The Market for Lemons

By Scott Stockdale,

Anyone who’s tried buying a used car will know the stresses involved.

After searching for hour upon hour, you find one you like.

It looks gorgeous and the dealer tells you it only has 10,000 miles on the clock.

Perfect.

Or is it?

You see, with it being second-hand, there’s always a chance it might be a bit s***.

The dealer has all the information about the car.

We punters don’t.

This clip by the brilliant Tim Harford goes someway to explaining this basic problem of what we economists call asymmetric information. 

Does this problem mean all second-hand used cars are likely to be a bit bad and have recurring problems- what we call lemons?

Or will there be an occasional good car out there – what we call a peach?

Economics can help us find out.

 

The Theory

Let’s picture the following.

Imagine all potential car buyers in a market are willing to pay up to £6000 for a second-hand car, depending on the type of the car.

A buyers’ willingness to pay (WTP) = Type x £6000

Similarly, suppose sellers’ cars are uniformly distributed (as types) between 0.5 and 1, with these types being hidden from buyers.

If the type is 0, it’s an absolute lemon.

If it’s 1, it’s an absolute peach.

A sellers’ willingness to accept a buyer’s offer (WTA) = Type x £5000

cars - probability density

 

Buyers’ willingness to pay will be the average of these two types – 0.75 – multiplied by £6000. This will give a market price of £4500.

However, this price won’t be satisfactory to sellers of types greater than 0.9 (4500/5000). They have close to absolute peaches and won’t want to sell them for less than £4500-£5000.

As a result, these cars will be withdrawn from the market.

Remaining cars are uniformly distributed between 0.5 and 0.9.

Buyers WTP will be 0.7 – average of 0.5 and 0.9 – multiplied by £6000.

cars 2

£4200.

However, this now won’t be satisfactory to sellers of types >0.84 (£4200/£5000) so more cars are withdrawn…

cars 3

 

This unravelling process eventually stops when cars of type <0.75 are left on the market. Buyers WTP becomes 0.625 x £6000 = £3750, and this price is satisfactory to a seller of a car <0.75.

There will be some good cars left in the market.

We won’t have a market for lemons.

 

Extension

How about if the uniform distribution of types of cars was between 0 and 1 rather than 0.5 to 1?

Using the same process as above, we find the market completely unravels.

Only type 0 cars would be traded on the market!

As the percentage of good cars drops, the price in the market drops and it ends up with only bad cars being sold (i.e. the market for lemons)

This, then, represents a problem.

What’s more, economics shows us this dependence of quality on price can throw up some interesting results…

 

Economics gets absurd

Suppose that buyers’ WTP (for a car of any given type) is also distributed across some range.

Given that the average car-type (quality) in this market is a decreasing function of the market price, this new supposition can lead to a demand curve (for some price range) which has a positive slope.

So what? Is this important?

As economists, we generally assume people buy less of a good when it’s price goes up. There’s an inverse relationship.

Price goes up, demand goes down.

Price goes down, demand goes up.

(Interestingly, there are some goods – well, maybe only one – which are called Giffen whereby an increase in its price will lead to people buying more of it)

We can plot this relationship between price of a good and the amount/quantity of the good demanded with what we call a demand curve.

Economics 101 kinda stuff.

basic demand curve

 

However, I mentioned the new supposition that can lead to a demand curve with (for some price range) a positive slope.

In other words, it could look like this:

Upwards sloping demand curve

 

How can this be true?

It’s time to get intuitive.

Because we’re in a market for lemons, and price is the main determinant of the quality of car types on offer, an increase in the market price should encourage more sellers to come onto the market.

Just as importantly, more buyers should follow once they realise the quality of the cars has increased.

Previously, the cars were all duds. Now, with the change in the market prices, a greater balance is achieved.

Sure, there might still be a few lemons. However, there’s now a greater chance of someone snapping up a peach for a price which is still well below the price of a brand new, equivalent car.

Higher prices can be a good thing for both consumers and sellers.

 

Further applications

We economists love this ‘market for lemons’ and its applications reach far and wide.

For example, you might have noticed banks have to turn down a lot of people wishing to borrow from them.

Why is this?

Why don’t they just get rid of this excess demand by increasing interest rates on the loans they offer?

Banks have clearly thought of this. Evidently, however, it’s not attractive.

Here’s why:

The only type of borrowers usually willing to accept such high interest rates are those who are desperate.

If such high rates are on offer, you may attract these borrowers – risk-seeking entrepreneurs, perhaps.

Because these loans are high-risk, banks might not see them returned.

They may lose their money.

As a result, they’d rather sift through thousands of applications than dish out funds to those unlikely to return them.

 

Girls…

Who runs the world?

Girls.

(And economics.)

(Probably economics.)

One comment

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s