Multi-Plant Monopoly

A monopoly produces homogeneous products and can expand its firm size by operating in more than one plant. This is a case of a multi-plant monopoly, where the monopolist can produce its output in more than one plant. For this, we can assume that:

• A monopoly firm has two plants, A and B
• The cost conditions of both plants are different
• The firm is aware of its AR and MR

The cost conditions of the two plants are given and shown in the following diagram. Total MC can be determined by horizontal summation of both MCA + MCB, which is shown in panel c of the following diagram. If the monopolist knows its MR and MC then it can easily determine its profit condition as shown by output OQ in panel c of the following diagram.

The output for each plant can be obtained by applying the profit maximizing rule, i.e. MR = MCA = MCB. The profit-maximizing output of each plant can be obtained by drawing a horizontal line MR = MC from point E through MCA and MCB.

Now this line intersects the respective MC of each plant at E1 and E2 and hence determines the output in each plant as OQA and OQB.

Now the profit maximization price is OP (determined at panel c), and that of plant A is Oa, and that of plant B is Oe. Hence, the total profit of plant A is abcd, and that of plant B is efgh.

However, in the long run, a multi-plant monopoly adjusts its size and number of plants in order to maximize its long-run profits. The monopolist makes long-run adjustments when the existing size of the minimum-cost plant is smaller compared to the size of the market and there exist economies of scale.

If such conditions do exist, the monopolist would adjust the size of each plant in the long run so that the minimum of SAC coincides with the minimum of MC.

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