Many schemes for price discrimination involvesome cost. For example, discount coupons take upthe time and resources of both the buyer and theseller. This question considers the implications ofcostly price discrimination. To keep things simple,let’s assume that our monopolist’s production costsare simply proportional to output so that averagetotal cost and marginal cost are constant and equalto each other.a. Draw the cost, demand, and marginal-revenuecurves for the monopolist. Show the pricethe monopolist would charge without pricediscrimination.b. In your diagram, mark the area equal to themonopolist’s profit and call it X. Mark thearea equal to consumer surplus and call it Y.Mark the area equal to the deadweight loss andcall it Z.c. Now suppose that the monopolist can perfectlyprice discriminate. What is the monopolist’sprofit? (Give your answer in terms of X, Y,and Z.)d. What is the change in the monopolist’s profit fromprice discrimination? What is the change in totalsurplus from price discrimination? Which changeis larger? Explain. (Give your answer in terms ofX, Y, and Z.)e. Now suppose that there is some cost associatedwith price discrimination. To model this cost, let’sassume that the monopolist has to pay a fixed costC to price discriminate. How would a monopolistmake the decision whether to pay this fixed cost?(Give your answer in terms of X, Y, Z, and C.)f. How would a benevolent social planner, whocares about total surplus, decide whether themonopolist should price discriminate? (Give youranswer in terms of X, Y, Z, and C.)g. Compare your answers to parts (e) and (f).How does the monopolist’s incentive to pricediscriminate differ from the social planner’s?Is it possible that the monopolist will pricediscriminate even though doing so is not sociallydesirable?
Many schemes for
some cost. For example, discount coupons take up
the time and resources of both the buyer and the
seller. This question considers the implications of
costly price discrimination. To keep things simple,
let’s assume that our monopolist’s production costs
are simply proportional to output so that average
total cost and marginal cost are constant and equal
to each other.
a. Draw the cost, demand, and marginal-revenue
curves for the monopolist. Show the price
the monopolist would charge without price
discrimination.
b. In your diagram, mark the area equal to the
monopolist’s profit and call it X. Mark the
area equal to
Mark the area equal to the
call it Z.
c. Now suppose that the monopolist can perfectly
price discriminate. What is the monopolist’s
profit? (Give your answer in terms of X, Y,
and Z.)
d. What is the change in the monopolist’s profit from
price discrimination? What is the change in total
surplus from price discrimination? Which change
is larger? Explain. (Give your answer in terms of
X, Y, and Z.)
e. Now suppose that there is some cost associated
with price discrimination. To model this cost, let’s
assume that the monopolist has to pay a fixed cost
C to price discriminate. How would a monopolist
make the decision whether to pay this fixed cost?
(Give your answer in terms of X, Y, Z, and C.)
f. How would a benevolent social planner, who
cares about total surplus, decide whether the
monopolist should price discriminate? (Give your
answer in terms of X, Y, Z, and C.)
g. Compare your answers to parts (e) and (f).
How does the monopolist’s incentive to price
discriminate differ from the social planner’s?
Is it possible that the monopolist will price
discriminate even though doing so is not socially
desirable?
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