world interest rate through its saving and investment decisions. D.In a small open economy, equilibrium occurs when saving equals investment; however, in a large open economy equilibrium occurs when desired saving...

Consider a consumer's preferences over consuming two goods that are represented by the following utility function:...

Consider a consumer's preferences over consuming two goods that are represented by the following utility function: U（x1，x2）= x1^a x2^1-α 0 < α < 1 x1，x2 ≥ 0 (a) Do her preferences satisfy monotonicity? (4 mark) (b) Do her preferences exhibit diminishing marginal utility? (c) Are her preferences convex? In other words, do her preferences exhibit diminishing marginal rate of substitution? (Hint: Find MRS and its rate of changes with respect to the good on the horizontal axis.) (d) Use a...

1) Consider a small open economy that initially starts in balanced trade. Another, "large" economy does...

1) Consider a small open economy that initially starts in balanced trade. Another, "large" economy does tight fiscal policy. As a result, the world real interest rate will _______ and the small open economy will experience a trade ______. a. increase; deficit b. decrease; deficit c. decrease; surplus d. increase; surplus 2) In economics, "domestic" means a. international b. American c. in autarky (not trading) d. actively trading

Subjects