Question

Suppose an economy is divided into two sectors, X and Y. For each unit of output in X, it requires 0.1 unit from other companies in sector X and 0.5 from sector Y. For each unit of output in sector Y, it uses 0.6 units from sector X and 0.2 units for itself. Construct a consumption matrix and find a production vector to satisfy a final external demand of 18 units in X and 11 units in Y.

Answer 1

To construct a consumption matrix and find a production vector for the given two-sector economy, input-output analysis is applied. The consumption matrix is formed from the inter-sectoral output requirements, and a system of linear equations is solved to determine the production vector needed to satisfy the given external demand.

Step-by-step explanation:

The student's question involves constructing a consumption matrix and finding a production vector to satisfy a set final demand in a two-sector economy. To handle this question, we apply concepts from input-output analysis, which is used in economics to understand how different sectors of an economy interact.

The consumption matrix for sectors X and Y will consist of the amount of output from each sector that is used by the other sector to produce a unit of output. Given the data:

• Sector X uses 0.1 units from X and 0.5 units from Y per unit of output.
• Sector Y uses 0.6 units from X and 0.2 units from Y per unit of output.

The consumption matrix A can be written as:

A = [0.1 0.5]
[0.6 0.2]

To find the production vector P that satisfies an external final demand of D (18 units for X and 11 units for Y), we need to solve the equation P = A*P + D. Rewriting gives us P - A*P = D, which implies (I - A)*P = D, where I is the identity matrix. Solving this system of linear equations will provide us with the production vector P necessary to meet the final demand.