Research
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When Should Organizations Change Their Mix of Products?

To formulate an optimal product mix, managers need to understand how departmental budgets and information sharing within a company can affect decision making, according to a new study co-authored by Yale SOM’s Rick Antle. 


By Roberta Kwok

Here’s a common dilemma in an organization: One team relies on another team to supply outputs, and the supplying department claims that it needs a certain budget to meet those demands. However, the supplying team may be inflating its cost estimates in order to give itself a comfortable cushion.

“People like to pad their budgets,” says Rick Antle, the William S. Beinecke Professor of Accounting at the Yale School of Management. “They like to get more resources.” This near-universal tendency for departments to leave themselves a little leeway can end up distorting the final choices managers make about product mix—creating a tendency to stick with existing proportions.

To take a simple hypothetical example, imagine a beverage company that makes lemonade and orange juice. The fruit-picking team knows that it costs around $2,000-5,000 per year to gather the fruit, depending on crop quality. But to be safe, they tell the juice production department that they require a budget of $5,000 every year.

If the company wants to adjust its mix of products—say, doubling lemonade production—the fruit-picking team could respond by claiming that lemons are much more difficult to obtain than oranges, and their overall budget will need to be nearly doubled. But that team could say the same about oranges if the firm wanted to increase orange juice production. In other words, the fruit-pickers could take advantage of either situation to increase their budget padding. As a result, the cost of adjusting the product mix may be too high, and managers may not make changes as often as would be optimal for maximizing profits. 

Antle and his collaborator, Peter Bogetoft at Copenhagen Business School, devised a mathematical model to investigate such scenarios. The model represented interactions between a principal (the entity that needs the goods or services) and the agent (the entity supplying them). Antle and Bogetoft found that whether a principal should stick with an existing product mix or make a change depended on the value of the final product and how information about costs is shared. The study could have implications for scenarios ranging from firm downsizing to health care, the researchers say.

In the model, the principal needs two outputs from the agent. The principal wants to maximize its profit, and the agent wants to maximize its budget padding, also called slack.

First, Antle and Bogetoft analyzed what happened if the principal and agent could not communicate about actual production costs. If the products were very valuable, the principal generally continued to choose the same product mix. Absolute amounts might change, but relative amounts remained the same—say, 50% lemonade and 50% orange juice. “The principal just throws up his hands and makes proportional adjustments,” Antle says. “And if that involves the agents getting budgetary slack, well, so be it.”

Why might that be the case? Because the products in this scenario are valuable, the principal does not want to risk making an offer that the agent will reject, which would halt production. To increase the amount of, say, lemonade and still guarantee that production will continue, the principal must assume that lemonade accounts for most of the agent’s budget. In that case, the principal might as well scale up orange juice as well and keep the mix proportions the same.

But if the products were not very valuable, then reducing slack became a higher priority. The principal was willing to risk making offers that the agent would refuse and stopping production. So the principal was more inclined to make drastic changes—for example, cutting orange juice entirely. Sometimes the principal “just gambles on one product,” Antle says. Having one product instead of two may reduce the agent’s opportunities to introduce slack.

Antle and Bogetoft also considered scenarios where the principal and agent could communicate about actual costs. If the principal’s profit margin was large, more communication increased the chances of changing the product mix. But if the profit margin was small, the researchers saw the opposite effect. Communication made it more likely that the principal would stick with the same mix.

The researchers then considered two practical applications. The first was downsizing: Firms might, say, cut production of all items by 10% or slash entire product lines. The research suggests that in many cases, the across-the-board “lawn mowing” approach is better. But if the company needs to downsize drastically and the principal and agent are not communicating, eliminating some products is optimal.

The second application was healthcare. The reasons for escalating healthcare costs are complex. But Antle suggests that one problem might be that some players know more than others about actual costs, and those with less knowledge don’t want to cut production. For example, perhaps doctors and hospitals understand costs better than Medicare does, and Medicare is unwilling to ration treatments.

“In healthcare, we don’t like to say we’re going to take away production,” Antle says. But without this rationing, budgetary padding “goes crazy,” he says. For instance, hospitals might overtreat patients or inflate costs.

Antle cautions that the model does not precisely reflect reality. It has only two players, and each player is an individual. If the “agent” refers collectively to doctors and hospitals, it’s not clear whether they actually act as one unified decision maker. Managers will need to consider the details of each situation, but Antle hopes the model can help them reshape their intuitions, in particular by being aware of the stickiness of product mix, and make the right call.

William S. Beinecke Professor of Accounting