Question

As economy of coal, electric, and steel industries. For each $1.00 of output, the coal industry needs $0.02 worth of coal, $0.30 worth of electricity, and 0.30 worth of steel, the electric industry needs $0.04 worth of coal, $0.04 worth of electricity, and 0.02 worth worth of steel, and the steel industry needs $0.10 worth of coal and $0.04 worth of steel. The sales demand is estimated to be $1 billion for coal, $1 billion for electricity, and $4 billion for steel. Suppose that the demand for electricity triples and demand for coal doubles, whereas the demand for for steel increases by only 50%. At what levels should the various industries produce in order to satisfy the new demand.

Answer 1

Explanation:

Let’s denote the production levels of coal, electricity and steel as x, y and z respectively. We can set up a system of equations to represent the inter-industry demand for each industry’s output.

For coal: 0.02x + 0.04y + 0.10z = x For electricity: 0.30x + 0.04y = y For steel: 0.30x + 0.02y + 0.04z = z

Solving this system of equations gives us x = (50/3)y and z = (25/2)y.

The new sales demand for coal is $2 billion (double the original), for electricity is $3 billion (triple the original) and for steel is $6 billion (an increase of 50%). Substituting these values into our equations gives us:

(50/3)y = $2 billion y = $3 billion (25/2)y = $6 billion

Solving these equations gives us y = $3 billion, x = $5 billion and z = $18.75 billion.

So to satisfy the new demand, the coal industry should produce at a level of $5 billion, the electric industry should produce at a level of $3 billion and the steel industry should produce at a level of $18.75 billion.