An expansion path of a firm is the locus of points joining the optimum combination of factors of production for different isocost lines. Suppose, a firm’s isocost line AB represents an expenditure of Rs. 100. Unit cost of both labour and capital are Rs. 10.
Assume that the firm uses a particular technology, which requires equal quantities labour and capital to be used for producing the final output. With a budget of Rs. 100, the firm can employ 5 units of labour and 5 units of capital. If the firm employs 5 units of both labour and capital, it can at most produce 5 units of output (point S).
When the isocost line shifts to CD, the firm’s ability to spend increases from Rs. 100 to Rs. 200, which enables it to employ double quantities of both the inputs. With this enhanced capacity of purchasing inputs, the maximum quantity of output that the firm can manufacture is 10 units (point T).
Both the points S and T are the points of tangency between isocost lines and the highest possible isoquant that can be attained within the cost constraints. Thus, if the points of tangency between isocosts and isoquants i.e., S, T and U, representing optimal combinations of factors of production, are joined we get OJ, which is the expansion path of the firm under consideration.
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It is to be noted that this expansion path is a long run phenomenon since levels of both the inputs are allowed to vary.