Competitive Supply Where Marginal Cost Equals Price

Given its.costs, demand, and desire to maximize profits, how does a competitive firm decide on the amount that it will supply? Say you are managing Billy Bob Tucker’s oil operations and must set the profit-maximizing output. Examine the data in Table ~I, which contains the same cost data in thousands as Table 7-3 in the previous chapter. For this example, assume that the market price for oil is $40 per unit. Say Billy Bob starts out by selling 3000 units. This yields total revenue of $40 X 3000 = $120,000, with total cost of $130,000, so the firm incurs a loss of $10,000.

Now you analyze your operations and see that if you sell more oil, the revenue from each unit is $40 while the marginal cost is only $21. Additional units bring in more revenue than they cost. So you raise production to 4000 units. At this output, the firm has revenues of $40 X 4000 = $160,000 and costs of $160,000, 50 profits are zero.

Flush with your success, you decide to boost output some more, to 5000 units. At this output, the firm has revenues of $40 X 5000 = $200,000 and costs of $210,900. Now you’re losing $10,000 again. What went wrong?

W’hen you go back to rour accounts, you see that at the output level of 5000, the marginal cost is $60,’ which is more than the market price of $40, so you are losing $20 (equal to price minus MC) on the last unit produced. Now you see the light: The maximum profit output at that output cost equals price.

The reason underlying this proposition is that the competitive firm can always mas., additional profit as long as the price is greater than the marginal cost of the last unit. Total profit reaches its peak-is maximized- when there is no longer any extra profit to be earned by selling extra output. At the maximum profit point, the last unit produced, brings in an amount of revenue exactly equal to that unit’s cost. What is that extra revenue? It is the price. per unit. What is that extra cost? It is the marginal cost.

Let’s test this rule by looking at Table 0_1. Starting at the profit-maximizing output of 4000 units, if Billy Bob seals 1 more unit, that unit would bring a price of $40 while the marginal cost of that unit is $40.01. So the firm would lose money on the 4OO1st unit. Similarly, the firm would lose $0.01 . if it produced 1 less .unit This shows that the firm’s maximum-profit output comes at exactly q = 4000, where price equals marginal cost.

Rule for a firm’s supply under perfect competition: A firm will maximize profits when it produces . at that level where marginal cost equals price: Marginal cost = price or Me =,P Figure 8-2 on page 150 illustrates a firm’s supply decision diagrammatically. When the market price of output is $40, the firm consults, its cost data in Table 8-1 and finds that the production level Corresponding to a marginal cost of $40 4s 4000 units. Hence, at a market price of $40, the firm will wish to produce
and’ sell 4000 units. We can find that profit-maximizing  amount in Figure 8-2 at the intersection of. the price line at $40 and the Me curve at point B.

In general, then, the firm’s marginal cost curve can be used to find its optimal production schedule: the profit-maximizing output will come where the price intersects the marginal cost curve.

We designed this example so that at the profit maximizing output the firm has zero profits, with total revenues equal to total costs. (Recall that-these are economic Profits and include all opportunity costs, including the owner’s labor and capital.) Point B is the zero-profit point, the production level at which the firm makes zero economic profits; at the zero profit point, price equals average cost, so revenues just cover costs.

What if the firm chooses the wrong output? Suppose the firm chooses output level A in Figure 8-2 when the market price is $40. It would be losing money became the last units have marginal cost above price. We can calculate the loss of profit if the firm mistakenly produces at A by the shaded gra), triangle in Figure 8-2. This depicts the surplus of Me over price for production between Band A.

The general then is: A profit-maximizing firm will set its out put at that level where marginal cost equals price. Diagrammatic this means that a firm’s marginal cost curve’ is also its supply curve.

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