Long run Cost Functions

Quite often, managers have to make long run production decisions with respect to change in the scale of plant (all inputs of the firm) and hence the firms' cost of production. Since all inputs are variable in the long run, there are no fixed costs in the long run. Ability to vary all inputs allows the firm to produce at lower costs in the long run than in the short run. In brief, flexibility is valuable.

Given the factor prices and a specific production function, we can draw an expansion path, which gives the least costs associated with various levels of output e., the long run total cost (LTC) schedule. The LTC gives the least cost for various level of output when all the factors of production are variable. The shape of the LTC curve is due to returns to scale, factor prices given. The LAC and LMC are derived from the LTC.

LAC = LTC/Q

LMC = ΔLTC/ΔQ

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