If a firm has increasing returns to scale (i.e., doubling inputs more than doubles output) would that firm logically end up being the sole firm in its sector in the long run?
If not, what is the advantage of displaying IRTS?
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Sign up to join this communityIf a firm has increasing returns to scale (i.e., doubling inputs more than doubles output) would that firm logically end up being the sole firm in its sector in the long run?
If not, what is the advantage of displaying IRTS?
Provided that increasing returns to scale apply over the whole production function of the company it is likely that it would become natural monopoly. For example, Mankiw in Principles of Economics (pp 292) in some passages even defines monopolies in relation to their cost function:
When a firm’s average-total-cost curve continually declines, the firm has what is called a natural monopoly.
Generally the average-total-cost curve will continually decline when firm has increasing returns to scale.
However, there are models with increased returns to scale where monopolies are not inevitable. For example, Wang (2016) presents a model of banking competition where firms face increasing returns to scale, and even though the model predicts increase in market concentration it does not necessary predict that a single bank will become monopoly.
It can be shown that a firm with increasing returns to scale (IRTS) and no market power makes a negative profit (and may not be observed at all, in the long run). Conclusion: either subsidies, or market power is necessary for a firm with global IRTS to be sustainable.
With usual notations, the claim follows from the first order condition for an (inner) optimum with perfect competition: $ c'(y) = p $. When multipling by $y/c$ we obtain the inverse of the rate of returns to scale: $c'(y)y/c = py/c$. With global IRTS, $c'(y)y/c < 1$, and this implies that profits are negative: $py-c<0$.
Besides the great answers already given, adding my two cents:
A firm ends up being a sole player in the sector when market entry for others is restricted, which may not be guaranteed by IRTS or even continual economies of scale.
First, it is important to realize that, contrary to our first naive intuition, IRTS does not imply economies if scale. See this for counter example and related discussion.
Second, lets be generous and assume that there is continual economies of scale. Below is a counter example to show that even now, competition can exist:
Consider a cournot duopoly with two identical firms, and marginal cost:
$$\frac{\partial C}{\partial q_i}=50-q_i/2$$
Inverse demand function for the product market is:
$$p=100-q=100-q_1-q_2$$
Writing the profit function for firm 1:
$$\pi_1 = q_1 (100-q_1-q_2) - C(q_1)$$
FOC:
$$\frac{\partial \pi}{\partial q_1}=50-3q_1/2-q_2$$
So we have following best response function (for $i\ne j$):
$$q_i=\frac{100-2q_j}{3}$$
So, at equilibrium:
$$q_1=q_2=20$$
This is clearly a permissible solution and shows existence of cournot duopoly with continual economies of scale.
The idea is that if same tech is available to all, anyone can enter market with big enough investment and take a share if market demand. On the other hand, if there is first mover advantage (for example ,because of consumers' inertia to move to new seller or capital constraints, etc) economies of scale can help create a monopoly by restricting market entry.
So to summarize, IRTS, or even economies if scale for that matter, does not guarantee monopoly.
What is the benefit of displaying IRTS: it can certainly deter a market entrant by (possible a credible) threat that incumbent can increase investment significantly to make entry costly.