0455 · 3.6Firms costs revenue and objectives

Fixed and variable costs

0:00A café can serve more customers and still earn less profit. Its ingredients might become more expensive, or its owner might reduce prices too far. Understanding business decisions requires us to separate money coming in from money going out. Costs, revenue and profit then shape the objectives a firm chooses to pursue. A firm is an organisation that produces goods or services. Output is the quantity produced during a particular period.

0:24Sales measure the quantity actually sold, which can differ from production if some goods remain unsold. Keep the period consistent throughout a calculation, so daily figures are compared with other daily amounts. Costs of production are the expenses incurred when producing goods or services. A café pays for ingredients, electricity, equipment and premises. Some expenses remain unchanged when it makes more drinks, while others rise. This distinction helps us understand why producing another item does not necessarily increase every expense.

0:54Fixed costs are expenses that do not change with output. A café normally pays its agreed rent even when it serves no customers. Insurance behaves in the same way, so rent and insurance are the standard examples. Producing additional drinks leaves those payments unchanged within the period we are examining. Making additional drinks requires more ingredients, so the café’s spending on them rises. Expenses like this, which change with output, are variable costs.

1:19Raw materials and the energy used in production are typical examples. Classify an expense by its relationship with production, rather than simply by its name. For example, an electricity bill can include a fixed connection charge and a variable charge for energy consumed. The connection charge remains payable even without production. Using more electrical equipment increases the energy component. Also, a fixed expense can change between periods without becoming variable, because the defining relationship concerns output.

Calculating total cost

1:49Total cost is the sum of fixed and variable costs. The formula is total cost equals fixed cost plus variable cost. We add them because both categories contribute to the overall expense of production. At zero output, variable cost is zero in our example, but the fixed payment remains. Consider a small workshop producing chairs each day, with fixed cost of one hundred dollars. At zero chairs, variable cost is zero dollars, so total cost is one hundred dollars.

2:18For one chair, fixed cost remains one hundred dollars and variable cost is forty dollars. Adding these gives total cost of one hundred and forty dollars. At two chairs, fixed cost is one hundred dollars and variable cost is seventy dollars, so total cost is one hundred and seventy dollars. For three chairs, the corresponding amounts are one hundred dollars and one hundred and twenty dollars, which total two hundred and twenty dollars.

2:41At four chairs, fixed cost remains one hundred dollars and variable cost reaches two hundred dollars. Total cost is therefore three hundred dollars. You can also rearrange the relationship when a table contains missing information. Fixed cost equals total cost minus variable cost. Variable cost is found by subtracting the fixed amount from the total. These rearrangements work because removing one part of the combined expense leaves the other. Suppose an exam table for a bakery leaves fixed cost blank.

3:12Its total cost is two hundred and fifty dollars a day, while variable cost is ninety dollars. Subtract ninety dollars from two hundred and fifty dollars. The missing fixed cost is one hundred and sixty dollars a day. Later in the table, the bakery’s total cost reaches three hundred and ninety dollars a day. Its fixed cost is still one hundred and sixty dollars. Subtract one hundred and sixty dollars from three hundred and ninety dollars.

3:36Variable cost at that output is two hundred and thirty dollars a day.

Average costs and cost diagrams

3:39Total figures tell us the whole bill, but average figures tell us the expense per unit produced. Average total cost is total cost per unit of output. We calculate it by dividing total cost by output. Division spreads the overall expense across the items made, rather like sharing a bill equally. Return to the chair workshop, whose total cost at four chairs is three hundred dollars. Dividing three hundred dollars by four chairs gives seventy-five dollars.

4:06Average total cost is therefore seventy-five dollars per chair. This includes each chair’s share of both the fixed expense and the variable expense. Average fixed cost is fixed cost per unit of output, so its formula is fixed cost divided by output. For the variable part, the matching measure is average variable cost: variable cost per unit produced. It equals variable cost divided by output. These averages separate the two components of the expense associated with each item.

4:34Take the workshop’s fixed cost of one hundred dollars and divide it by four chairs. The result is an average fixed cost of twenty-five dollars per chair. At one chair, the whole one hundred dollars falls on that single chair. A larger output shares the same fixed payment across more items, so this average falls. For average variable cost, start from the two hundred dollars of variable cost at four chairs.

4:56Two hundred dollars divided by four chairs is fifty dollars per chair. Adding the twenty-five dollars of average fixed cost brings us back to seventy-five dollars per chair. That matches the average total cost found earlier. There is no average cost at zero output because division by zero is undefined. The workshop still has a total expense, but there are no chairs across which to spread it. Every average describes the amount per unit across the entire output.

5:21On a total-cost diagram, output belongs on the horizontal axis and cost on the vertical axis. The fixed-cost line is horizontal because its value stays unchanged as production rises. Variable cost starts at the origin and increases with output. Total cost begins at the fixed-cost intercept, because that expense exists before anything is produced. The total-cost curve remains above the variable-cost curve by the fixed amount. That vertical gap follows directly from adding the same payment at every output.

5:51The rising curves need not be straight, because production expenses can increase at different rates. When drawing them, keep the gap between total cost and variable cost equal to the height of the fixed-cost line at every output. Average-cost diagrams use cost per unit on the vertical axis. Average fixed cost falls continuously because the unchanged payment is spread across increasing production. It approaches zero but does not reach it while fixed cost remains positive.

6:17This curve can fall even though the firm’s overall fixed expense stays exactly the same. Average variable cost and average total cost are commonly drawn as U-shaped curves. Initially, better use of workers and equipment can reduce the expense per item. Beyond a certain output, overcrowding or pressure on equipment can raise it. The precise shapes depend on production conditions, rather than following from division alone. Average total cost lies above average variable cost because it also includes the fixed component per item.

6:48Their vertical gap equals average fixed cost. As production increases, that gap narrows because the fixed payment is spread more widely. Meanwhile, total cost keeps rising with output, so check whether the vertical axis shows totals or amounts per unit.

Revenue and profit

7:03Revenue is income received from selling goods or services. Total revenue is the income a firm receives from all its sales. We calculate it as price multiplied by quantity sold. Each sale brings in the selling price, so multiplication adds together the receipts from all the items purchased. For example, a café sells eighty drinks at six dollars each during a day. Multiply six dollars by eighty drinks. Total revenue is four hundred and eighty dollars for that day.

7:31This is money received from customers before production expenses are deducted. Average revenue is revenue per unit sold. Its formula is total revenue divided by quantity sold. When every item sells at the same price, this calculation gives that selling price. We are simply sharing the sales receipts across the items that generated them. The café received four hundred and eighty dollars from eighty drinks. Divide four hundred and eighty dollars by eighty drinks.

7:58Average revenue is six dollars per drink. This equals the price because each sale contributed that amount to the total receipts. At an unchanged price, selling more units increases total revenue. If the price changes as well, we must compare both influences. A price reduction brings in less money from each sale, but it can attract enough additional purchases to raise overall receipts. Total revenue rises only when the extra sales outweigh the lower price per item.

8:26Suppose a shop initially sells thirty items at twelve dollars each. Its total revenue is three hundred and sixty dollars. It then reduces the price to nine dollars and sells thirty-five items. Multiplication gives new total revenue of three hundred and fifteen dollars, so revenue has decreased by forty-five dollars. Here, the extra sales are too few to make up for the lower price. Profit is total revenue minus total cost.

8:51Revenue measures sales income, whereas profit measures what remains after production expenses. If total cost exceeds total revenue, the firm makes a loss. Return to the café with daily total revenue of four hundred and eighty dollars. Suppose its total cost is three hundred and fifty dollars. Subtract three hundred and fifty dollars from four hundred and eighty dollars. Daily profit is one hundred and thirty dollars, so not all its sales income is available to the owner.

Business objectives

9:17A firm aiming for profit maximisation seeks the greatest possible difference between total revenue and total cost. It compares the profits available from different decisions. Selling the largest quantity is not necessarily best, because extra production can be expensive. Equally, the highest price can discourage enough purchases to reduce profit. Survival is the objective of continuing to operate and avoiding closure. This objective can become especially important for a new firm or during difficult trading conditions.

9:47An owner might accept a smaller profit to retain customers and meet essential payments. Survival takes priority when the alternative is losing the business altogether. For a firm seeking growth, the aim is to increase its size through higher sales, greater output or additional premises. Market share is the proportion of total market sales accounted for by a firm. A business might lower prices or spend more on promotion to expand that proportion, even if current profit falls.

10:14Social welfare is the wellbeing of society as a whole. Some social enterprises and public sector firms prioritise benefits to people rather than the highest possible profit. Their objectives can include affordable services, employment opportunities or reduced environmental damage. For example, a recycling enterprise might accept higher expenses to keep waste out of landfill. These objectives can support one another, but they can also conflict. Profit can finance expansion, while environmentally responsible production can attract customers.

10:45However, using cleaner materials might raise expenses before additional sales develop. A firm must also earn enough revenue to stay in business while it pursues these goals.

Exam skills and recap

10:55Common calculation errors arise from confusing whole-business totals with amounts per unit. Write dollars per item beside an average, and dollars per period beside a total. For revenue, multiply the price by the quantity sold, which can be smaller than the quantity produced. On diagrams, check whether the vertical axis shows an overall expense or an expense per unit. In multiple-choice questions, identify the defining relationship before considering the options.

11:22A fixed expense stays unchanged with output, while its average falls as production increases. Structured questions can ask you to complete a table, interpret a diagram or explain an objective. Show your calculation method and connect explanations to the particular firm. A define question wants the precise meaning, while state means expressing the point in clear terms. To explain, set out the reasons why or how something happens. Analysing goes further by examining relationships in detail, such as how a price reduction affects receipts and profit.

11:54Discuss questions are answered in a structured way, with both sides and a supported judgement. Consider this question: discuss whether a recycling firm should prioritise social welfare rather than profit maximisation. On one side, putting social welfare first keeps more waste out of landfill and improves society’s wellbeing. On the other side, if total revenue stays below total cost, the firm makes a loss and cannot meet its expenses. Closure would then remove its recycling service and every benefit it provides.

12:25On balance, this firm should usually prioritise social welfare, as long as its revenue covers its costs. Its environmental purpose is the reason it exists. Survival matters too, because only a firm that keeps operating can deliver lasting benefits. Some profit is therefore needed, but the firm need not maximise it. The central relationship is that total cost combines fixed and variable expenses, while averages spread those amounts across output.

12:50Sales income depends on price and quantity sold, and average revenue gives income per sale. Subtracting production expenses from receipts reveals profit or loss. Firms then use these relationships to pursue survival, social welfare, profit maximisation or growth.