1.Suppose an economy has only two sectors: Goods and Services. Each year, Goods

Question

1.Suppose an economy has only two sectors: Goods and Services. Each year, Goods sells 70% of its output to Services and and keeps the rest, while Services sells 55% 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. Assume that the price of the total output of the economy is $1,000,000,000. Give your answers in dollars, with at least four significant figures.

a. What's the equilibrium price of the Goods sector?

b. What's the equilibrium price of the Services sector?

2.Consider an economy with three sectors: Fuels and Power, Manufacturing, and Services. Fuels and Power sells

80% of its output to Manufacturing, 10% to Services, and retains the rest. Manufacturing sells 15% of its output to Fuels and Power, 70% to Services, and retains the rest. Services sells 30% to Fuels and Power, 40% to Manufacturing, and retains the rest. Find the equilibrium price for each sector. Assume the total economy is valued at $1,000,000,000.

a. What's the equilibrium price of the Fuels and Power sector?

b. What's the equilibrium price of the Manufacturing sector?

c. What's the equilibrium price of the Services sector?

Explanation / Answer

Let x be the price of goods.
Let y be the price of services.

Given that Goods sells 70% of its output to Services which equals 0.70x

Given that Services sells 55% of its output to Goods which equals 0.55y

In equilibrium both will be equal so we get:
0.70x=0.55y
or
x=0.55/0.70y
or
x=11/14y...(i)

Given that price of the total output of the economy is $1,000,000,000 means:
x+y=1000000000...(ii)

plug (i) into (ii)

11/14y+y=1000000000
25/14y=1000000000
y=560000000

plug value of y into (i)
x=11/14*560000000
x=440000000

Ans1.a.
Equilibrium price of the Goods sector=$440000000

Ans1.b.
Equilibrium price of the Services sector=$560000000

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