Unit 7 The firm and its customers

7.2 Breakfast cereal: Choosing a price

How does a firm decide what price to charge for its product? To maximize profit, it needs to consider the price at which the product can be sold, and the quantity it should produce, given its production costs.

Revenue, costs, and profit

Imagine a firm that makes and sells a brand of breakfast cereal.

total costs

The sum of all the costs a firm incurs to produce its total output.

total revenue, revenue

A firm’s total revenue is the number of units sold times the price per unit.

Its profit is the difference between the revenue it receives from selling cereal, and the costs of producing it. Suppose that the unit cost is $2: the cereal costs $2 per pound to make. If Q pounds are produced per week, and sold at a price P, we can calculate its total costs, revenue and profit:

\[\begin{align*} \text{total costs} &= \text{unit cost} \times \text{quantity} \\ &= 2 \times Q \\ \text{total revenue} &= \text{price} \times \text{quantity} \\ &= P \times Q \\ \text{profit} &= \text{total revenue} - \text{total costs} \\ &= (P \times Q) - (2 \times Q) \end{align*}\]

So we have a formula for profit:

\[\text{profit} = (P-2) \times Q\]

and we can calculate the profit the firm would obtain if it could sell Q pounds at price P. For example, when P = 4 and Q = 50,000, profit = 100,000.

Figure 7.2a shows three-dimensional pictures of how profit depends on Q and P. Each point on the horizontal grid corresponds to a particular (Q, P) combination. The height of the coloured surface above the grid represents the profit at each point. Profit forms a ‘hill’, with height starting at zero where Q = 0 and where P = 2 (price equals unit cost). As P and Q increase, profit gets higher and higher. We have drawn contours joining points of equal height (profit): the point where P = 4 and Q = 50,000 is on the 100,000 contour.

isoprofit curve

A curve that joins together the combinations of prices and quantities of a good that provide equal profits to a firm.

indifference curve

A curve that joins together all the combinations of goods that provide a given level of utility to the individual.

In Figure 7.2b, we represent profit in two dimensions, by drawing the contours of the profit ‘hill’ on the (Q, P) grid. We call these isoprofit curves (with isoprofit meaning ‘equal profit’): they join together all the (Q, P) points that give the same level of profit.

We could describe the isoprofit curves as the firm’s indifference curves: the firm is indifferent between combinations of price and quantity giving the same level of profit.

Demand

The firm would like both price and quantity to be high. But if it sets the price too high, no one will want to buy. It needs information about demand: how much potential consumers are willing to pay.

demand curve

A demand curve shows the number of units of a good that buyers would wish to buy at any given price. Also known as: demand function.

Figure 7.3 shows the demand curve for Apple Cinnamon Cheerios, a ready-to-eat breakfast cereal introduced by the firm General Mills in 1989. In 1996, Jerry Hausman, an economist, used data on weekly sales of family breakfast cereals in US cities to estimate how the weekly quantity of cereal that customers in a typical city would wish to buy would vary with its price per pound. For example, Figure 7.3 shows that if the price were $3, customers would demand 25,000 pounds of Apple Cinnamon Cheerios. For most products, the lower the price, the more customers wish to buy.

Maximizing profit

If you were the manager at General Mills, how would you choose the price for Apple Cinnamon Cheerios, and how many pounds of cereal would you produce?

We will assume that the unit cost of Apple Cinnamon Cheerios is $2. Then:

• Your indifference curves are the ones drawn in Figure 7.2b. To achieve a high profit, you would like both P and Q to be as high as possible (they are both ‘goods’).
• But you are constrained by the demand curve (Figure 7.3), which determines what is feasible. It shows how many Apple Cinnamon Cheerios consumers are willing to buy at each price. If you choose a high price, you will only be able to sell a small quantity, and if you want to sell a large quantity, you must choose a low price.

Figure 7.4a shows the isoprofit curves and demand curve together. You face a similar problem to Karim, the worker in Unit 3 who wants to choose the point in his feasible set where his utility is maximized. You want to choose a feasible price and quantity that will maximize your profit.

Your best strategy is to choose point E in Figure 7.4a. You should produce 15,000 pounds of cereal, and sell it at a price of $4.23 per pound, making $33,450 profit.

constrained choice problem

A problem in which a decision-maker chooses the values of one or more variables to achieve an objective (such as maximizing profit, or utility) subject to a constraint that determines the feasible set (such as the demand curve, or budget constraint).

The profit maximization problem is a constrained choice problem, with the same structure as Karim’s choice of working hours in Unit 3.

• The decision-maker wants to choose the values of one or more variables to achieve a goal, or objective. For Apple Cinnamon Cheerios, the variables are price and quantity; for Karim, they are consumption and free time.
• The objective is to optimize something: the worker maximizes utility; the firm maximizes profit; in other models, the firm might minimize costs.
• The decision-maker faces a constraint that limits what is feasible: Karim’s budget constraint; the demand curve for Apple Cinnamon Cheerios.

In each case, we have represented the decision-maker’s choice graphically, using indifference curves to capture the objective (utility, or profit), and plotting the feasible set of outcomes determined by the constraint. And we have found the solution of the problem at the tangency point of the indifference curves and the constraint.

As a manager who cares about profit, your profit-maximizing choice balances two trade-offs between price and quantity:

• the trade-off you are constrained to make by the demand curve
• the trade-off you are willing to make on the isoprofit curve (where all points give you the same profit).

The manager at General Mills probably didn’t think about the decision in this way.

Perhaps the price was chosen more by trial and error, informed by past experience and market research. But we expect that a firm will find its way, somehow, to a profit-maximizing price and quantity. The purpose of our economic analysis is not to model the manager’s thought process, but to understand the outcome, and how it depends on the firm’s cost and consumer demand.

Even for an economist, there are other ways to think about profit maximization. In Figure 7.4b, we have calculated how much profit would be made at each point along the demand curve, so that we can find the point where profit is highest.

The graph in the lower panel is the profit function: it shows the profit you would achieve if you chose to produce a quantity, Q, and set the highest price that would enable you to sell that quantity. And it tells us, again, that you would achieve the maximum profit at point E.