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Explain why firms want to operate at a tangency between an isoquant and an isocost

Explain why firms want to operate at a tangency between an isoquant and an isocost

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Suppose a firm wishes to produce q1 output. Suppose firm spends C0 on inputs but the firm can not achieve q1 with C0 cost. q1 can be achieved with C2 cost by using K2 capital, L2 labor or by using K3 capital, L3 labor. But C2 is not the minimum cost. The same output q1 can be achieved more cheaply by spending C1 by using K1 units of capital and L1 units of labor. C1 is the lowest isocost line that produces q1 output. At this point the slope of isoquant and isocost line are equal.

The point of tangency between isocost line and isoquant gives cost minimizing choice of inputs so firms want to operate at this tangency point.

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