Page 715 - Microeconomics, Fourth Edition

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PROBLEMS 689
11. Explain how the conditions of utility maximization, 12. What is comparative advantage? What is absolute
cost minimization, and profit maximization in competi- advantage? Which of these two concepts is more impor-
tive markets imply that the allocation arising in a general tant in determining the benefits from free trade?
competitive equilibrium is economically efficient.

PROBLEMS

16.1. Consider the markets for butter (B) and mar- 16.4. Suppose that the demand for steel in Japan is
d
d
garine (M), where the demand curves are Q M 20 given by the equation Q S 1200 4P S P A P T ,
d
2P M P B and Q B 60 6P B 4P M and the supply where Q S is the quantity of steel purchased (millions of
s s
curves are Q M 2P M and Q B 3P B . tons per year), P S is the price of steel (yen per ton), P A
a) Find the equilibrium prices and quantities for butter is the price of aluminum (yen per ton), and P T is the
and margarine. price of titanium (yen per ton). The supply curve for
s
steel is given by Q S 4P S . Similarly, the demand and
b) Suppose that an increase in the price of vegetable oil
s
shifts the supply curve of margarine to Q M P M . How supply curves for aluminum and for titanium are given
d
does this change affect the equilibrium prices and quan- by Q A 1200 4P A P S P T (demand curve for
s
tities for butter and margarine? Using words and graphs, aluminum), Q A 4P A (supply curve for aluminum),
d
explain why a shift in the supply curve for margarine Q T 1200 4P T P S P A (demand curve for tita-
s
would change the price of butter. nium), and Q T 4P T (supply curve for aluminum).
a) Find the equilibrium prices of steel, aluminum, and
16.2. Suppose that the demand curve for new automo-
d
biles is given by Q A 20 0.7P A P G , where Q A and titanium in Japan.
P A are the quantity (millions of vehicles) and average b) Suppose that a strike in the Japanese steel industry
s
price (thousands of dollars per vehicle), respectively, of shifts the supply curve for steel to Q S P S . What does
automobiles in the United States, and P G is the price this do to the prices of steel, aluminum, and titanium?
of gasoline (dollars per gallon). The supply of automo- c) Suppose that growth in the Japanese beer industry,
s
biles is given by Q A 0.3P A . Suppose that the demand a big buyer of aluminum cans, fuels an increase in the
d demand for aluminum so that the demand curve for
and supply curves for gasoline are Q G 3 P G and d
s
Q G P G . aluminum becomes Q A 1500 4P A P S P T .
a) Find the equilibrium prices of gasoline and auto- How does this affect the prices of steel, aluminum, and
mobiles. titanium?
b) Sketch a graph that shows how an exogenous increase 16.5. Consider a simple economy that produces two
in the supply of gasoline affects the prices of new cars in goods, beer (denoted by x) and quiche (denoted by y),
the United States. using labor and capital (denoted by L and K, respec-
16.3. Studies indicate that the supply and demand tively) that are supplied by two types of households,
schedules for ties (t) and jackets ( j) in a market are as those consisting of wimps (denoted by W ) and those
follows: consisting of hunks (denoted by H ). Each household of
hunks supplies 100 units of labor and no units of capital.
d
Demand for ties: Q t 410 5P t 2P j Each household of wimps supplies 10 units of capital and
s
Supply of ties: Q t 60 3P t no units of labor. There are 100 households of each type.
d
Demand for jackets: Q j 295 P t 3P j Both beer and quiche are produced with technologies
s
Supply of jackets: Q j 120 2P j exhibiting constant returns to scale. The market supply
curves for beer and quiche are
The estimates of the schedules are valid only for prices at
1
which quantities are positive. P x w r 5 6
6
a) Find the equilibrium prices and quantities for ties and 3 4 4 1
jackets. P y w r
b) Do the demand schedules indicate that jackets and ties where w denotes the price of labor and r denotes the
are substitute goods, complementary goods, or inde- price of capital. The market demand curves for beer and
pendent goods in consumption? How do you know? quiche are given by