1. Economics of Management Strategy BEE3027 Lecture 7

2. Quality Most of the models we have covered assume that quality of a product can be determined before purchasing (search goods). However, in lots of cases, one can only find out whether the good is of high quality once we purchase it (experience goods). What happens when the sellers and buyers have different information regarding the good?

3. The market for lemons George Akerlof first posed this problem in 1970, in what became a Nobel prize-winning paper. He used the analogy of the market for used cars. In the US, a bad quality used car is called a ‘lemon’, hence the name for the model. Assume an economy where one can purchase a new or used car. Cars can either be good quality cars or lemons.

4. The market for lemons Let: –Ng be the value of a new good car; –Nl be the value of a new lemon; –Ug be the value of a good used car; –Ul be the value of a lemon. Let’s make three assumptions (for simplicity): 1.The value of a lemon is zero (i.e. Nl = Ul = 0); 2.Half of all cars are lemons (so half are good cars); 3.New good cars are worth more than good used cars: (Ng > Ug > 0).

5. The market for lemons So the expected value of a new car is: –EN = 0.5*Ng + 0.5 Nl = 0.5*Ng Also, the expected value of a used car is: –EU = 0.5*Ug + 0.5 Ul = 0.5*Ug So, a new car is worth on average more than a used car: –EN > EU

6. The market for lemons There are four types of agents in the economy: –New car dealers who only sell new cars; –First time car buyers; –Owners of good used cars; –Owners of used lemons. Importantly, the quality of a new car is unknown even to the seller; hence the price of a new car is Pn. However, the quality of a used car is known to the seller but not the buyer. Still a buyer cannot distinguish a good used car from a used lemon. Hence the price of a used car is Pu.

7. The market for lemons A first time buyer’s utility is equal to: –EN – Pn if (s)he buys a new car; –EU – Pu if (s)he buys a used car. The owner of a used car has the choice of selling his car to buy a new one or keeping it: –EN – Pn + Pu in the former case; –Ug in the latter. Finally the seller of a lemon also has the choice of selling his car to buy a new one or keeping it: –EN – Pn + Pu in the former case; –Ul in the latter.

8. The problem of the first-time buyers Since first-time buyers do not own a car, they will buy whichever type gives them the highest level of utility. Hence they will buy a used car if: –EU – Pu ≥ EN – Pn. Solving this inequality for Pu, we get: –Pu ≤ EU – EN + Pn, or premium –Pu ≤ Pn – (Ng – Ug)/2

9. The problem of the lemon seller The lemon seller can either keep his car and get 0 utility, or selling it to buy a new one. He will sell his car, as long as: –0 ≤ EN – Pn + Pu Solving for Pu: –Pu ≥ Pn – EN, or –Pu ≥ Pn – 0.5 Ng

10. The problem of the good used-car seller The good used-car seller can either keep his car and get Ug utility, or selling it to buy a new one. He will sell his car, as long as: –Ug ≤ EN – Pn + Pu Solving for Pu: –Pu ≥ Pn + Ug – EN, or –Pu ≥ Pn + Ug – 0.5Ng

11. The market for lemons The upshot of the model is that the prices at which good used car owners are willing to sell and the prices at which first time buyers are willing to buy used cars don’t coincide. Therefore, lemons drive out good used cars! Is this realistic? Are lemons so widespread? –Bond (1982) and Offer (2007) test this model in the used pick-up truck and car markets. They find little evidence of the lemon hypothesis.

12. The market for lemons However, this model provides a rationale as to why cars (and most objects) lose value immediately after they are sold. If someone immediately sells their car after purchasing it (say within 1 year), there is a chance (s)he is selling a lemon!

13. Quality revisited We turn to another issue associated with quality: warranties. In lemons model, both used and new sellers of the good were forced to charge a unique price for the good they were selling. This, along with the asymmetry of information, caused the owners of good quality used goods not to sell.

14. Quality revisited However, it may be possible for a firm to overcome this by providing a warranty. We will now go over a simple model of warranties to illustrate the point.

15. Warranties Let’s make a few simplifying assumptions: –A product can either be fully operational or fully defective; –The value of a defective product is zero and it cannot be resold. –At the time of purchase, neither sellers nor buyers know whether the product is defective or not. –The seller can either sell the product with full warranty or no warranty. In the former case, it will replace faulty items without charge, as well as the replacements themselves.

16. Warranties Consider a good whose value to a consumer is: –V is functional; –0 if faulty. The probability of it being functional is x. –This probability is exogenous and known to both seller and buyer. Let P be the monopoly price and C the production cost for the good.

17. Warranties The consumer’s utility function is as follows: –V – P if he buys the good with a full warranty; –xV – P if he buys the good without a warranty; –0 if he does not buy the good. We assume also that xV > C, to ensure the product is always sold.

18. Warranties The monopolist must choose whether to provide a warranty or not. If the monopolist does not provide a warranty: P = xV and π = xV – C If the monopolist provides a warranty, it is forced to replace any faulty goods to the buyer.

19. Warranties The basic cost of producing the good is C. If the good is faulty, the expected cost increases by (1-x)C: –C + (1-x)C If the replacement is also faulty, then the expected cost goes up by (1-x)²C: –C + (1-x)C + (1-x)²C So, the expected cost is equal to: –C +(1-x)C+(1-x)²C + (1-x)³C+ …= C/(1 – (1-x)) = C/x

20. Warranties Expected cost = c/x. As x gets close to 1: –The likelihood of there being a need for a replacement is low, hence the cost is close to C. As x gets closer to 0: –The more likely replacements will be needed; hence the expected cost of production becomes extremely large.

21. Warranties If the monopolist provides a warranty: –P = V and π = V – C/x So, which action is more profitable for the monopolist? It will provide a warranty if: –V – C/x > xV – C –Rearranging: –V – xV > C/x – C, which simplified gives: –xV>C, which must always hold.

22. Warranties Providing a warranty enables the monopolist to charge a higher price for the good. Furthermore, the rise in price is higher than the rise in the cost –As long as that the monopolist can extract all consumer surplus, i.e. P = V In essence, the consumer values a warranty more than it costs the monopoly to provide it.

23. Warranties In an oligopoly where there are high quality and low quality firms, warranties may be used as a signal of quality. A high-quality firm may distinguish itself from a low-quality one: –It may do so by selling its product with a warranty at a price such that the low quality firm does not find it profitable to sell. –The warranty works as a signal of quality.