Suppose an economy has only two sectors: Goods and

Chapter 1, Problem 1E

(choose chapter or problem)

Problem 1E

Suppose an economy has only two sectors: Goods and Services. Each year, Goods sells 80% of its output to Services and keeps the rest, while Services sells 70% of its output to Goods and retains the rest. Find equilibrium prices for the annual outputs of the Goods and Services sectors that make each sector’s income match its expenditures.

Example 1:

Suppose an economy consists of the Coal, Electric (power), and Steel sectors, and the output of each sector is distributed among the various sectors as shown in Table 1 on page 50, where the entries in a column represent the fractional parts of a sector’s total output. The second column of Table 1, for instance, says that the total output of the Electric sector is divided as follows: 40% to Coal, 50% to Steel, and the remaining 10% to Electric. (Electric treats this 10% as an expense it incurs in order to operate its business.) Since all output must be taken into account, the decimal fractions in each column must sum to 1.

Denote the prices (i.e., dollar values) of the total annual outputs of the Coal, Electric, and Steel sectors by pC, pE, and pS, respectively. If possible, find equilibrium prices that make each sector’s income match its expenditures.

TABLE  1  A Simple Economy_______________________________________

Distribution of Output from:

Coal	Electric	Steel	Purchased by:
.0	.4	.6	Coal
.6	.1	.2	Electric
.4	.5	.2	Steel