Download ECON-101 Midterm 1 Practice Key

Part 1 Practice Problems 1-10 Solutions
1. During a given year, the following activities occur:
i. A silver mining company pays its workers $200,000 to mine 75 pounds of silver. The silver is then sold
to a jewelry manufacturer for $300,000.
ii. The jewelry manufacturer pays its workers $250,000 to make silver necklaces, which the
manufacturer sells directly to consumers for $1,000,000.
a. The GDP for this economy, according to the final goods approach equals $1 million, the amount that
the jewelry is sold for.
b. Stage 1 Value-added = $300,000, the amount the silver is sold to the jewelry manufacturer for.
Stage 2 Value- Added = the extra valued created by the jewelry firm = 1,000,000300,000 = $700,000. GDP by value-added is 300,000 + 700,000 = $1,000,000.
c. Total wages = 200,000 + 250,000 = $450,000.
Stage 1 profits = Revenue – wages = 300,000 – 200,000 = $100,000.
Stage 2 profits = Revenue – intermediate inputs – wages
= 1,000,000 – 300,000 – 250,000 = $450,000.
Total profits = 100,000 + 450,000 = $550,000.
GDP according to the income approach = 450,000 + 550,000 = $1,000,000.
2. The following table gives the quantities sold and prices in a simple 2-good economy for 2009 and
2010.
Year
No. of computers
sold
Price per
computer
No. of cars sold
Price per car
2009
2,000,000
$1,000
1,200,000
$10,000
2010
3,000,000
$800
1,200,000
$11,000
2. a. Real GDP in 2010 (2009 base year) = 3m x 1,000 + 1.2m x 10,000 = $15.0bn
b. Real GDP in 2009 (2009 base year) (=nominal GDP in 2009)
= 2m x 1,000 + 1.2m x $10,000 = $14.0bn
c. % change from 2009 to 2010 = (15-14)/14 x 100 = 7.1%
ratio = 15/14 = 1.071
d. Real GDP in 2010 (2010 base year) (=nominal GDP in 2010)
=3m x 800 + 1.2m x 11,000 = $15.6bn
Real GDP in 2009 (2010 base year)
= 2m x 800 + 1.2m x 11,000 = $14.8bn
Percentage change = (15.6 -14.8)/14.8 x 100 = 5.4%
Ratio = 15.6/14.8 = 1.054
e. Geometric mean = sqrt(1.071x1.054) = 1.062
f. % change = (1.062-1.000)x100 = 6.2%
It lies approximately half-way between those in c. and d..
3. a. 2009 base year for the CPI means that we use 2009 quantities and measure the change in
prices from 2009 to 2010.
CPI(2010) (2009=100) = (cost of 2009 basket in 2010 prices/cost of 2009 basket in 2009
prices) x 100
= 14.8/14.0 x 100 = 105.7
b. GDP Deflator for 2010 (2009 = 100) = nom GDP 2010/real GDP 2010 (2009 base year)
= 15.6/15.0 x 100 = 104.0
c. CPI % change = 5.7%
GDP def. % change = 4.0%
Here, unlike in real life, the baskets used to calculate the 2 indexes are the same, so the
difference comes entirely from how they are calculated. The effect of the price changes
is reduced in the GDP deflator relative to the CPI because, in the former, account is
taken of the increased production of the good for which the price fell, whereas this is
not taken into account in calculating the CPI.
4. The Differences between GDP and GNP
Give yes or no as to whether each transaction is included in GDP and GNP in the following table:
Included in
U.S. GDP
Included
in U.S.
GNP
Explanation
a. Bruno Mars performs a
concert in New York.
Yes
Yes
Work performed in US and income
earned by US citizen
b. Bruno Mars performs a
concert in London.
No
Yes
Work performed abroad but income
earned by US citizen
c. Adele performs a
concert in New York.
Yes
No
Work performed in US but income
earned by foreign citizen
d. Adele performs a
No
No
Work performed abroad and income
earned by foreign citizen
Event
concert in London.
e. Toyota earns profits
from its car factory in
California.
Yes
No
Work performed in US, but profits
earned by foreign company
f.
No
Yes
Work performed abroad, but profits
earned by US company
Ford earns profits from
its car factory in
Germany.
5. For each of the following transactions, indicate whether it represents an increase in the U.S. gross
domestic product, and, if so, state whether it represents U.S. consumption (C), investment (I),
government purchases of goods or services (G), or net exports (NX).
a. You buy a new Ford Mustang automobile. Increase - C
b. The government buys a new fighter jet for $1 billion. Increase - G
c. You buy a used computer from a friend. No Increase – not currently produced good.
d. IBM builds a new factory in Massachusetts. Increase - I
e. GM’s inventories of steel rise by 50,000 tons. Increase - I
f. The government sends your unemployed cousin an unemployment benefit check. No Increase –
transfer payment, not direct government expenditure on goods and services.
6 Consider the following Cobb-Douglas production function:
Y = 100K1/4L3/4
a. Complete the following table:
K
81
162
243
L
Y = 100K1/4L3/4
16
32
48
2400
4800
7200
Explain how these results illustrate the property of constant returns to scale.
Going from the 1st line to the 2nd, the inputs are doubled, and we see that the output has
doubled from 2400 to 4800. Similarly, from the first line to the 3rd, the inputs are tripled and
the output is tripled. Thus, multiplying the inputs by a factor results in the output increasing
by the same factor.
b. Derive the algebraic expression for the marginal product of labor (MPL) by differentiating the
right-hand side of the production function with respect to L.
c.
d.
e.
f.
g.
h.
i.
MPL = dY/dL = ¾* 100K1/4L-1/4 = 75 K1/4L-1/4
Evaluate the expression you just derived – that is, find the numerical value of MPL – when K = 81
and L = 16.
MPL(81, 16) = 75 (81)1/4(16)-1/4 = 112.5
Given your answer in c., what must the equilibrium real wage be according to the neoclassical
theory, if K=81 and L=16 are the economy’s stocks of capital and labor?
Since firms hire workers to the point where the MPL = real wage, in equilibrium if K = 81 and L
= 16, the real wage must be 112.5.
Derive the algebraic expression for the MPK.
MPK = dY/dK = ¼*100K-3/4L3/4 = 25 K-3/4L3/4
Evaluate the expression you found in e. when K = 81 and L = 16.
MPK(81, 16) = 25(81)-3/4(16)3/4 = 7.4
Given your answer in f., what must the equilibrium real rental price of capital be?
Since firms hire capital to the point where the MPK = real rental rate of capital, in equilibrium
if K = 81 and L = 16, the real rental rate of capital must be 7.4.
For K = 81 and L = 16, show that the exponents in the production function represent the shares
of labor and capital in total output by calculating total real labor and capital payments.
Share of total output earned by labor = ((w/p)*L)/Y = (112.5*16)/2400 = ¾ = exponent on L in
the production function.
Share of total output earned by capital = ((r/p)*K)/Y = (7.4*81)/2400 = ¼ = exponent on K in
the production function.
Use the algebraic expressions you found in b. and e. to prove your result in h. algebraically.
Share of total output earned by L = (75 K1/4L-1/4 * L)/( 100K1/4L3/4) = ¾.
Share of total output earned by K = (25 K-3/4L3/4 * K)/( 100K1/4L3/4) = ¼.
7. (15 points) Fill out the following table using the per person production function (relative to the US),
y = A k1/3
Capital per
person
GDP per
person
Capital per
person
relative to
US
GDP per
person
relative to
US
y* predicted
by model
when
assuming no
difference in
TFP (A)
Implied
value of TFP
(A) needed
to reconcile
actual and
predicted
relative GDP
per person
United
States
124,162
41, 365
1.000
1.00
1.00
1.00
France
100,668
31,299
0.81
0.76
0.93
0.82
Argentina
29,390
12,340
0.24
0.30
0.62
0.48
1,247
0.02
0.03
0.26
0.12
Kenya
2,125
8. Soon after his election in 1992, President Clinton proposed to reduce government spending and
increase taxes. Based on the loanable funds model :
a. What effect would this have on the government budget deficit?
The government budget deficit is T – G. Since T increases and G decreases this will reduce
the deficit.
b. State and explain what the long-run effects of this policy would be on private saving, public
saving, and national saving.
Public saving is T – G so, as we see in a., it increases.
Private saving is Y – T – C. When T increases, households experience a reduction in
disposable income. To see how private savings changes, we need to see how C
changes with a change in T. ΔPvS = ΔY – ΔT – MPC *( ΔY – ΔT)
= (1-MPC)* ΔY – (1-MPC)* ΔT.
Since ΔY = 0 and ΔT > 0, this gives ΔPvS < 0. That is, private saving decreases. However
since (1-MPC)* ΔT < ΔT, the net effect on total savings just from the tax increase is
positive, and since the change in savings from the change in G is also positive, national
saving must increase.
c. Use the loanable funds diagram to state and illustrate what the long-run impact of this
program would be on national saving, investment and the real interest rate.
The increase in available loanable funds results in a decrease in the real interest rate, and
thus an increase in investment.
9. Suppose the marginal propensity to consume (MPC) is 0.7 and marginal product of labor (MPL) is 25.
Use the national saving equation to give ΔS in each of the following cases:
The national savings equation is:
S=Y–C–G
ΔS = ΔY – ΔC – ΔG
= ΔY – MPC*( ΔY – ΔT) – ΔG
= (1-MPC)* ΔY + MPC* ΔT – ΔG
Here, MPC = 0.7, so
ΔS = 0.3 ΔY + 0.7 ΔT – ΔG.
a. ΔG = 150
Here, ΔS = - ΔG = -150.
b. ΔT = -100
Here ΔS = 0.7* ΔT = -70.
c. ΔL = 40
To find ΔS here, we must first find ΔY. Since MPL = 25, if ΔL = 40, then (assuming that the
MPL is constant over this range), ΔY = 25 x 40 = 1000.
ΔS = 0.3*1000 = 300.
10. Consider an economy described by the following equations:
Y=C+I+G
Y = 5,000
G = 1,000
T = 1,000
C = 250 + 0.75(Y – T)
I = 1,000 – 50r
a. In this economy, compute private saving, public saving and national saving.
Plugging the values for Y and T into the consumption equation, we get:
C = 250 + 0.75*4000 = 3250
PvS = Y – T – C = 5000 – 4000 – 3250 = 750
PbS = T – G = 0
National Saving S = PvS + PbS = 750
b. Find the equilibrium interest rate.
In equilibrium, S = I, so we can put the value for S on the left-had side of the investment
equation and solve for r.
750 = 1000 – 50r
50r = 250
r=5
c. Now suppose that G rises to 1200. Compute private saving, public saving and national
saving.
When G rises to 1200, private saving doesn’t change, PbS = 1000 – 1200 = -200, so national
saving S = 750 – 200 = 550
d. Find the new equilibrium interest rate.
Now we have for S = I
550 = 1000 – 50r
50r = 450
r=9