Download Problem Set 1 Solution

Problem Set 1 Solution
Econ 302
Problem 1
Consider the following closed economy. There are three firms (F1 F2 and F3)
and two households (HA and HB). Household HA has the property of all the 3
firms. Three workers form household HB. Worker no.1 of HB works in firm F1,
worker no.2 in firm F2 and worker no.3 in Firm F3. Firm F1 is an agricultural
firm and produces sugar for 90 monetary units (m.u.). Firm F2 uses all this
sugar to produce marmalade for 200 m.u. Finally firm F3 buys 100 m.u. of the
marmalade to put in nice glasses and sell all to the final consumers for a value
of 220 m.u. Each worker receives a wage of 50 m.u. Both households spend all
the income they earn to buy either raw marmalade or marmalade in glasses.
1. Calculate the added value in each firm and the GDP of this economy.
F 1 = 90, F 2 = 200
90 = 110, F 3 = 220
100 = 120. Hence GDP = 320.
2. Calculate the income received by each household and the total expenditure
in goods in this economy.
Profits = (90 50) + (200
= 50 ⇥ 3 = 150.
90
50) + (220
100
50) = 170. Wages
Total Income = GDP = 320.
Total Expenditure: Consumption = 100 + 220 = 320 = GDP.
Problem 2
Consider the country Badgerland where there are two firms. The firm CheeseFactory produces 100 cheeses using Badgerland’s labor. The firm Sishi produces
100 Sushis using Badgerland’s labor. The price of a cheese is 0.5 sushis i.e 0.5
sushis/cheese.
1. What is the GDP in units of cheeses? What is the GDP in units of sushis?
GDP = 300 cheeses or 150 sushis.
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2. Suppose that the residents of another country, called Jipin, own the firm
Sishi. The profit of the firm Sishi are 50 sushis and paid to the residents
of Jipin. Badgerland does not own any firm in Jipin. Every Badgerland’s
resident lives in Badgerland. What is the GNP of Badgerland?
GNP = 150
50 = 100 sushis or 200 cheeses.
Problem 3
Hamburgers and beer are the sole goods in a simple economy. In year 1 a
hamburger costs $5.0 and a beer $2.0, whereas in year 2 a hamburger costs
$10.0 and a beer $2.0. In year 1, 10 hamburgers are produced and 10 beers are
produced. In year 2, 6 hamburgers are produced and 8 beers are produced. The
basket of goods defining the Consumer Price Index (CPI) is 10 hamburgers and
10 beers.
1. Calculate the nominal GDP in period 1 and period 2.
Year 1 nominal GDP: 5 ⇥ 10 + 2 ⇥ 10 = 70. Year 2 nominal GDP: 10 ⇥
6 + 2 ⇥ 8 = 76.
2. Calculate the real GDP in period 1 and period 2 when year 1 is treated
as the base year.
Year 1 real GDP: 5 ⇥ 10 + 2 ⇥ 10 = 70. Year 2 real GDP: 5 ⇥ 6 + 2 ⇥ 8 = 46.
3. Calculate the real GDP in period 1 and period 2 when year 2 is treated
as the base year.
Year 1 real GDP: 10⇥10+2⇥10 = 120. Year 2 real GDP: 10⇥6+2⇥8 = 76.
4. Calculate the growth rates of real GDP using a chain-weighting approach.
RGDP 1
GDP ratios: g1 = RGDP11 = 46
70 = 0.6571 and g2 =
2
0.6333.
p
p
gc = g1 g2 = 0.6571 ⇥ 0.6333 = 0.645
Growth rate in real gdp: (0.645 1) ⇥ 100% = 35.5%
RGDP22
RGDP12
=
76
120
=
5. Calculate the rate of inflation using the implicit GDP price deflator when
year 1 is treated as the base year.
GDP deflator in year 1 = 100. GDP deflator =
76
46
⇥ 100 = 165.22.
6. What is the CPI in year 1 and year 2, when year 1 is treated as the base
year?
CPI in year 1 = 100. CPI in year 2 =
10⇥10+2⇥10
10⇥5+2⇥10
⇥ 100 = 171
7. Does the change in the CPI between year 1 and 2 overstate, understate or
correctly state the change in the “cost of living”? Explain carefully.
The change in CPI may overstate an increase in the cost of living as it
suffers from a substitution bias. Following the increase in the price of
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hamburgers, consumption of beers goes up relative to the consumption of
hamburgers. The weight of hamburgers in the CPI is too high.
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