Adverse selection and monopoly power Flashcards
explain adverse selection model with monopoly power in words
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)
for adverse selection and monopoly power what does the x and f mean when the firm posts contracts (x,F) *
x is the quantity of the good,
F is the total (not per-unit) price
what is the utility of an individual with endowment y who takes a contract (x,F) *
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)
what can the monopoly firm do under full information
under full information the firm can post one contract for each type of consumers, that is, one contract for each value of τ
do all consumers have the same τ value
no, they have different preferences for the monopoly good, the higher the τ the higher the preference for the good
what is the monopoly firms profit function given just two types a and b *
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
why is PCA binding
since firm is monopolistic, it cannot be optimal for it to post a contract that gives a strictly positive utility to its customers
where is initial equilibrium in monopoly adverse selection with full information
optimal contract (x,F) is such that the consumer is indifferent between it and just consuming the initial wealth
what is the case at the optimum for full information equilibrium in monopoly adverse selection when the two types have different preferences
slopes of both indifference curves are equal to -c (marginal cost of producing monopoly good) at the optimum (11/36 lec slides monopoly)
what is one of the problems in the monopoly model when you move from full information to asymmetric information
because firms cannot see the types they cannot prevent type A from taking the contract intended for type B
how does the maximisation problem change with asymmetric information for monopoly *
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
what is the case for a pooling contract in monopoly asymmetric information
(xa,Fa) = (xb,Fb)
what do you not need to worry about for pooling contracts for monopoly asymmetric information
incentive constraints
is there a pooling equilibrium for asymmetric information monopoly game
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)
why is there no pooling equilibrium for asymmetric monopoly case
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)
what is the first thing you need to do when looking for a separating equilibrium for asymmetric information in the monopoly case
need to look at each of the constraints to assess which may be binding or slack at the optimum
how do you check to see if the constraint is binding or slack at the optimum
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)
what is one of the results of monopoly power separating equilibrium asymmetric information
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
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 *
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’
for monopoly game which type has a steeper indifference curve at all points
type a, the type with the higher preference towards the monopoly good,
willing to forgo lots of y in order to get more x
what does the monopolist do under full information *
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
what does the monopolist do under asymmetric information *
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)
can what the monopolist wants to do be achieved with a pooling contract
no
can what the monopolist wants to do be achieved through a separating equilibrium *
yes they can achieve the second best
what are the features of the optimum for asymmetric information monopoly *
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
