The Equality between Marginal Cost and Marginal Revenue in Firm Equilibrium

An Introduction to Equilibrium
Equilibrium in a firm occurs when it maximizes its profits by producing and selling a certain quantity of goods or services. This equilibrium point is where the firm's marginal cost (MC) is equal to its marginal revenue (MR). Marginal cost represents the additional cost incurred by the firm when producing one more unit of output, while marginal revenue indicates the additional revenue generated by selling one more unit of output.

The Importance of Equality
The equality between marginal cost and marginal revenue is crucial for a firm to achieve equilibrium due to the following reasons:

1. Profit Maximization: In order to maximize profits, a firm needs to produce the quantity of goods or services where its marginal cost equals its marginal revenue. At this point, the firm is neither overproducing nor underproducing, ensuring that it is efficiently allocating its resources.

2. Cost and Revenue Optimization: When marginal cost is greater than marginal revenue, it implies that the cost of producing one more unit exceeds the revenue generated from selling it. This would result in a decrease in profits. On the other hand, if marginal revenue exceeds marginal cost, the firm can increase its profits by producing more units until the equality between the two is achieved.

3. Market Competition: In a perfectly competitive market, firms are price takers and face a horizontal demand curve. The market price is equal to the marginal revenue for each unit sold. Therefore, for a firm to maximize profits, it must produce the quantity where marginal cost equals the market price (which is also equal to marginal revenue).

Equilibrium Diagram and Schedule

To illustrate the equilibrium condition, let's consider a diagram and schedule:

Diagram:
In the diagram, the x-axis represents the quantity of output produced, while the y-axis represents the cost and revenue. The marginal cost (MC) curve is upward sloping, indicating that as more units are produced, the cost of production increases. The marginal revenue (MR) curve is horizontal and coincides with the demand curve in a perfectly competitive market.

At the equilibrium point, the MC curve intersects the MR curve. This intersection represents the quantity of output where marginal cost is equal to marginal revenue, indicating that the firm is in equilibrium.

[Insert diagram here]

Schedule:
Let's consider a hypothetical schedule to further understand the equilibrium condition.

Quantity | Total Cost | Marginal Cost | Total Revenue | Marginal Revenue
----------------------------------------------------------------------
1 | $10 | $10 | $20 | $20
2 | $20 | $10 | $40 | $20
3 | $30 | $10 | $60 | $20
4 | $40 | $10 | $80 | $20

In this schedule, as the firm increases its output from 1 unit to 4 units, the marginal cost remains constant at $10, while the marginal revenue remains constant at $20. The equality between marginal cost and marginal revenue is maintained throughout, indicating equilibrium.

Conclusion
The equality between marginal cost and marginal revenue is necessary for a firm to be in equilibrium as it allows for profit maximization and cost optimization. When the equality is achieved, the firm is producing