Homework #3

1. Small Open Economy

Use the following set of Classical Model equations for a small open economy to answer the following questions.

Y = F (K, L) = AKαL1-α
C = 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 + NX
Y = C + SP + T
G = 220
T = 155
K = 1000
L = 8000
A = 0.3

Capital's Share of Income = 1/3

a. What is aggregate output, Y, for this economy?

b. What is the level of consumption, C, for this economy?

c. What is the level of investment, I, for this economy if the world real interest rate (r*) is 7%?

d. Given the information you have found in parts a-c, find the level of net exports for this economy.

e. Is this country borrowing from or lending to foreigners? What is the relationship between domestic spending and domestic production in this economy, and how do these two topics relate to one another?

f. Suppose government spending increases by 25. What are the effects of the increased government spending on the level of output, consumption, investment, and net exports in this economy?

g. Did the increase in government spending completely crowd out investment spending as it would have in a closed economy? Explain your answer.

h. What happens to the 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?

i. 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?

2. Small Economy: Different Proposed Policies

A 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 = 6000
S_P = 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 rate
Y = C + I + G (Currently in the Closed Economy)
Y = C + I + G + NX (Proposed by some candidates in a Open Economy)
Y = C + SP + T

The 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 questions evaluate 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?

b. For each presidential candidate, what would be the level of private saving if their proposed policies were enacted?

c. For each presidential candidate, what would be the level of investment spending if their proposed policies were enacted?

d. For each presidential candidate, what would be the level of net capital outflows if their proposed policies were enacted? If appropriate, would the country be lending to or borrowing from foreigners in the financial markets?

e. For each presidential candidate, what would be the level of consumption spending if their proposed policies were enacted?

f. If you were a producer of a one-of-a-kind product in this country, which presidential candidate would you support and why?

g. Advisors for the first candidate have proposed two different but similar arguments against the trade policies of the second and third candidates. The first argument is that trade will hurt the local economy and decrease the level of GDP as a result of a trade deficit. The second argument is that trade will hurt the local economy and the level of expenditure in the economy as a result of a trade deficit. As a classical economist do you support or refute these arguments?

h. Advisors for the second candidate have proposed two arguments against the other two candidates. The first argument is that an open economy is better than a closed economy as it promotes investment and economic growth. The second argument is that a balanced budget is needed for foreigners to invest in the country and promote economic growth. As a classical economist do you support or refute these arguments?

i. Advisors for the third candidate have proposed two different but similar arguments against the other two candidates. The first argument is that government spending exceeding taxes allows individuals to consume more and promotes long-term growth via larger investment levels. The second argument is that a balanced budget hinders economic growth of the country by dampening consumption and investment. As a classical economist do you support or refute these arguments?

3. Consider the island economy of LaLaLand which has a labor force of 4,000. There are currently 400 discouraged workers on the island, and these workers are not considered part of the labor force. Everyone on the island fishes, but in order to fish they must be hired on as crew of a boat. In a given week 5% of all employed individuals will lose their job. At the same time, 25% of all unemployed workers get hired by a boat.

a. What is the natural rate of unemployment on the island?

b. Suppose a fish virus causes demand to fall drastically, and as such only 1,000 individuals are employed January 1st 2007. Immediately after the fall in demand, the virus is found to be linked to lemons and the demand for fish returns to normal levels. Suppose that the job separation rate and job finding rate remain the same as described above, and that the labor force remains constant. What is the level of employment January 8th 2007, one week after the initial virus scare? (Hint: Find the change in employment by considering the number of employed that lose their job in addition to the number of unemployed that find a job.)

c. Assume that the job finding rate, the job separation rate, and the labor force remain constant again. Repeat the above step for 26 weeks. Fill in the table below for weeks 0-26.

d. What happens to the unemployment rate over time? How does this relate to the natural rate of unemployment?

e. What would you expect to happen to the unemployment rate initially and over time if at the end of the 26th week (July 2nd 2007) the discouraged workers decided to look for a job and are thus considered unemployed?

f. Continue the table you created for part c for another 13 weeks. Make sure to incorporate the change in the labor force in week 27 associated with the formerly discouraged workers now looking for a job.

g. On October 1st 2007, a new fleet of fishing boats comes to the island and hires additional individuals. As a result of this action the job finding rate increases to 40% and the job destruction rate falls to 4%. Continue the table you created for parts c and f for another 13 weeks with the new rates.

h. If there are no changes in the labor force, the job separation rate, or to the job finding rate, then what unemployment rate would you expect this small island economy to have at the end of 2008? What is the new natural rate of unemployment?

i. Would your predictions for the unemployment rate in part (h) hold if there was a one-time change in the labor force? (Hint: Look at your answer to part f and consider changes in the labor force at different times of the year.)