I have already submitted this, but the answers were not explained and not all of

Question

I have already submitted this, but the answers were not explained and not all of the questions were answered.

Input-Output Model. Suppose an economy has two industries, agriculture and minerals. Each unit of agricultural output requires a 0.3 unit of agricultural input and 0.1 unit of mineral input. Each unit of mineral output requires 0.1 unit of agricultural input and 0.2 unit of mineral input.

a. Write the technology matrix for this economy.

b. How many units of minerals are required to produce 100 units of agricultural products?

c. How many units of agricultural products and minerals are required to produce 100 units of minerals?

d. If surpluses of 60 units of agricultural products and 70 units of textiles are desired, what is the technology equation for the model? e. Find the gross production of each industry.

Explanation / Answer

Let x, y represent the number of agriculture units and minerals units respectively in the input

X , Y represent the no of agriculture and mineral unit in the output

hence with the given data we can write the model as :

( X,Y)T = [0 .3 0 .1 (x,y)T   ----(1)

0 .1 0.2]

b . In Agricultural product for 1 unit 0.1 unit mineral is required

for 100 unit 10 units of mineral is required

c . In minearal product for 1 unit 0.1 unit of agriculture product is required

for 100 units 10 units of agrivultural product is required

d. from matrix eqn given in eqn 1 we put X=60 and Y=70 and we get the following eqns

60 = 0.3x+0.1y => 3x+y=600

70 = 0.1x+0.2y => x+2y=700

solving the above simultaneous eqns we get x= 100 and y=300

to get surplus of 60 agricultural unit and 70 units of textiles as output

we most put 100 units of agricultural product and300 units of mineral product as input

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