Test 6 – Sections 7 & 8
Section 7
3. The economy of Macro States estimates its aggregate production function as Y/L =
50(K/L)1/2 when technology and human capital per worker are held constant. In the
equation Y is real GDP, L is the number of workers, and K is the quantity of physical
capital. Macro States has 500 workers.
a. Calculate real GDP per worker (Y/L) and physical capital per worker (K/L) for
the given levels of physical capital in the following table. Round (K/L) to the
nearest hundredth and (Y/L) to the nearest whole number.
K
K/L
Y/L
$0
$20
$40
$60
$80
$100
$200
$400
b. Plot Macro State’s aggregate production function on a graph. Physical capital per
worker is measured on the x-axis and real GDP per worker is measured on the yaxis.
c. As physical capital per worker increases, what happens to real GDP per worker?
3. a.
K
$0
$20
$40
$60
$80
$100
$200
$400
K/L
$0
0.04
0.08
0.12
0.16
0.2
0.4
0.8
Y/L
$0
10
14
17
20
22
32
45
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c. Real GDP per worker increases as physical capital per worker increases, but it
increases at a diminishing rate. For example, if we hold the number of workers and all
other variables constant, real GDP per worker increases by $4 when physical capital
increases from $20 to $40, but real GDP per worker increases by $3.50 when physical
capital increases from $40 to $60.
4. Suppose that Macro States increases its level of technology and human capital per
worker relative to its economic condition in Problem 3 (previous problem). Now, Macro
States economists estimate that the aggregate production function is given by the
equation Y/L = 60(K/L) ½.
a. Relative to the aggregate production function you plotted in Problem 3b (previous
problem), what do you anticipate will happen to Macro State’s aggregate
production function as a result of this increase in human capital per worker and
technology?
b. Compare productivity in Macro States in the initial situation to its new situation,
assuming that Macro States has $100 in physical capital.
c. Why are increases in productivity important?
4. a. Macro States aggregate production function will shift up relative to its initial
position for every level of physical capital per worker. We can see this by recalculating
output per worker, given the new aggregate production function.
K
$0
$20
$40
$60
$80
$100
K/L
$0
0.20
0.28
0.35
0.40
0.45
Y/L
$0
12.80
16.80
21.00
24.00
27.00
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b. Productivity is defined as output per worker. When physical capital equals $100,
output per worker is initially $22.50, while after the increase in human capital per
worker and technology output per worker increases to $27.00
c. Increases in productivity are important because they indicate that each worker on
average is now producing a greater level of output. This, in turn, makes it possible for
people on average to experience higher standards of living.
Section 8
1. The following graphs represent the loanable funds market in Macroland and
Funland, the only two economies in the world.
Residents in Macroland and Funland believe that foreign assets and liabilities are as good
as domestic assets and liabilities.
a. Given the two graphs, which country is likely to attract capital? Why?
b. Given the Macroland graph, what do you predict will happen to the interest rate in
Macroland over time? Explain your answer.
c. Given the Funland graph, what do you predict will happen to the interest rate in
Funland over time? Explain your answer.
d. Briefly describe the capital flows between Macroland and Funland.
2.a. Funland will attract capital because its equilibrium interest rate is higher than the
equilibrium interest rate in Macroland.
b. Over time, the interest rate in Macroland will rise due to capital outflows. Because
Macroland initially has a lower equilibrium interest rate than Funland, some
Macroland lenders will decide to send their funds to Funland to take advantage of the
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higher interest rate. Over time, this will cause the interest rate in the two countries to
equalize.
c. Over time, the interest rate in Funland will fall due to capital inflows from
Macroland. As funds from Macroland are attracted to Funland’s loanable funds
market, due to its initially higher equilibrium interest rate, the interest rate will fall in
Funland. Eventually, the interest rates in the two countries will equalize.
d. Capital will flow out of Macroland and into Funland. Thus, Macroland will
experience capital outflows while Funland will experience capital inflows.
5. Suppose initially, the nominal exchange rate is 20 Macroland dollars per 1 Funland
dollar, and the aggregate price index in both countries has a value of 100.
a. What is the real exchange rate expressed as Macroland dollars per Funland dollar?
b. Suppose the real exchange rate increases to 25 Macroland dollars per Funland
dollar when the aggregate price index in Funland increases to 150. Assuming the
nominal exchange rate is unchanged, what is the aggregate price index in
Macroland?
c. Suppose the aggregate price index in Funland is 150 and the aggregate price index
in Macroland is 125. If the nominal exchange rate increases to 25 Macroland
dollars per Funland dollar, what is the real exchange rate?
d. If the real exchange rate measured as Macroland dollars per Funland dollar
increases, holding everything else constant, what happens to the level of exports
and imports in Macroland?
5. a. The real exchange rate in Macroland dollars per Funland dollar = (20
Macroland dollars per Funland dollar)(100/100) = 20 Macroland dollars per
Funland dollar.
b. To answer this question, use the following equation:
Real exchange rate =
(nominal exchange rate)[(price index in Funland)/(price index in Macroland)]
Thus, 25 Macroland dollars per Funland dollar = (20 Macroland dollars per
Funland dollar)[(150/price index in Macroland)] and solving for the price index in
Macroland, we find that the price index in Macroland equals 120.
c. To answer this question, use the equation given in part (b):
Real exchange rate =
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(nominal exchange rate)[(price index in Funland)/(price index in Macroland)]
Thus, the real exchange rate = (25 Macroland dollars per Funland
dollar)[(150)/(125)], and solving this equation for the real exchange rate yields a real
exchange rate of 30 Macroland dollars per Funland dollar.
d. When the real exchange rate increases, Macroland’s currency appreciates, and
this appreciation will make Macroland’s products more expensive to foreigners.
Macroland will export less and import more when the real exchange rate increases,
holding everything else constant.
10. Consider each of the following transactions and identify how the transaction would be
categorized in the U.S. balance of payments accounts. For each transaction, identify
whether it would be counted as part of the balance of payments in the current account or
the financial account. Lastly, identify whether the transaction will increase or decrease
the relevant account.
a. A U.S. company purchases machinery produced in Germany by a German
company.
b. A U.S. citizen donates money to the foreign group organizing an international
sporting event in another country.
c. A French citizen purchases cheese produced in the United States.
d. A U.S. citizen purchases 100 shares of a Swiss company
10. a. When the U.S. company purchases machinery produced in Germany by a
German company, this transaction enters the U.S. balance of payments current
account as an import. This transaction will reduce the balance of payments on the U.S.
current account.
b. When the U.S. citizen donates money to the foreign group organizing an
international sporting event, this enters the current account as a transfer payment to a
foreigner. This transaction will reduce the balance on the U.S. current account.
c.When a French citizen purchases cheese produced in the United States, this
transaction enters the U.S. balance of payments on the current account as an export.
This transaction will increase the balance of payments on the U.S. current account.
d. When the U.S. citizen purchase 100 shares of a Swiss company, this transaction is
categorized as part of the U.S. balance of payments on the financial account. The
balance of payments on the U.S. financial account will fall.
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