Q. Optimal Input Combination for Maximisation of Output?

Equilibrium conditions of the firm are identical to the above situation which is, iso-cost line must be tangent to the highest possible isoquant and isoquant should be convex. Though the present problem is theoretically different. In this case firm has to maximise its output for a given cost. This is elucidated in the figure:

Figure: Maximisation of Output

Firm's cost constraint is given by iso-cost line AB. The maximum level of output that firm can produce is Q₂since the point 'e' lies on the isoquant Q₂. Point 'e' is the equilibrium point since at this point the iso-cost line AB is tangent to the isoquant Q₂. Other points on the isocost line which is S and T, lie on a lower isoquant Q₁. Points to the right of 'e' indicate higher levels of output that are desirable, however aren't attainable because of the cost constraint. Therefore Q₂ is the maximum output possible for given cost. The optimal combination of factors is OK₁ and OL₁.

The above analysis illustrates that optimal combination of inputs required for a firm to minimise the cost of producing a given level of output or to maximise the output for a given cost outlay is given at tangency point of an isoquant and is cost line.

The above analysis is based on constant factor prices. If factor prices change, firm will choose another factor combination which will minimise the cost of production for given output or maximise the level of output for a given cost