Many schemes for price discrimination involve some cost. For...

Many schemes for price discrimination involve 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 consumer surplus and call it $Y$. Mark the area equal to the deadweight loss and 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 $X$. $Y, Z, \text { and } C .)$ 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?

Many schemes for price discrimination involve 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 consumer surplus and call it $Y$. Mark the area equal to the deadweight loss and 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 $X$. $Y, Z, \text { and } C .)$
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?

Key Concepts

Welfare Analysis

Welfare analysis evaluates the distribution of economic surplus among participants in the market, including both consumer surplus and producer surplus (or profits). In the context of monopolies and price discrimination, comparing total surplus before and after discrimination helps determine changes in overall societal welfare. This analysis is crucial for understanding the trade-offs between increased monopolist profits and potential losses in consumer welfare or efficiency.

Fixed Costs and Decision Making

Fixed costs in the context of price discrimination represent the additional, non-variable expenses that a firm incurs when implementing discriminatory pricing strategies. This concept requires examining whether the incremental profits from price discrimination exceed these costs. It also contrasts a firm's private incentive to maximize profits with a social planner's goal of maximizing total surplus, highlighting potential conflicts between private gains and social efficiency.

Price Discrimination

Price discrimination happens when a seller charges different prices to different consumers for the same product based on their willingness to pay. Perfect price discrimination enables a monopolist to capture all available consumer surplus by tailoring prices to each buyer's valuation, theoretically eliminating deadweight loss but potentially raising issues of equity and fairness. It is key in analyzing variations in market outcomes when practices like discount coupons are employed.

Deadweight Loss

Deadweight loss is the loss in total surplus that occurs when a market is not operating at maximum efficiency. In a monopolistic market, deadweight loss arises because the monopolist produces less than the socially optimal output level, resulting in missed opportunities for transactions that would have benefited both buyers and sellers. This concept is central to understanding why monopoly outcomes are considered inefficient.

Consumer Surplus

Consumer surplus represents the difference between what consumers are willing to pay for a good and what they actually pay. It is illustrated as the area between the demand curve and the market price. In monopoly settings, consumer surplus is typically reduced compared to competitive markets, highlighting the loss in consumer welfare due to monopolistic pricing.

Marginal Revenue

Marginal revenue is the additional revenue that a firm earns from selling one extra unit of output. For a monopolist, the marginal revenue curve lies below the demand curve because increasing output requires lowering the price on all units sold. Understanding marginal revenue is critical in analyzing how monopolies determine their production levels and pricing strategies.

Monopoly Pricing

Monopoly pricing refers to how a firm that is the sole supplier determines the optimal price and quantity. In a market without competition, the monopolist sets output where marginal revenue equals marginal cost, leading to a price that is higher than marginal cost. This concept is fundamental because it explains how monopolies create inefficiencies and generate profits at the expense of overall economic welfare.

Transcript

00:01 Okay, guys, this is chapter 15, problem 12.

00:06 In this problem, we're talking about price discrimination and monopoly, and we're given that there are constant average cost and constant marginal costs that are equal to each other.

00:17 And so for parts a and b, we're asked to graph the monopolist problem without price discrimination, then label the monopolist profit at consumer surplus and the deadweight loss.

00:31 So that's our pretty standard monopoly graph.

00:34 You have downward -loping demands.

00:36 You have marginal revenue below the demand curve.

00:40 And we're given that the marginal cost is constant.

00:44 So here's marginal cost.

00:46 And marginal revenue, here's quantity, and here's price.

00:52 As always, a monopolist is going to profit maximize where marginal cost equals marginal revenue.

00:58 And then it'll charge a price.

01:00 Up here where that line would continue hit the demand curve and here's the quantity.

01:08 So profits for the monopolist are here.

01:14 This is x.

01:17 Here is the consumer surplus is here with y.

01:22 And then the deadweight loss is here, which is d.

01:28 And so make sure that you do this first part, you understand this first part before we move on to the rest because the rest of this question is going to be referring to these regions x y and z so part c then asks us what is the monopolist profit when the monopolist can perfectly price discriminate and in terms of x y and z the profits are going to be x y and z because when the monops can perfectly price discriminate it's going to be able to charge every single person out here on the demand curve.

02:08 And so this marginal revenue curve becomes more relevant.

02:11 And so all of this is the profits.

02:20 For part d, we're asked, what is the change in the monopolist's profits and the change in the total surplus because of the price discrimination and which one is larger? so the change in profits, right, is they added y.

02:36 So it's going to be y plus z because the monopolist profits took over to consumer surplus and the dead weight loss...

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