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PROBLEM SET 1
Problems for Perkins, Ch. 2, 3 and 4
1.
Suppose you want to estimate GNP per capita for the U.S. and Mexico
and use the information to compare their standards of living. The
information below provides the information you need.
PRODUCTION AND PRICES IN US AND MEXICO
Tradable Good
U.S.
Mexico
Non-tradable
good
Price of
Price of an
Production
Production and
Steel per
Emerald
and
Consumption of
ton
Ring
Consumption
Custom-Made
(local
(local
of Steel (tons)
Emerald Rings
currency)
currency)
per Capita
per Capita
100
4
$200
$5000
8,000
60,000
pesos
pesos
50
2
a.
Calculate the level of GNP per capita for each country measured in
b.
its own currency.
Calculate the “official” exchange rate between the dollar and the
peso (# $ per peso), assuming that the law of one price holds for
tradable goods.
c.
d.
e.
f.
Calculate Mexican GNP per capita in dollars using the official
exchange rate.
Calculate the purchasing power parity (PPP) exchange rate between
the dollar and the peso (# $ per peso).
Calculate Mexican GNP per capita in dollars using the PPP exchange
rate.
According to GNP per capita converted at the official exchange rate,
how do Mexican and U.S. standards of living compare? According
to GNP per capita converted at the PPP exchange rate, how do
Mexican and U.S. standards of living compare?
2
2.
Though not a complete model of growth, analysts sometimes use the
Harrod-Domar model when they are interested in determining the productivity
of capital in a particular country or doing a quick forecast of growth over the
next few years.
Below are the overall growth rates of total national income/output (GDP),
the savings rates, and the depreciation rates for several countries.
AVERAGE
ANNUAL
CAPITAL-
GROWTH
OUTPUT
RATE OF GDP
SAVINGS
DEPRECIATION
RATIO (v)
COUNTRY
(1990-99)
RATE (s)
RATE (d)
(calculate)
S. Korea
.057
.37
.03
Singapore
.080
.44
.03
Brazil
.030
.21
.03
Chile
.072
.28
.03
Morocco
.023
.19
.03
Jordan
.053
.01
.03
Kenya
.022
.14
.03
Senegal
.033
.09
.03
a.
Calculate the capital-output ratio (v) implied by the Harrod-Domar
Model for each country. Which nation had the highest productivity of capital
and which had the lowest?
b.
South Korea and Jordan had similar growth rates of output over the
period 1990-99 (see chart above). According to the Harrod-Domar Model, in
what sense were their growth patterns different? (HINT: Compare the savings
rate and capital-output ratio for each country).
c.
Morocco and Kenya are the two slowest growing countries in the
sample. Assuming that their depreciation rates (d) and capital-output ratios (v)
3
stay the same, calculate the savings rate needed to bring the average annual
growth rate of each up to .05 (5%).
3.
Use the diagram (drawn below) of the Solow/Neoclassical Growth Model
with no change in resource productivity (also referred to as no “technological
change”) to help you detemine the impact of each of the following separate
events on:
i.
The steady-state level of output/income per worker.
ii.
The growth rate of output/income per worker as the
iii.
economy moves toward the new steady state.
The growth rate of output/income in the new steady state.
y = Y/L
y = Af(k)
y1*
(n + d) k
S/L = sy
k1*
k = K/L
a.
The savings rate (s) decreases from .20 to .15.
b.
The population growth rate (n) decreases from .03 to .025.
c.
The depreciation rate (d) decreases from .03 to .02.
4
4.
Suppose the savings rate increases from .20 to .30, i.e. the average
person permanently saves a larger share of his or her income each year.
a.
According to the Harrod-Domar Model, what will happen to the
“growth rate” (NOTE: the Harrod-Domar Model defines “growth” as an increase
in aggregate output or income. However, since labor force growth and
population growth are both assumed constant, an increase in output is
equivalent to an increase in output per person or per worker)?
b.
According to the Solow/Neoclassical Model with no change in
resource productivity (or technological change in the broad sense), what will
happen to the “growth rate” (defined as an increase in output per worker or per
person)?
5
5.
Suppose that aggregate production (Y) in the country of El Dici has grown
at an annual average of 10% over the last 40 years, while annual production in
Dependencia has grown by 4.7% over the same period. Suppose that the share
of total income going to capital (wK) in each country is .4 and the share of total
income going to labor (wL) in each is .6. The average annual growth rate of
capital and labor in each country is given in the chart below.
AVERAGE ANNUAL
AVERAGE ANNUAL
GROWTH RATE OF
GROWTH RATE OF
CAPITAL (gK)
LABOR (gL)
El Dici
6%
3%
Dependencia
3%
2%
COUNTRY
a.
Use the “Growth Accounting” technique to fill in the following charts:
Contribution
Contribution
Contribution
gY
of capital
of labor
(Growth) of
(%)
wK gK (%)
wL gL (%)
TFP (a) in %
El Dici
10.0
Dependencia
4.7
Share of gy due
to capital
(wK gK/ gY) x 100
Share of gy due to Percent of gy due
labor
to TFP
(wL gL/ gY)x100
(a/ gY) x 100
El Dici
Dependencia
b.
Based on your solutions above, which country’s growth rate is
explained mostly by accumulation of inputs (capital and labor) and which
country’s growth rate is based mostly on factor productivity (i.e. total factor
productivity or TFP)?
6
SELECTED ANSWERS
1.
a.
$GNPPCUS = $40,000
PesoGNPPCMEX = 520,000 pesos
b.
official exchange rate = $200/8000pesos = $.025 per peso
c.
$GNPPCMEX (official) = 520,000 pesos x $.025 = $13,000
d.
The US and Mexico (“the world”) both consume 25 tons of steel per
capita for 1 ring per capita. Use these to weight the prices of steel and rings in
each country.
Price IndexUS = ($200 x 25) + ($5000 x 1) = $10,000
Price IndexMEX = (8000 pesos x 25) + (60,000 pesos x 1)
= 260,000 pesos
Exchange rate (PPP) = $10,000/260,000 pesos = $.0384615 per peso
e.
$GNPPCMEX (PPP) = 520,000 pesos x $.0384615 = $19,999.99
≈ $20,000
f.
Converted at the official exchange rate, Mexico’s standard of living
is 32.5% ($13,000/$40,000) of that of the U.S.
Converted at the PPP exchange rate, Mexico’s standard of living is
50% ($20,000/$40,000) of that of the U.S.
7
2.
a.
COUNTRY
CAPITAL – OUTPUT RATIO
S. Korea
4.25
Singapore
4.00
Brazil
3.50
Chile
2.75
Morocco
3.58
Jordan
0.12
Kenya
2.69
Senegal
1.43
Jordan has the highest productivity of capital (because it has the lowest
capital output ratio); South Korea has the lowest productivity of capital (because
it has the highest capital output ratio).
b.
COUNTRY
SAVINGS RATE
CAPITAL-OUTPUT RATIO
S. Korea
.37
4.25
Jordan
.01
0.12
South Korea’s growth was mostly determined by high savings, while
Jordan’s was mostly due to high productivity of capital (low capital-output
ratio).
c.
Morocco’s savings rate must be brought up to .29, while Kenya’s must be
brought up to .21.
8
3.
a.
y = Y/L
y = Af(k)
y1*
(n + d) k
S/L = sy
k = K/L
Steady-state y decreases; growth rate is negative as move to new steady-state; growth rate
is zero in new steady state.
9
b.
y = Y/L
y = Af(k)
y1*
(n + d) k
S/L = sy
k = K/L
Steady-state y increases; growth rate is positive as move to new steady-state; growth rate
is zero in new steady state.
c.
Same answer as part b.
4.
a.
The growth rate will permanently increase to a higher “percentage.”
b.
The growth rate will temporarily increase (i.e. be greater than zero)
as the economy moves to a higher steady state level of output/income per
worker. However, because of diminishing returns to capital, the growth rate
will move back to zero when the economy gets to the new steady state.
10
5.
a.
Factor/resource accumulation = wK gK + wL gL
Contribution of TFP: a = gY – wK gK - wL gL
El Dici
Dependencia
El Dici
Dependencia
b.
gY
(%)
10
4.7
Contribution
of capital
wK gK (%)
2.4
1.2
Share of gy due
to capital
(wK gK/ gY) x 100
24.0%
25.6%
Contribution
of labor
wL gL (%)
1.8
1.2
Contribution
(Growth) of
TFP (a) in %
5.8
2.3
Share of gy due to Percent of gy due
labor
to TFP
(wL gL/ gY)x100
(a/ gY) x 100
18.0%
58.0%
25.6%
48.9%
Looking at the shares of growth due to the three factors, we see
that more of Dependencia’s growth is explained by factor accumulation
compared with El Dici’s. More of El Dici’s growth is explained by growth of TFP.