ECON207 - Week 7 - Information

Mean - Expected Value

E.g. When rolling a dice the probability that any number between 1 and 6 is rolled is 1/6. 

E(x)= 1/6(1) + 1/6(2) + 1/6(3) + 1/6(4) + 1/6(5) + 1/6(6) = 3.5

Variance - Measure of Risk

Greater utility from a sure outcome rather than a gamble. 

Example - A consumer has £10 of wealth. A gamble gives him a 50% chance of winning £5 and a 50% chance of loosing £5. 50% probability of getting £15 and 50% probability of getting £5.

Expected Value of Wealth = 1/2(15) + 1/2(5) = £10.

Utility from the expected value of wealth is : 1/2u(£15) + 1/2u(£5)

Expected utility of wealth     the utility of expected wealth.  1/2u(15) + 1/2u(5)     u(10). 

Prefers a gamble over a sure outcome. 

Indifferent to a gamble but wants to maximise expected profits. 

Consumers don't know the price charged by all stores for a homogenous product. Costs (C) denotes the cost of obtaining information at an individual store.

3/4 of stores charge £100 and 1/4 charge £40.

There is a 1/4 chance of saving £60.

Expected Benefit from an additional search : 1/4(100-40) + 3/4(100-100) = £15.

A consumer should search for a lower price as long as Expected Benefit    Cost

Reservation Price - Consumer is indifferent between purchasing or searching EB=C.

When P   Reservation Price = Search

When P   Reservation Price = Buy

E[MR] = MC

Example

There is a 30% change that the market price will be £2 and a 70% chance it will be £1. The firms cost function is : C = 200 + 0.0005Q^2.

As price is uncertain the firms revenues and profit are uncertain. To maximise expected profits equate expected price with marginal cost.

E[p] = (0.3 x £2) + (0.7 x £1) = £1.30

MC = 0.001Q

£1.30 = 0.001Q     Q = 1300 

Expected profit = E[   ] = E[p]Q - C = £645

When some people have better information than otheres in the market.

Example - Used Car Market

1/2 the cars in the market are plums (good) and 1/2 are lemons (bad). Current owners know if their car is a plum or a lemon but buyers don't. 

Owner of a lemon expects atleast £1000. Owner of a plum expects atleast £2000.

Buyer of a lemon is willing to pay £1200. Buyer of a plum is willing to pay £2400.

E[p] = 1/2(2400) + 1/2(1200) = £1800

Owners of a plum would not sell at this price - only lemons would be for sale

But if a buyer knew he was certain to get a lemon he wouldnt pay £1800. 

Even though they're are buyers willing to pay more than what an owner expects for a plum - no plums would get sold. MARKET FAILURE.

One party has better information before a transaction occurs.

Example - Car Insurance 

• The insurance company doesn't know whether a driver with a bad record is a true poor driver or unlucky events have caused past accidents.
• Poor drivers know their true driving style - hidden characteristics.
• Insurance company charges a high premuim to cover future claims to everybody.
• The only people willing to pay that high price are those who know they are most likely to crash
• Only policies are sold to bad drivers. 

One party has an incentive to behave differently once an agreement is made and after the transaction has occured.

Example - Car Renting Company

The rental company fully insures against damage to the cars. 

And the company can't observe how the renters drive the cars and the effort to avoid damage to the cars. 

Renters don't care about the damage as they are fully insured.

Moral Hazard! 

A way to mitigate Adverse Selection and Moral Hazard.

The informed party sends an observable indicator of their hidden characteristics or hidden actions. 

Examples:

• Product Market - firms signal the quality of the product: money back guarentees, free-trial periods, advertising the winning of awards. 
• Labour Market - Job applicants CV, degree class