Adverse selection and monopoly power

Question 1

explain adverse selection model with monopoly power in words

Answer 1

asymmetry of information arising from monopolist’s ignorance of consumer’s tastes,
monopolist may screen consumers by setting a specific fee schedule (menu of contracts for consumers to choose from)

Question 2

for adverse selection and monopoly power what does the x and f mean when the firm posts contracts (x,F) *

Answer 2

x is the quantity of the good,

F is the total (not per-unit) price

Question 3

what is the utility of an individual with endowment y who takes a contract (x,F) *

Answer 3

τψ(x) + y-F,
utility from monopoly good + utility from other goods
τ scalar and varies across individuals (consumers have heterogenous preferences),
F total price of x number of units consumed,
ψ concave function (twice differentiable)

Question 4

what can the monopoly firm do under full information

Answer 4

under full information the firm can post one contract for each type of consumers, that is, one contract for each value of τ

Question 5

do all consumers have the same τ value

Answer 5

no, they have different preferences for the monopoly good, the higher the τ the higher the preference for the good

Question 6

what is the monopoly firms profit function given just two types a and b *

Answer 6

π=θ(Fa-cxa) + (1-θ)(Fb-cxb),
θ proportion of a types,
F total price of good,
c is marginal cost of producing good,
x is number of units consumed

Question 7

why is PCA binding

Answer 7

since firm is monopolistic, it cannot be optimal for it to post a contract that gives a strictly positive utility to its customers

Question 8

where is initial equilibrium in monopoly adverse selection with full information

Answer 8

optimal contract (x,F) is such that the consumer is indifferent between it and just consuming the initial wealth

Question 9

what is the case at the optimum for full information equilibrium in monopoly adverse selection when the two types have different preferences

Answer 9

slopes of both indifference curves are equal to -c (marginal cost of producing monopoly good) at the optimum (11/36 lec slides monopoly)

Question 10

what is one of the problems in the monopoly model when you move from full information to asymmetric information

Answer 10

because firms cannot see the types they cannot prevent type A from taking the contract intended for type B

Question 11

how does the maximisation problem change with asymmetric information for monopoly *

Answer 11

same max and participation constraints but now there is also an incentive constraint that the utility from the types own contract must be greater than their utility should they take the other types’ contract

Question 12

what is the case for a pooling contract in monopoly asymmetric information

Answer 12

(xa,Fa) = (xb,Fb)

Question 13

what do you not need to worry about for pooling contracts for monopoly asymmetric information

Answer 13

incentive constraints

Question 14

is there a pooling equilibrium for asymmetric information monopoly game

Answer 14

no, the monopolist can increase its profit by offering a second contract that will be preferred to (x,F) only by the A types, hence there is no pooling equilibrium (11 notes)

Question 15

why is there no pooling equilibrium for asymmetric monopoly case

Answer 15

indifference curves of two types are different gradients so firms can increase profit (shift downward of isoprofit curve) whilst individuals also increase their utility by offering two different contracts (11 notes)

Question 16

what is the first thing you need to do when looking for a separating equilibrium for asymmetric information in the monopoly case

Answer 16

need to look at each of the constraints to assess which may be binding or slack at the optimum

Question 17

how do you check to see if the constraint is binding or slack at the optimum

Answer 17

use other inequalities to manipulate the constraint,
see if you can increase F by a small amount without violating any of the constraints, if you can then the firm can increase its profits so the constraint must bind (back 11)

Question 18

what is one of the results of monopoly power separating equilibrium asymmetric information

Answer 18

xa>xb, high valuation type consumes more,

xa is equal to its first best value and xb is strictly below what it would be under full information

Question 19

for asymmetric monopoly game separating equilibrium how can B’s marginal willingness to pay exceed that of A, when A has a greater preference for the good *

Answer 19

greater preference means A’s marginal willingness to pay is greater than B’s for any fixed consumption level x, but this does mean that it is possible to find pairs x and x’ such that B’s indifference curve at x is steeper than A’s indifference curve at x’

Question 20

for monopoly game which type has a steeper indifference curve at all points

Answer 20

type a, the type with the higher preference towards the monopoly good,
willing to forgo lots of y in order to get more x

Question 21

what does the monopolist do under full information *

Answer 21

monopolist can maximise profit by setting two-part tariffs, or equivalently take-it-or-leave-it contracts, specific to each type of consumers, these are the first best contracts

Question 22

what does the monopolist do under asymmetric information *

Answer 22

high valuation type may masquerade and take contracts that were designed for consumers with a lower marginal willingness to pay, therefore monopolist has to set second-best contracts that maximise profits subject to all types participating (PC) and not masquerading (IC)

Question 23

can what the monopolist wants to do be achieved with a pooling contract

Answer 23

no

Question 24

can what the monopolist wants to do be achieved through a separating equilibrium *

Answer 24

yes they can achieve the second best

Question 25

what are the features of the optimum for asymmetric information monopoly *

Answer 25

participation constraint of low types and incentive constraint of high types are binding, other constraints are slack,
relative to first-best solution of marginal willingness to pay equal to marginal cost of production, there is no distortion for the high type,
there is distortion for low type as their marginal willingness to pay is now higher than marginal cost at the optimum