Quick question.

A baseball and a bat cost \$1.10 in total. The bat costs \$1 more than the ball. How much does the ball cost?

Quick!

You probably said \$0.10 cents. And you're wrong. The correct answer is \$0.05.

Don't feel bad if you got this wrong. Psychologist Daniel Kahneman says more than 50% of students at Harvard and MIT can't answer the bat-and-ball question correctly. I've heard it a dozen times and know the right answer, but I'm still tempted to blurt out "10 cents!" It just feels right. And what feels right is more common than what is right.

Math is hard. Money is emotional. Put the two together, and you get some crazy results. In economic textbooks, consumers are portrayed as rational decision makers who calmly calculate optimal outcomes. In real life, they more often resemble a couple drunks wandering around a bar, bumping into each other. They're sure of their decisions, but have no idea what's going on.

Take these five examples:

1. The \$500 \$20 bill
I have a \$20 bill. I'll sell it to you for whatever you want. Bidding starts at \$1 and moves in \$1 increments.

But there's a catch. Other people get to bid on this \$20 bill. If someone outbids you and you throw in the towel, you still have to pay me your final bid. You get nothing in return.

How much are you willing to pay for my \$20 bill?

Psychologists have been conducting this experiment for years, usually on students. It always goes the same way. People get excited at first at the prospect of bidding \$1, or \$5, or \$10, for a \$20 bill. It's free money. At around \$17 or \$18, a bidding war arises between two players who realize they could end up having to pay a lot of money for nothing in return. Not wanting to lose, they each bid higher and higher.

Eventually, someone bids \$21 for a \$20 bill -- which actually makes sense, because at that price the winner loses \$1 while the loser is out \$20.

Things blow up from there. The bidding war becomes a fight to lose the least, rather than to win the most. And as psychologists know, people hate losing more than they enjoy winning. It's called loss aversion, and it pushes bids for a \$20 bill to absurd heights.

Wharton management professor Adam Grant, who plays this game in consulting sessions, says a military officer once paid close to \$500 for a \$20 bill. Harvard Business School professor Max Bazerman claims to have earned \$17,000 auctioning \$20 bills to his students, with at least one student paying \$204 for a \$20 bill. Guys, I think we found the culprit of the student loan bubble.

The insurance market is a breeding ground for poor decisions because it combines money with the fear of something bad happening. Those two mix like gasoline and flames.

Take a 1993 study by four economists from Penn State, Temple University, and the University of Pennsylvania. They asked a group of participants how much they'd be willing to pay for \$100,000 of travel insurance on a trip from the U.S. to Thailand. Participants were given two options. One, they could buy insurance covering death caused by acts of terrorism. Two, they could buy insurance covering death for any reason.

For terrorism insurance, the average participant was willing to pay \$14.12. For insurance covering all causes of death, they were willing to pay \$12.03.

Yes, people were willing to pay more for insurance covering terrorism than they were for insurance covering everything... including terrorism.

In his book The Science of Fear, Daniel Gardner wrote: "Logically that makes no sense, but 'terrorist acts' is a vivid phrase dripping with bad feelings, while 'all possible causes' is bland and empty." The emotions of hearing the word "terrorism" made people willing to pay more.

3. Incentivizing yourself to failure
Want someone to perform better? Logic says that if you offer a bigger reward, like a bigger potential bonus, they'll work harder and perform better.

But economist Dan Ariely showed it isn't this straightforward. It can actually be the other way around.

Ariely and a few colleagues set up a series of problem-solving games in a rural village in India. The tasks ranged from memorizing random numbers to trying to fit nine quarters into a small square.

Ariely's assistants hailed down participants off the street. Participants rolled a die that determined how much money they could earn for completing the tasks. It ranged from the equivalent of one day of the participants' regular pay to a massive five months' of the participants' pay. (Ariely conducted the experiment in India so he could offer participants the equivalent of a large financial award without it costing a lot of dollars).

What do you think happened? Here's Ariely:

Those who stood to earn the most demonstrated the lowest level of performance. Relative to those in the low- or medium-bonus conditions, they achieved good or very good performance less than a third of the time. The experience was so stressful to those in the very-large-bonus condition that they choked under the pressure.

All those who stood to make the most money could think about was their bonus, Ariely wrote in his book, The Upside of Irrationality. Those who stood to make smaller sums had less to lose, and could focus more on the task at hand. So they performed better.

4. You'd rather earn less than be poorer than your neighbor
In one famous 1995 study, researchers from the Harvard School of Public Health asked students and faculty which they preferred:

• Earning \$50,000 a year when everyone else around them makes \$25,000.
• Earning \$100,000 a year when everyone else around them makes \$200,000.

"The researchers stipulated that prices of goods and services would be the same in both cases," Arthur Brooks wrote in his book The Battle, "so a higher salary really meant being able to own a nicer home or buy a nicer car."

Fifty percent chose the first option, leaving \$50,000 on the table just to avoid earning less than their neighbors.

5. The Red Cross charged for doughnuts and people never forgave it
"Most of us think of the Red Cross as a pretty mom-and-apple-pie organization," economist Russ Roberts told NPR last year. But Roberts found that wasn't the case. He kept hearing stories about people, particularly veterans, not trusting and holding a grudge against the Red Cross.

Why?

Two words kept coming up: "The doughnuts."

"I swear, you could go to any VFW hall today, mention the Red Cross, they will bring up the doughnuts," Roberts said. NPR traveled to several VFW halls and found exactly that. "The doughnuts," said one veteran. "It was a disgrace."

Here's what happened.

During World War II, the Red Cross built "comfort stations" across Europe that served coffee and doughnuts to U.S. soldiers. All of it was free. The British soldiers had their own comfort stations, but had to pay for their goods. This caused animosity between ally soldiers. It caused so much jealousy that Secretary of War Henry Stimson wrote the Red Cross and asked the organization to charge U.S. soldiers for doughnuts at comfort stations. So it did. For a brief period soldiers had to pay a few pennies for their doughnuts.

Soldiers were so outraged that the policy was soon reversed. But 70 years later, they still haven't found forgiveness.

Once you offer something for free, charging for it completely changes the relationship between the customer and the giver. If a business charges \$1 and raises the price to \$1.01, you might be annoyed, but you probably won't think differently about the business. But if something goes from free to \$0.01, what you thought was a charity now looks like a business. And that changes everything. You suddenly question its motives and its goals. In soldiers' eyes, the Red Cross went from a caring grandmother to a profit-driven corporation. That change, some psychologists propose, made soldiers wonder whether they were in a bait-and-switch scheme. That's a bad feeling to have. And those feelings last a long time.

Here's to more rational decisions.

Check back every Tuesday and Friday for Morgan Housel's columns on finance and economics.