Question

a) A firm's long-run total cost function is given by LTC = 115,000 Q – 500 Q ² + Q ³, where long-run marginal cost is given by LMC = 115,000 – 1,000 Q + 3 Q ². At what range of output does this firm have economies of scale?

Answer 1

As per the question firms Long-run total cost (LTC) = 115,000Q – 500 Q² + Q³

Long run Average cost (LAC) = LTC/Q = 115,000 – 500 Q + Q²

Long run Marginal cost (LMC) = 115,000 – 1,000Q + 3Q²

At Equilibrium level of output in long-run, Long run Average cost (LAC) = Long run Marginal cost (LMC)

115,000 – 500 Q + Q² =115,000 – 1,000Q + 3Q²

1000Q – 500Q = 3Q² - Q²

500Q = 2Q²

2Q² = 500Q

2Q = 500

Q= 250

The long-run equilibrium output is 250 units, because at this level of output the LMC is equal with LAC and LMC intersects LAC from its below.

Therefore economies of scale occur at the range of output less than 250 units.

Explanation: Due to economies of scale the LAC is falling and its reaches to minimum at equilibrium level of output. Hence the range of output less than the equilibrium level of output represent economies of scale. In the below diagram the horizontal axis represents output and the vertical axis represents cost. the long-run equilibrium output is 250 units, because at this level of output the LMC is equal with LAC and LMC intersects LAC from its below. So the range of output less than 250 units represents economies of scale.