Economics 302Spring 2008Answers to Homework #3Homework will be graded on completeness and content as well as neatness. Sloppy or illegible work will not receive full credit. This homework requires the use of Microsoft Excel. If your answer requires rounding, round to two decimal places.1. Small Open EconomyUse the following set of Classical Model equation for a small open economy to answer the following questions. Y = F (K, L) = AKαL1-αC = C (Y – T) = 23 + .72 (Y – T)I = I (r*) = 325 – 15.5 r* (Where r is expressed as a percentage, i.e. if the interest rate is 5% then r = 5 in the equation.)Y = C + I + G + NXY = C + SP + TG = 220T = 155K = 1000L = 8000A = 0.3 Capital’s Share of Income = 1/3a. What is aggregate output, Y, for this economy?Y = AKαL1-α = 0.3 * 10001/3 * 80002/3 = 0.3 * 10 * 400 = 1200b. What is the level of consumption, C, for this economy?C = 23 + .72 (Y – T) = 23 + 0.72 (1200 – 155) = 775.4c. What is the level of investment, I, for this economy if the world real interest rate (r*) is 7%?I = I (r*) = 325 – 15.5 r* = 325 – 15.5*7 = 216.5d. Given the information you have found in parts a-c, find the level of net exports forthis economy.NX = Y – C – I – G = 1200 – 775.4 – 216.5 – 220 = -11.9NX = NS – I = SP + SG – I = (Y – C – T) + (T – G) – I = (1200 – 775.4 – 155) + (155 – 220) - 216.51= (269.6) + (-65) – 216.5 = -11.9e. Is this country borrowing from or lending to foreigners? What is the relationship between domestic spending and domestic production in this economy, and how dothese two topics relate to one another?Spending (C + I + G) in this economy exceeds domestic production (Y). This results in imports exceeding exports and the necessity of this economy borrowing from abroad. These two questions get at the same relationship: if you import more than you export you must be borrowing from foreigners to finance the extra purchases.f. Suppose government spending increases by 25. What are the effects of the increased government spending on output, consumption, investment, and net exports in this economy?Y = 1200 (K, A, L, and α are all constant)C = 775.4 (Y and T are constant)I = 216.5 (world real interest rate does not change with small economy)SP = 269.6 (the same as Y, C, and T remain the same)SG = (T – G) = (155 – 245) = -90 (25 less than before)NX = -36.9 (25 less than before as I and Sp remained the same)g. Did the increase in government spending completely crowd out investment spending as it would have in a closed economy? Explain your answer.No, there is no change in investment spending in the open economy as a result of the increase in government spending. In the closed economy we would have seen a complete crowding out of investment spending with theincrease in government spending. The increase in government spending causes a decrease in public saving. This in turn reduces the level of national saving. This leads to more imports and more capital flowing into this economy. The trade balance falls and we arrive at a new equilibrium.h. What happens to this country’s real exchange rate when government spending increases, holding everything else constant? Explain your answer. Will foreign or domestic goods become more attractive with the change in the real exchange rate?The increase in government spending causes national saving to decrease, which results in a shift left in the NCO (NS – I) line and a higher real exchange rate for the economy. This economy will find its exports less attractive to other economies as their currency increases in value relative to other currencies, so they will export less. On the other hand, foreign goods become more attractive as they are now cheaper and imports will increase.2i. Assume that the Money Supply for this small open economy is 300 and that the velocity of money is 6. If the real exchange is 3 US goods for each domestic good and the price level in the US is 2.25 then what is the nominal exchange rate between this country and the US?Using the quantity theory of money we know that Mv = PY(300) * 6 = 1800 = P * 1200P = 1.5Real Exchange Rate = RER = e (P/P*)RER = 3 (US / domestic goods) = e (1.5/2.25) = e (2/3)e = 4.5 $/domestic currency 2. Small Economy: Different Proposed PoliciesA small economy, which historically has been closed to capital flows and trade, is holding a democratic election for the very first time. There are three candidates for president, each with different proposed domestic and foreign policies. Assume the small economy can be described by the set of equations below.Y = 6000SP = SP (r, Y – T) = –1,100 + 16,375r + 0.25(Y – T)I = I (r) = 2,000 – 250 r (Where r is expressed as a decimal, i.e. if the interest rate is 5% then r = 0.05 in the equation.)r* = 0.08 is the world real interest rateY = C + I + G (Currently in the Closed Economy)Y = C + I + G + NX (Proposed by some candidates in a Open Economy)Y = C + SP + TThe first candidate (1) believes that the economy should remain a closed economy, the government should have a balanced budget, and that the government should collect 250 in taxes. The second candidate (2) believes that the country should allow imports and exports, the government should have a balanced budget, and that the government should collect 500 in taxes. The third candidate (3) believes that the country should allow imports and exports, that the government should collect 300 in taxes, and that the government should spend 500. For each of the following questionsevaluate the proposed policies by each of the presidential candidates.a. For each presidential candidate, what would be the level of public saving if their proposed policies were enacted?Candidate (1): Balanced Budget implies T = G implies SG = 0Candidate (2): Balanced Budget implies T = G implies SG = 0Candidate (3): SG = T - G = 300 – 500 = –2003b. For each presidential candidate, what would be the level of private saving if their proposed policies were enacted?Candidate (1): Closed economy implies that NS = I in equilibrium.NS = SP + SG = SP = ISP = –1,100 + 16,375r + 0.25(6000 – 250) = = –1,100 + 16,375r + 1437.5 = 337.5 + 16,375rI = 2,000 – 250 r SP = 337.5 + 16,375r = 2,000 – 250 r = I 16,625r = 1662.5 implies r = 0.1 or 10% in equilibrium SP = 337.5 + 16,375(0.1) = 337.5 + 1,637.5 = 1,975 Candidate (2): Open economy implies that world real interest rate will be the equilibrium interest rate. (r = r*, T = 500)SP …