Question

4) large oil company produces two grades of gasoline: regular and super-unleaded. To produce these gasolines, equipment is used which requires as input certain amounts of each of the 2 worth of a dollar's worth of super-unleaded requires inputs of $0.15 worth of regular, and $0.11 worth of super-unleaded. In addition, the oil company has final demands for each of the different grades of gasoline, 10 million for regular and 15 million for super-unleaded. Find the production levels. Suppose that the external demand for regular rises by 1 million and the external demand forsuper unleaded grades of gasoline. To produce a dollar's worth of regular requires inputs of $0.14 regular, and $0.17 worth of super-unleaded. To produce rises by 2 million. How do the total outputs of the two sectors have to change?

Answer 1

The given question involve input-output model:

The model involves following equations

X₁= a₁₁X₁+a₁₂X₂+c₁-------eq(1)

X2= a₂₁X₁+a₂₂X₂+c₂-------eq(2)

Where X₁ is the value of the total production of good 1, X2 is the value of the total production of good 2;

c₁ is the value of the final consumption of good 1, c₂ is the value of the final consumption of good 2;

a₁₁ is worth good 1 required to produce good 1, a₁₂ is worth good 2 required to produce good 1;

a₂₁ is worth good 1 required to produce good 2, a₂₂ is worth good 2 required to produce good 2;

Solving eq(1)and (2) we will get the following value of X₁ and X₂

_{$\tiny X_{1}=\frac{(1-a_{22})c_{1}+a_{12}c_{2}}{(1-a_{11})(1-a_{22})-a_{12}a_{21}}$ -------------eq3}

_{$\tiny X_{2}=\frac{(1-a_{11})c_{2}+a_{21}c_{1}}{(1-a_{11})(1-a_{22})-a_{12}a_{21}}$ --------------eq4}

Now, for this question

a₁₁= $0.14, a₂₁= $0.15, c₁= $10 million ( assume each regular cost $1 )

a₁₂= $0.17,  a₂₂= $0.11, c₂= $15 million ( assume each super-unleaded cost $1 )

Put all value into eq3 and eq4 to find out X1 and X2

X₁= 15.47

X2= 19.46

If final consumption c₁ increases by $1million and c₂ increases by $2million. Then new c₁ would be $11million and c₂ would be $17million.

Corresponding new outputs in two sectors, after solving with eq3 and eq4, would be

X₁= 17.13

X2= 21.98

Good luck!!

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