2.11.4 Rational producer behaviour Notes

In Section 2.4.3, we introduced the idea that the main goal of firms is profit maximisation:

1. At its core, profit maximisation is about finding the level of output where a firm earns the highest possible profit.
2. This happens when a firm compares its revenues and costs and adjusts its output accordingly.

We will also discover there are three types of profits firms can have:

1. Normal profit.
2. Abnormal profit.
3. Losses (negative profit).

Total profit = Total revenue - Total costs

Total revenue (TR)

Total revenue (TR) is the total amount of money earned by a firm in a period of time. It is found by using the following formula:

$$TR= P \times Q$$

where:

• $P$ = Price of the good or service.
• $Q$ = Quantity of goods (or services) sold.

Total costs (TC)

Total costs (TC) is the total expenditure incurred by a firm in the production of goods or services over a given period. It is calculated using the following formula:

$$TC=TFC+TVC$$

where:

• $TFC$ = Total Fixed Costs: costs that do not change with output (rent, salaries...)
• $TVC$ = Total Variable Costs: costs that change with output (raw materials, shipping...)

Total profit (TP)

Total profit (TP) is the total financial gain a firm makes after deducting total costs (TC) from total revenue (TR). It is calculated using the following formula:

$$TP=TR−TC$$

where:

• $TR$ = Total Revenue
• $TC$ = Total Costs

Marginal revenue (MR) = Marginal cost (MC)

Marginal revenue (MR)

Marginal revenue (MR) is the additional revenue earned from selling one more unit of output. It can be expressed by the following formula:

$$MR = \frac{\Delta TR}{\Delta Q}$$

where:

• $\Delta TR = \text{New } TR - \text{Old } TR = \text{Change in } TR$.
• $\Delta Q = \text{New } Q \text{ sold } - \text{Old } Q \text{ sold } = \text{Change in } Q \text{sold }$.

The marginal revenue curve

If the price at which a firm sells its good remains constant, regardless of its price:

1. The marginal revenue is always the same.
2. The marginal revenue equals the price.
3. This can be seen in Table 1 below.

However, if the firm increase its prices as quantities sold increase (as dictated by the supply curve):

1. The marginal revenue decreases as quantity sold increases, eventually becoming negative.
2. The marginal revenue is not equal to the price.
3. This can be seen in Table 2 below.

Therefore, if we plot the relationship between marginal revenue, price, and quantity produced (sold), then we have two different graphs (Figure 1):

Marginal cost (MC)

Marginal cost (MC) is the additional cost incurred from producing one more unit of output. It can be calculated through the following formula:

$$MC = \frac{\Delta TC}{\Delta Q}$$

where:

• $\Delta TC = \text{New } TC - \text{Old } TC = \text{ Change in } TC$.
• $\Delta Q = \text{New } Q \text{ sold } - \text{Old } Q \text{ sold }= \text{Change in } Q \text{ sold}$.

The marginal cost curve

As we saw in Subtopic 2.1.1, marginal costs increase as the quantity produced increases. This was due to:

1. Inefficiencies: as explained earlier, adding more variable inputs leads to less efficient production.
   1. For every additional unit of output there is more input (higher costs).
   2. As seen by the law of diminishing marginal returns, for every additional unit of output lesser marginal product (lower return).
   3. Therefore, the cost per each additional unit of output increases.
2. Scarcity of efficient resources: expanding production often requires using less efficient resources.
   1. For example, a factory might need to pay higher, overtime wages or use older, less efficient machinery to meet higher production targets.

Therefore, if we plot the relationship between marginal cost (MC) and quantity produced (sold) in Table 3, we obtain the marginal cost (MC) curve (Figure 2):

Firms maximising profits at MR = MC

All firms, regardless whether their selling price is constant or varying, maximise profits when their marginal revenue equals their marginal cost. This is because:

1. If firms produce at a price and quantity where MR > MC:
   1. Producing more increases profit because additional revenue is greater than additional costs.
   2. Therefore, firms will increase output to take advantage of extra profit opportunities.
2. Contrarily, if firms produce at a price and quantity where MR < MC:
   1. Producing more reduces profit because additional costs are greater than additional revenue.
   2. Therefore, firms will reduce output to avoid making losses.
3. However, if firms produce at a price and quantity where MR = MC:
   1. This is the profit-maximising level of production.
   2. Producing more or less would reduce profit.
   3. Firms have no incentive to change their output.

Normal profit (AR = AC)

Average revenue (AR)

Average revenue (AR) is the revenue a firm earns per unit of output sold.

$$AR = \frac{TR}{Q}$$

where:

• $TR$ = Total revenue
• $Q$ = Quantity of output sold

The average revenue curve

If the price at which a firm sells its good remains constant, regardless of its price:

1. The average revenue is always the same.
2. The average revenue equals the price.
3. This can be seen in Table 4 below.

However, if firm increase their prices as quantities sold increase (as dictated by the supply curve):

1. The average revenue decreases as quantity sold increases.
2. However, the average revenue is still equal to the price.
3. This can be seen in Table 5 below.

Therefore, if we plot the relationship between average revenue, marginal revenue, price, and quantity produced (sold), then we have two different graphs (Figure 3):

Average costs

Average cost (AC) is the total cost per unit of output produced.

$$AC = \frac{TC}{Q}$$

where:

• $TC$ = Total Cost
• $Q$ = Quantity of output produced

If we add average cost (AC) to our pizza example from above (Table 3), we can see the relationship between quantity produced and AC (Table 6):

The relationship between marginal cost, average cost, and quantity produced, and AC can be observed in Figure 4:

Normal profit at AR = AC

Normal profit occurs when a firm’s total revenue exactly covers total costs. Expressed as a formula, normal profit occurs when:

$$AR = AC$$

When a firm is making normal profit:

1. The firm is self-sustaining but not growing.
2. It occurs at the break-even point, where AR = AC.

Abnormal profits (AR > AC)

Abnormal profit occurs when a firm’s total revenue exceeds total costs. Expressed as a formula, abnormal profit occurs when:

$$AR>AC$$

This means:

1. Total Revenue (TR) > Total Cost (TC)
2. The firm earns extra profit beyond covering costs.

Losses (AR < AC)

A firm makes a loss when its total revenue is less than total costs.

$$AR<AC$$

This means:

• Total Revenue (TR) < Total Cost (TC)
• The firm is spending more than it earns.

Firms never operate in a loss in the long-run. They either cut costs, increase their revenue, or close.