When significant economies of scale are present over a wide range of initial output, average cost of production goes on falling over a wide range of output and reaches its minimum at an output that is large enough for a single firm to meet the entire market demand at a profitable price. In such a situation if more than one firm operates each firm must be producing at a price higher than the minimum average cost. In such a situation each firm is inclined to cut prices to increase its output and reduce the average cost of production. This leads to price warfare and one who survives this economic warfare is the monopolist. Such monopolies with significant economies of scale are called natural monopolies. These are often regulated by the government so that they might not charge very high prices.
E.g. Distribution of water: To provide water to a town a firm must build a network of pipes through the town. If two or more firms were to compete for this, each would have to pay the fixed cost of building a network which would raise the average cost.
An allocation is called as Pareto efficient if from that allocation it is impossible to make anyone better off without making someone worse off by any relocation of resources or distribution of outputs. Monopolies are regarded as inefficient as they do not have competitive prices of P=MC. Many argue that incase of natural monopolies, the output can only be successfully and profitably provided by a single large firm rather than multiple small firms. Breaking up of such natural monopolies or large firms would lead to competitive pricing of P = MC. At the same time the firm owners would become worse off because they can no longer operate at their min. average cost and hence may run into losses. However I disagree because the term efficient change is often used to describe changes in which some may become better off while others are worse off but in which those who gain or receive benefits that are greater than the cost imposed on those who lost. Thus the breakup would be efficient because the consumers will gain much more than the shareholders may lose.
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