Question

Consider a firm that pays fixed cost F to construct a plant and variable cost C to produce goods. Let q be the quantity that this firm produces. For each case below, do the economics of scale occur for any q? (Hint: Economies of scale occur when marginal cost is less than average cost, MC < AC.)

A. F= 100, c= 10q

B. F= 12, c= 2q^2

C. F= 10, c= 100q

please explain as thoroughly as possible with step by step!!

Answer 1

A) TC = 100+10Q

MC = dTC/dQ = 10

AC = TC/Q = 10 + 100/Q

Economies of scale occurs when AC > MC

That is, 10 + 100/Q > 10

This takes place for all values of Q > 0

B) TC = 12 + 2Q^2

MC = 4Q

AC = 2Q + 12/Q

Economies of scale takes place when AC > MC

That is,

2Q + 12/Q > 4Q

2Q + 12/Q > 0

This takes place for values of Q > 0

C) TC = 10 + 100Q

MC = 100

AC = 100 + 10/Q

Economies of scale takes place when AC > MC

100+10/Q > 100

This takes place at all values of Q > 0