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690 CHAPTER 16 GENERAL EQUILIBRIUM THEORY

20I W 90I H d) In equilibrium how will the income of each white-
P x
X collar family compare with the income of each blue-collar
family?
80I W 10I H
P y
Y 16.7. One of the implications of Walras’ Law is that
the ratios of prices (rather than the absolute levels of
where X and Y denote the aggregate quantities of beer prices) are determined in general equilibrium. In
and quiche demanded in this economy and I W and I H are Learning-By-Doing Exercise 16.2, show that price labor
the household incomes of wimps and hunks, respec- will be 25 0.48 of the price of capital, as illustrated in
52
tively. Finally, the market demand curves for labor and Figure 16.9.
capital are given by
16.8. One of the implications of Walras’ Law is that
5 1 the ratios of prices (rather than the absolute levels of
X r 6 3Y r 4
L a b a b prices) are determined in general equilibrium. In
6 w 4 w
1 3 Learning-By-Doing Exercise 16.2, show that the ratio of
5X w 6 Y w 4 the price of energy to the price of capital is about 0.79,
K a b a b
6 r 4 r as illustrated in Figure 16.9.
16.9. One of the implications of Walras’ Law is that
There are four unknowns in our simple economy:
the prices of beer and quiche, P x and P y , and the prices the ratios of prices (rather than the absolute levels of
of labor and capital, w and r. Write the four equations prices) are determined in general equilibrium. In
that determine the equilibrium values of these un- Learning-By-Doing Exercise 16.2, show that the ratio of
knowns. the price of food to the price of capital is about 0.7, as
illustrated in Figure 16.9.
16.6. In an economy, there are 40 “white-collar”
households, each producing 10 units of capital (and no 16.10. Two consumers, Josh and Mary, together have
labor); the income from each unit of capital is r. There 10 apples and 4 oranges.
are also 50 “blue-collar” households, each producing a) Draw the Edgeworth box that shows the set of feasible
20 units of labor (and no capital); the income from each allocations that are available in this simple economy.
unit of labor is w. b) Suppose Josh has 5 apples and 1 orange, while Mary
Each white-collar household’s demand for energy is has 5 apples and 3 oranges. Identify this allocation in the
X W 0.8M W /P X , where M W is income in the house- Edgeworth box.
hold. Each white-collar household’s demand for food is
Y W 0.2M W /P Y . c) Suppose Josh and Mary have identical utility functions,
Each blue-collar household’s demand for energy is and assume that this utility function exhibits positive
X B 0.5M B /P X , where M B is income in the household. marginal utilities for both apples and oranges and a di-
Each blue-collar household’s demand for food is Y B minishing marginal rate of substitution of apples for
0.5M B /P Y . oranges. Could the allocation in part (b)—5 apples and 1
Energy is produced using only capital. Each unit orange for Josh; 5 apples and 3 oranges for Mary—be
of capital produces one unit of energy, so r is the mar- economically efficient?
ginal cost of energy. The supply curve for energy is 16.11. Ted and Joe each consume peaches, x, and
described by P X r, where P X is the price of a unit of plums, y. The consumers have identical utility functions,
energy. Food is produced using only labor. Each unit with MRS x, y 10y J/ x J , MRS x, y 10y T/ x T . Together,
Joe
Ted
of labor produces one unit of food, so w is the mar- they have 10 peaches and 10 plums. Verify whether each
ginal cost of food. The supply curve for labor is de- of the following allocations is on the contract curve:
scribed by P Y w, where P Y is the price of a unit of a) Ted: 8 plums and 9 peaches; Joe: 2 plums and 1 peach.
food.
b) Ted: 1 plum and 1 peach; Joe: 9 plums and 9 peaches.
a) In this economy, show that the amount of labor de-
manded and supplied will be 1,000 units. Show also that c) Ted: 4 plums and 3 peaches; Joe: 6 plums and 7
the amount of capital demanded and supplied will be peaches.
400 units. d) Ted: 8 plums and 2 peaches; Joe: 2 plums and 8
peaches.
b) Write down the supply-equals-demand conditions for
the energy and food markets. 16.12. Two consumers, Ron and David, together own
c) In equilibrium how will the price of a unit of energy 1,000 baseball cards and 5,000 Pokémon cards. Let x R
compare with the price of a unit of food? denote the quantity of baseball cards owned by Ron and