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ECON 371 Spring 2010 Answer Key for Problem Set 3 (Chapters 16-17) Instructor: Kanda Naknoi March 8, 2010 ANSWER 1 (2 points) By definition, a debtor country has negative external wealth: W = A – L < 0, where W denotes external wealth, A denotes external assets and L denotes external liabilities. Net capital income (NCIF) flows accrued on external liabilities and assets are recorded in the net factor income account (NFIA) which is a part of current account. Specifically, NCIF is the difference between capital income accrued on external assets and capital income accrued on external liabilities: NCIF = rA A – rL L, (1) where rA and rL are the rate of return on external assets and external liabilities, respectively. It is possible for the U.S. to receive positive NCIF if rA > rL. In fact, this is the case in the actual balance of payments statistics. The return on U.S. external assets is found to be 2%-3% higher than the return on U.S. external liabilities. To give a numerical example, suppose A = $4 trillion, L = $5 trillion, rA=7% and rL= 5%. Substituting these numbers into Equation (1) yields NCIF: NCIF = 0.07(4) – 0.05(5) = 0.28-0.25 = $0.05 trillion > 0. We can also verify that these numbers make the U.S. a debtor country by showing that they produce negative external wealth: W = 4-5 = - $1 trillion < 0. ANSWER 2.a (1 point) There is a one-time increase in output by 20%. The increase amounts to 0.20($1700)=$340. The present value of output is: PV(Q) = (1700+340) + 1700/1.07 + 1700/1.072+ 1700/1.073+ … = 340 + (1700 + 1700/1.07 + 1700/1.072+ 1700/1.073+ …) = 340 + 1700(1.07)/0.07 = 26,325.71 1 In the closed economy, the country must absorb the entire change in output into consumption in the initial period because international borrowing or lending is not possible. Therefore, C0=2040 and Ct=1700 for t>0. ANSWER 2.b (1 point) In the open economy, the present value of consumption is the same as in the closed economy. The difference is that the country is able to save the gain in output to increase consumption by a small amount today and increase consumption in subsequent years too. To determine the level of consumption each period, the representative consumer plans a constant level of consumption: Ct= C0 for all t: PV(Q) = C0 + C0/1.07 + C0/1.072 + C0/1.073 + … 340 + 1700(1.07)/0.07 = C0 (1.07)/0.07 C0 = 340(0.07)/1.07 + 1700 = 1722.24 ANSWER 3.a (1 point) Yes, this U.S. should fund this project. The criterion for investing in a project is that: PV(Cost of investment) < PV (Return on investment) (2) Since there is no new investment from Year 1,PV(Cost of Investment) = $30 billion. The present value of return on investment now depends on the interest rate. Here, the domestic interest rate if the economy is closed is the same as the MPK. The world interest rate is 0.04. However, when this country opens to the world capital market, the domestic interest rate becomes the same as the world interest rate. Thus, we use the world interest rate to evaluate the present value of the return on investment. Every period this project pays 6% of $30 billion. Hence, PV(Return on Investment) = 0+0.06(30)/1.04+ 0.06(30)/1.042 +… = 0.06(30)/0.04= $45 billion. In this case, PV(cost of investment) < PV(Return on Investment). As a result, this investment project should be undertaken. ANSWER 3.b (1 point) Present value of payoff is $45 billion. (See ANSWER 3.a) ANSWER 3.c (1 point) 2 Note that the home country can borrow less than the cost of investment project. In other words, the home country faces “borrowing constraint” in the world capital market. Before solving for paths of consumption and other variables in this case, it is instructive to consider the two cases we studied in class: (1) Closed economy without international borrowing; and (2) Open economy with international borrowing without borrowing constraint. In Case 1, the closed economy must finance investment with domestic saving or Q – C. This is because the closed economy is subject to the static budget constraint: Q = I + C. Case 1: Closed economy, no international borrowing : r = MPK = 0.06; investment return = 0.06(30) = 1.80 (Unit = $billion) Time 0 1 2 3 … Present Value Q 300 301.80 301.80 301.80 … 5631.80 I 30 0 0 0 … 30.00 C 270 301.80 301.80 301.80 … 5601.80 In Case 2, the home country can borrow as much as it desires. Thus, the home residents can smooth consumption and finance its investment from borrowing. They choose constant consumption path C0 such that: PV(Q)= PV(C) + PV(I). Substitute the paths of Q and I into this lifetime budget constraint: 300+301.80/1.04 + 301.80/1.042 +… = (C0+ C0/1.04 + C0/1.042 + …) + 30 300 + 301.80/0.04 = C0(1.04)/0.04 + 30 C0 = (7845-30)0.04/1.04 = 312.18 Case 2: Open economy without borrowing constraint: r = r* = 0.04; investment return = 0.06(30) = 1.80 (Unit =$billion) Present Time 0 1 2 3 … Value Q 300 301.80 301.80 301.80 … 7845 I 30 0 0 0 … 30 C 300.58 300.58 300.58 300.58 … 7815 TB = Q-I-C -30.58 1.22 1.22 1.22 … 0 NFIA = -0.04(30), t>0 0 -1.20 -1.20 -1.20 … 30 CA = TB + NFIA -30.58 0.02 0.02 0.02 … -30 W(t) = W(t-1) + CA(t) -30.58 -30.56 -30.54 -30.52 … Note that the present value of income is different from that in Case 2, because the interest rate is now 4%. We can calculate trade balance by substituting C0 = 312.18 into the trade balance equation: TB = Q – I – C. In Year 0, the consumer borrows to finance both investment and an increase in consumption. This is because they foresee “permanent increases” in their output and lifetime income. Thus, they can afford to increase consumption even before the investment begins to pay off. Note that the external debt keeps shrinking, because the investment return is higher than the cost of borrowing. As this continues indefinitely, the external wealth position can 3 becomes positive and the home country can switch from being a debtor to a creditor! This is possible simply because the home country possess more advanced technology than the rest of the world. Finally, let us consider the situation in Question 3, and call it Case 3. In this case, the home country faces the borrowing constraint. This implies that the investment project must be partially financed by the domestic fund. The only way to do this is to cut consumption in Year 0. Thus, the static budget constraint binds in Year 0. From Year 1, the static budget constraint also binds because the home residents do not need to borrow any more. The home residents use income to consume and to service debt. Again, we assume that the foreign lenders do not require payment of the principal. Thus, from Year 1 the home residents will run trade surplus only to service the interest rate payment = 0.04(20), and consume the rest of output. Case 3: Open economy with borrowing constraint: r = r*= 0.04; investment return = 0.06(30) = 1.80 (Unit = $billion) Time 0 1 2 3 Q 300 301.80 301.80 301.80 I with foreign fund 20 0 0 0 I with home fund 10 0 0 0 C = Q – I – TB 290 301.00 301.00 301.00 TB = - NFIA -20 0.80 0.80 0.80 NFIA = - 0.04(20), t>0 0 -0.80 -0.80 -0.80 CA = TB + NFIA -20 0 0 0 W(t) = W(t-1) + CA(t) -20 -20 -20 -20 … … … … … … … … … Present Value 7845 20 10 7815 0 -20 -20 Let us compare the paths of consumption in all cases. Even with the borrowing constraint, consumption still displays smaller volatility than consumption in the closed economy. Thus, the home residents are still better off with borrowing despite the borrowing constraint. ANSWER 3.d (1 point) See Case 3 in ANSWER 3.c. ANSWER 4 (2 points) If the interest rates rise to 8%, the interest payments needed to service its debt will be doubled from $0.80 billion to 0.08($20) = $1.6 billion. To finance the increase in debt service burden, the consumers must reduce its consumption to finance the increase in debt service. The reduction of consumption can be alleviated if the firms can find a way to increase productivity among workers without a need to finance a new technology. 4