12.5 Deciding how much to produce and what price to set

principle of trade-offs and opportunity cost

The gains you make by choosing some action typically come at the cost of gains that would have been possible had you acted differently.

Let’s revisit our price, quantity, total revenue, and total costs information, evaluating a few possible price and output options for your beer. In thinking through this exercise it will be helpful to recall the trade-offs and opportunity costs principle.

A thought experiment about what price to charge

Using the price and total costs data from Table 12.6 as a reference, consider the following prices: $400, $200, and $40. Recall that fixed costs are $100 regardless of output, and follow the thinking process summarized in Table 12.7.

principle of trade-offs and opportunity cost

The gains you make by choosing some action typically come at the cost of gains that would have been possible had you acted differently.

Clearly, you don’t want to set the price too high, which would drive away all the buyers. At the same time, you don’t want to produce too much beer, which forces you to lower the price significantly just to attract enough buyers. This scenario illustrates the principle of trade-offs and opportunity costs in action.

To sell more kegs, you are willing to give up a higher price per keg. Conversely, to charge a higher price, you are willing to sell fewer kegs. This trade-off highlights the opportunity costs of your decisions. When you lower the price to increase the number of kegs sold, the opportunity cost is what you give up in order to sell more kegs—here, the loss in per-unit revenue. Understanding this trade-off is important in doing the best you can to maximize your profits.

While the exercise summarized in Table 12.7 provides a good starting point, you are still not entirely confident about the exact price you should set.

Thinking at the margin: Marginal benefits and marginal costs

In the real world, firms such as CORE Brewing don’t always have a complete picture of total revenue and total costs at every level of output, and this can make the thought exercise presented in Table 12.7 a bit challenging. Breweries might have a better sense of what happens if they produce one more keg of beer.

Another approach to making price and quantity decisions is to think incrementally about how much to produce, breaking down this big decision into smaller, more manageable choices. Consider a marginal decision: Should I produce one more keg, or one fewer keg? If I produce one more keg, what will it cost me to produce it? How much can I sell the extra keg for? Is producing one more keg worth it? This kind of marginal thinking can be useful because it allows firms to do the best they can even in the face of uncertainty.

Let’s now do another thought exercise in which we evaluate whether it makes sense to increase or decrease production by one keg based on the data in Table 12.6.

marginal revenue

Marginal revenue is the change in revenue obtained by increasing the quantity sold by one unit.

marginal cost

A firm’s marginal costs are the increase in total costs when one additional unit of output is produced.

Table 12.8 summarizes your thought process. As a brewer, your marginal benefit is the extra revenue earned from selling one more keg of beer. This is your marginal revenue. Your marginal costs are the additional costs incurred in producing one more keg. By comparing these two numbers, you can determine whether increasing or decreasing production is the right decision.

You can determine your marginal costs by taking the change in total costs from one output level to the next and dividing it by the change in quantity. We use the Greek symbol delta (\(\Delta\)) to denote changes.

For example, as CORE Brewing’s beer production increases from 1 to 2 kegs, the total costs increase from $180 to $260, an increase (or we can use the Greek symbol \(\Delta\)to denote the change) of $80. This number represents marginal costs, sometimes denoted as MC, of producing another keg of beer. As CORE’s output increases from 2 to 3 kegs, your total costs increase from $260 to $340, which is an increase (or \(\Delta\)) of $80. Column 4 of Table 12.9 shows that marginal costs are $80 at every level of output. In other words, for each additional keg of beer that you produce, you must spend an extra $80.

We can follow a similar approach with marginal revenue, denoted as MR. For example, when you compare selling 1 kegs to 2 kegs, total revenue increases from $360 to $640, a change in revenue of $280, which is your marginal revenue of producing the second keg of beer. When you compare selling 2 kegs to 3 kegs, total revenue increases from $640 to $840, and marginal revenue is $200. Column 6 of Table 12.9 shows these values.

The data in Table 12.9 make it easier to analyze your production decisions. By comparing the values in columns 4 and 6, you can evaluate marginal costs (MC) and marginal revenue (MR) to determine whether producing an additional keg of beer is profitable.

The data shows that marginal revenue exceeds marginal costs when you produce up to 4 kegs. If you produce a 5th, 6th, 7th, 8th, 9th, or 10th keg, marginal revenue will be less than your marginal costs. Your marginal revenue is negative when you produce 6 or more kegs. Marginal revenue turns negative when total revenue begins to decrease because you are charging very low prices in an attempt to sell more kegs of beer. Even though you are selling more kegs, the price for each keg is so low that your revenue starts to decline. You are close to giving away your beer for free!

In comparing marginal revenue against marginal costs in Table 12.9 you determined that you will produce up to 4 kegs of beer. When you produce 4 kegs of beer, each keg sells for $240. You can confirm that your decision is correct by looking at Column 7 of Table 12.9, which shows your profits at each output level. Your original intuition was correct. You don’t want to sell at a very high or very low price, because you will incur losses when you set the price too high or too low. Looking at the profits column (Column 7), we see that the highest profit occurs when you produce and sell 4 kegs of beer for $240, the price and quantity you selected when comparing marginal costs and marginal revenue.

Table 12.9 shows us that when MR > MC, CORE Brewing can increase its profits by increasing Q. When MR < MC, CORE Brewing is better off by decreasing Q. When MR = MC, profit is the highest. At MR = MC, you are doing the best you can. Among all your possible choices, you are choosing the action that leads to the highest possible profit given the constraints imposed on you by buyers.