Term 1 Lecture 5 Flashcards
(22 cards)
Message of adverse selection model with good and bad cars
Impossible to trade some kinds of goods even though there are buyers and sellers
- without asymmetric info, would be separate markets for good and bad cars, with own equilibrium price and quantity
- so buyers cant distinguish, so all cars at the same market price
Akerlof’s market for lemons model
- perfectly competitive market with good and bad used cars
- if quality was known, would be two separate markets, each with its own equilibrium price and quantity
- sellers of good and bad cars set high prices, claiming their cars are good
Supply curves for good and bad used cars
- sellers of good cars require a higher price to sell
- at low prices, only bad cars are supplied
- as prices increase, more good cars enter the market
Total supply: - sum of the two individual supply curves, initially mostly bad cars are supplied, as price rises, share of good cars rises
Demand curves for good and bad used cars
3 types of buyers:
- optimistic buyers - demand is high as assume all cars are good
- pessimistic buyers, demand is low as assume all cars are bad
- intermediate buyers, assuming a 50/50 mix
Over time, as transactions occur, buyers observe quality of traded cars, and as they see bad cars, demand curves shift down to pessimistic curve, driving good cars out of the market.
Demand and supply interactions
As demand falls, and sellers leave the market
- supply and demand will converge at a point where only bad cars are supplied and buyers believe all cars are bad
- low quality squeezes out high quality - adverse selection
Cursed equilibrium in the lemon’s model
CE is when buyers fail to fully account for adverse selection in the market
- in standard Lemon’s, buyers are rational and correctly infer the proportion of good vs bad cars
- CE modifies this assumption, says some are irrationally optimistic and overestimate the share of good cars in the market, end up with Winner’s Curse
Adverse selection in the insurance market model
- perfectly competitive, so firms must make 0 profit
- buyers know more about their riskiness than insurers - asymmetric info
- leads to market failure caused by adverse selection
Buyers of insurance
K = probability of having an accident, 0 < k < 1
- e.g. if we found that buyers with riskiness above k = 3/4 brought insurance, we have a demand for insurance equal to 1/4
- assume each buyer has wealth w, accident means cost L
- utility of wealth u(w) = w^0.5
- utility of no insurance = K(w-L)^0.5 + (1-k)(w)^0.5
- utility of insurance = k(w-P)^0.5 + (1-k)(w-P)^0.5 = (w-P)^0.5
When would buyer buy insurance
When utility of insurance > utility of no insurance, gives the function h(p), condition is when K is greater than h(p)
- riskier buyers are more likely to buy insurance
- P = 0, insurance is free, h(p) is 0 and everyone buys
- P = L, insurance costs as much as loss, h(p) = 1, and no one will buy insurance
Demand for insurance = 1 - h(P), area on the right on the graph, can sub in h(p) into the area formula to get exact demand function
Adverse selection of buyers of insurance
- as P increases, only high-risk buyers remain in the market
- low risk buyers exit, reducing the average quality of the insured pool and making insurance more expensive
- feedback loop exacerbates inefficient and leads to market failure where only the riskiest buyers are insured
Sellers of insurance, supply
Cost of consumer = KL + (1-k)(0) = KL
- profit of customer of known riskiness = P - KL
- only consumers with riskiness above h(p) will buy, so midpoint of insured group is 0.5( 1 + h(p) )
- expected cost = 0.5L( 1 + h(p) )
- therefore supply infinite if P > L/2( 1 + h(p) ) and vice versa 0
So supply is a horizontal line satisfying equality.
Equilibrium in a perfectly competitive economy
S = D
- P = 0.5L(1 + h(P))
- one equilibrium is always P = L, where no one buys insurance
- mathematical condition for multiple equilibria is that the slope of expected costs function at P = L is greater than 1
Equilibrium with monopoly
- monopolist selling insurance
Profit function = number of customers x profit per customer
-> (1 - h(P)) x (P - 0.5L(1+h(P)))
- then choose P to maximise this expression
Two main solutions to adverse selection
Signalling: informed party provide credible info about their type to the uninformed
Screening: uninformed design products to encourage different types of customers to self-select into distinct groups
Model of screening: two part tariffs
Monopolist offers two contracts: A and B
- deals are structured so that low-risk customers prefer A and high risk customers prefer B
- goal is that each customer type self-selects into the deal designed for them
- expected outcome is that the monopolist increases profits by segmenting the market and reducing AS
Monopoly pricing model without adverse selection, identical consumers:
- each consumer has income y, utility is v(x), concave
- v(x) - px + y is consumer total value
- FOC, p = v’(x), where price equals marginal benefit
- introduce fixed fee F, so consumer will still buy if total utility is positive, so max F = v(x) - px
Sub this back into profit = revenue - cost and solve for FOC, getting p = MC and take the rest as a lump sum
Introducing adverse selection into monopoly pricing model
- high and low value customers
High value: av(x) + y, population o
Low value: Bv(x) + y, population 1-o
a>B
- ideally firm would like to charge a different fixed fee F for each group, but high value customers will pretend to be Lo to get the lower fee - adverse selection problem.
Introducing adverse selection into monopoly pricing model
- screening solution
Monopolist offers a menu of deals to encourage customers to self select based on value assigned
- high value: (Xa,Fa), where is x is the quantity purchased and F is the fixed fee
- low value customers (Xb,Fb)
Profit = o(Fa - cXa) + (1-o)(Fb - cXb)
Introducing adverse selection into monopoly pricing model
- individual rationality constraints
High values utility from A deal >/ utility from not buying
Low values utility from B deal >/ utility from not buying
Introducing adverse selection into monopoly pricing model
- incentive compatibility constraints, getting customers to buy the right deal
High values from A deal >/ high values utility from B deal
Low values utility from B deal >/ low values utility from A deal
Introducing adverse selection into monopoly pricing model
- reducing the number of constraints
Constraints (2) and (3) imply (1), so we can remove (1)
- IRC for low value customers becomes 0 as adding a fixed fee is not possible, so it becomes an equality
- IC for high value customers also becomes an equality as cant increase Fa that much
- IC for low value customers remains as it is
Then can maximise utility subject to these constraints.
Conclusion to Introducing adverse selection into monopoly pricing model problem
Efficiently serve the high value customers and treat the low value types suboptimally
- this is as high value need some excess utility or they’ll pretend to be low value types, whereas all low utility surplus is extracted.
