The input-output matrix of a closed economic model is A = 0 5 1 1= =6 6. Solve

the closed Leontief economic model equation (I-A)x = 0 for the production

vector x.

2: In village of 90 people, each person either goes fishing or gathers nuts. All

food is shared between the villagers and none is traded outside the village.

The production of 3 units of fish requires two people and one unit of fish.

The production of 1 unit of nuts requires one person. Each person in the

village requires 1=3 units of fish and 2=3 units of nuts.

(a) Write the input-output matrix A for the closed Leontief economic model

which describes this village. Hint: the matrix is 3 × 3 and the sectors

are fish, nuts and people (labour).

(b) Solve the closed Leontief economic model equation (I - A)x = 0 by

Gauss{Jordan elimination to find the production of fish and nuts. Hint:

There are 90 people in the village so set the people component of the

production vector x to 90.

(c) In this village, how many people go fishing and how many people gather

nuts?

3: Consider matrix A = 2 40 2 3 0 1 2 1 1 -23 5.

(a) Calculate det(A).

(b) Find all cofactors of A and find A-1.

4: Three neighbours have backyard vegetable gardens. Neighbour T grows

tomatoes, neighbour C grows corn and neighbour L grows lettuce. The

neighbours only sell their produce to each other. Neighbour T buys 1=5 of

the tomatoes, 1=5 of the corn and 3=5 of the lettuce. Neighbour C buys 2=5

of the tomatoes, 1=5 of the corn and 1=5 of the lettuce.

(a) What portion of each crop does neighbour L get?

(b) What is the production vector x?

(c) If the highest priced crop sells for $42, what prices should be assigned

to each of the crops?

5: The matrix

B =

266664

0:2 0 0:2 0:3 0:1

∗ ∗ ∗ ∗ ∗

0 0:4 0:5 0:5 0:5

0:3 0 0:2 0 0

0:2 0:2 0:1 0:2 0

377775

is the input-output matrix of a closed Leontief economic model.

(a) Complete the missing row.

(b) If industry four (that is, the industry described by the fourth column)

produces 360 units, find the production vector x. Give your final answers correct to one decimal place. (Hint: MATLAB might be helpful

here.)  

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AccountingQueen

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