Question

Orion Limited’s total cost is C = a + bQ, where Q is output, a is total fixed cost, and bQ is total variable cost.

Use calculus to determine the impact on Orion’s average total cost of (i) market size X, the number of firms held constant, and of (ii) the number of firms N, market size X held constant.

Answer 1

C = a+bQ

AC = C/Q = (a/Q) + b

X = N*Q

As total market size = number of Firms * each Firm output level

Q = X/N

Then , AC = (aN)/X + b

a) dAC/dX = -(aN)/X^{​​​​​​2}

so , dAC/dX < 0

thus as X rises, with N being unchanged, ATC falls

.

B) dAC/dN = (a/X) > 0

So as N rises, with X unchanged, ATC rises