Q.Prepare an input-output table for Transport industry (TI) and Food industry (FI). Food industry produces 50 units. Out of these 20 units consumed by FI and 25 units by TI. Whereas Transport industry produces 40 units and out of these 10 units used by FI and 25 units by TI. Construct input-output matrix. Check the condition of Hawkins-Simon condition and decide whether system is viable. If so find the input to fulfil the demand 100 of FI and 80 of TI.

Input-Output Analysis: The Intuition

Imagine a simple economy with just two industries: Steel and Cars. To make steel, you need steel itself (for machinery) and cars (to transport workers). To make cars, you need steel (for the body) and cars (for the assembly line). Each industry consumes some of its own output and some of the other's output just to keep running.

Now suppose the government wants to produce 100 extra cars for public transport. You can't just build 100 cars — you first need more steel to build them, and more cars to transport the steelworkers. But to get that extra steel, you need even more steel for the steel plant, and more cars for those workers. This creates a chain reaction: every new unit of output demands inputs from both industries, which in turn demand more inputs, and so on.

Input-Output Analysis is the mathematical tool that captures this entire chain in one clean calculation. It answers the question: If we want a certain final output (say, cars for the public), what total output must each industry actually produce, after accounting for all the inter-industry demands?

The Precise Statement

We model an economy with $n$ industries. Let:

• $x_i$ = total output of industry $i$ (what it must produce in total)
• $f_i$ = final demand for industry $i$'s product (what goes to consumers, government, exports — not to other industries)
• $a_{ij}$ = input coefficient — the amount of industry $j$'s output needed to produce one unit of industry $i$'s output

The input coefficient $a_{ij}$ is the key. It tells us the technology: "To make one car, you need 0.3 tons of steel and 0.1 cars' worth of transport." These coefficients are assumed fixed in the short run.

Now, the total output of industry $i$ must satisfy two things: …