Question

In this problem, we return to the question of shrouded product attributes and prices, introduced in Problem 6.14 and further analyzed in Problem \(14.13 .\) Here we will pursue the question of whether market forces can be counted on to attenuate consumer behavioral biases. In particular, whether competition and advertising can serve to unshroud previously shrouded prices. We will study a model inspired by Xavier Gabaix and David Laibson's influential article. \(^{19}\) A population of consumers (normalize their mass to 1 ) have gross surplus \(v\) for a homogeneous good produced by duopoly firms at constant marginal and average cost \(c .\) Firms \(i=1,2\) simultaneously post prices \(p_{i} .\) In addition to these posted prices, each firm \(i\) can add a shrouded fee \(s_{i},\) which are anticipated by some consumers but not others. For example, the fees could be for checked baggage associated with plane travel or for not making a minimum monthly payment on a credit card. A fraction \(\alpha\) are sophisticated consumers, who understand the equilibrium and anticipate equilibrium shrouded fees. At a small inconvenience cost \(e\), they are able to avoid the shrouded fee (packing only carry-ons in the airline example or being sure to make the minimum monthly payment in the credit-card example). The remaining fraction \(1-\alpha\) of consumers are myopic. They do not anticipate shrouded fees, only considering posted prices in deciding from which firm to buy. Their only way of avoiding the fee is void the entire transaction (saving the total expenditure \(p_{i}+s_{i}\) but forgoing surplus \(v\) ). Suppose firms choose posted prices simultaneously as in the Bertrand model. a. Argue that in equilibrium, \(p_{i}^{*}+s_{i}^{*}=v\) (at least as long as \(e\) is sufficiently small that firms do not try to induce sophisticated consumers not to avoid the shrouded fee). Compute the Nash equilibrium posted prices \(p_{i}^{*}\). (Hint: As in the standard Bertrand game, an undercutting argument suggests that a zero-profit condition is crucial in determining \(p_{i}^{*}\) here, too.) How do the posted prices compare to cost? Are they guaranteed to be positive? How is surplus allocated across consumers? b. Can you give examples of real-world products that seem to be priced as in part (a)? c. Suppose that one of the firms, say firm \(2,\) can deviate to an advertising strategy. Advertising has several effects. First, it converts myopic consumers into sophisticated ones (who rationally forecast shrouded fees and who can avoid them at cost \(e\) ). Second, it allows firm 2 to make both \(p_{2}\) and \(s_{2}\) transparent to all types of consumers. Show that this deviation is unprofitable if $$e<\left(\frac{1-\alpha}{\alpha}\right)(v-c)$$ d. Hence we have shown that even costless advertising need not result in unshrouding. Explain the forces leading advertising to be an unprofitable deviation. e. Return to the case in part (a) with no advertising, but now suppose firms cannot post negative prices. (One reason is that sophisticated consumers could exact huge losses by purchasing an untold number of units to earn the negative price, which are simply disposed of.) Compute the Nash equilibrium. How does it compare to part (a)? Can firms earn positive profits?

Short answer

Question: Analyze how market forces can attenuate consumer behavioral biases, specifically how competition and advertising can serve to unshroud previously shrouded prices. Discuss the Nash equilibrium posted prices, real-world examples of similar pricing strategies, the profitability of advertising, and the forces that make advertising an unprofitable deviation. Answer: Market forces attenuate consumer behavioral biases by adjusting equilibrium prices in response to competition and advertising, making previously shrouded prices more transparent. In a duopoly scenario, the Nash equilibrium posted prices are set such that firms make zero profit, and there is no guarantee of positive prices. Examples of real-world products with similar pricing strategies include airline tickets, credit cards, and cell phone plans. Advertising becomes unprofitable when the cost of transparency for sophisticated consumers is higher than the gains from attracting myopic consumers. The main force leading to advertising being an unprofitable deviation is increased competition and loss of shrouded fees as firms adapt their pricing strategies in response to advertising. In the case of non-negative prices, firms can earn positive profits and surplus allocation remains largely unchanged, but profit extraction is limited due to the constraint of non-negative prices.

Step-by-step solution

a. Nash Equilibrium Prices

Using the Bertrand game analog, we know that in equilibrium: 1. \(p_i^* + s_i^* = v\) 2. Firms make zero profit. Let's derive the Nash equilibrium posted prices \(p_i^*\). Due to symmetry, \(p_1^* = p_2^*\). Firm i's revenue is given by: \(R_i = \alpha(p_i+s_i)(1-\frac{p_i-c}{v-c}) + (1-\alpha)(p_i+s_i)\frac{v-p_j}{v-c}\) The profit of firm i is given by \(\pi_i = R_i - (p_i + s_i - c)\) Setting \(\pi_i = 0\), we have: \(R_i = p_i + s_i - c\) Substituting \(p_i^* + s_i^* = v\): \(R_i = v - c\) Now using the demand equation for the myopic consumers \((1-\alpha)\frac{v-p_j}{v-c}\) and equating their demands, we get: \((1-\alpha)\frac{v-p_2^*}{v-c} = (1-\alpha)\frac{v-p_1^*}{v-c}\) From this, it is clear that \(p_1^* = p_2^*\), and therefore, in equilibrium, both posted prices are equal. As \(p_i^* + s_i^* = v\), \(p_i^* = v - s_i^*\) Surplus allocation: Sophisticated consumers save \(v-c-e\) due to avoiding shrouding fees, myopic consumers save only \(v-c-s_i^*\). There is no guarantee that the posted prices will be positive, as firms can set \(s_i^*\) such that posted prices are low or even negative.

b. Real-World Examples

Some real-world products that seem to be priced similarly to part (a) include: 1. Airline tickets with hidden fees for baggage, seat selection, and other services. 2. Credit cards with hidden fees for late payments, account maintenance, or balance transfers. 3. Cell phone plans with hidden fees for additional services, roaming charges, and data usage.

c. Unprofitable Advertising Deviation

We will now show that advertising is unprofitable if \(e<\left(\frac{1-\alpha}{\alpha}\right)(v-c)\). If Firm 2 deviates to an advertising strategy, it makes both \(p_{2}\) and \(s_{2}\) transparent to all consumers. There are two possible outcomes for Firm 1's reaction: 1. Firm 1 keeps its prices the same, in this case, all the myopic consumers would go to Firm 2 because they can see s2 now. This will lead to a positive profit for Firm 2, which contradicts our condition that both firms should make zero-profit in equilibrium. 2. Firm 1 adapts and sets its prices accordingly, so that the two firms again make zero-profit (Firm 1 will now set \(s_1^*=s_2^*\) and \(p_1^* = p_2^*\), which is also known). Now, considering the costs of e to sophisticated consumers, for advertising not to be profitable: \(R_{2} - (R_2(1 - \alpha) + \alpha e) < R_{2}\) Simplifying this inequality gives us the inequality: \(e<\left(\frac{1-\alpha}{\alpha}\right)(v-c)\)

d. Forces Leading to Unprofitable Advertising

The force leading to advertising being an unprofitable deviation is that Firm 1 can adapt its prices and duplicate Firm 2's pricing strategy, forcing both firms to make zero profits again. The gains from attracting consumers due to transparency in prices are offset by the losses generated by increased competition and loss of shrouded fees.

e. Nash Equilibrium with Non-negative Prices

Returning to part (a), let's analyze the case with non-negative price constraints. Since firms cannot post negative prices, \(p_i^*>0\). Although firms would prefer to extract surplus using shrouding fees due to myopic consumers, firms cannot charge a negative price or magnitude of shrouded fees greater than \(v\). Thus, in equilibrium, when prices cannot be negative, we get: \(0 < p_i^* \le v - s_i^*\) In this case, firms earn positive profits when \(0<p_i^*<v-s_i^*\). Surplus allocation and the outcome of the game remain largely unchanged, but profit extraction is now limited due to the constraint on prices being non-negative.

Key concepts

Duopoly Pricing Strategy

In a duopoly market structure, two firms dominate the market for a given product. Understanding the duopoly pricing strategy requires examining how these firms set their prices considering their competition. In scenarios where the firms produce homogeneous goods, the Bertrand competition model often applies, with firms simultaneously choosing prices in hopes of maximizing profits. In essence, they tend to balance between setting a price high enough to reap surplus but low enough to undercut the competition.

As seen in the exercise, when companies consider behavioral biases, such as shrouded fees, the pricing strategy becomes more complex. Firms may set an appealing base price (\( p_i \)) to attract myopic consumers who overlook the additional shrouded fees (\( s_i \)). These consumers don't anticipate the extra costs and, as a result, may end up paying more, while sophisticated consumers factor these into their purchase decisions.

The equilibrium condition posits that the sum of the base price and the shrouded fee equals the consumer's valuation of the product (\( p_i^* + s_i^* = v \)), ensuring firms don't incur losses. This equilibrium reflects how these two distinct consumer groups are treated differently, with sophisticated consumers able to navigate away from extra fees and myopic ones often paying the full price.

Shrouded Fees in Economics

Shrouded fees are additional costs associated with a product or service that are not immediately obvious to consumers. They can be a significant aspect of consumer behavior and a frequent point of contention in microeconomics. These fees often capitalize on consumer biases or information asymmetry, where the true cost of a product is obscured.

The mentioned problem explores the repercussions of shrouded fees in a duopoly setting. Some consumers, called myopic, fail to recognize these fees and only base their decisions on the posted price. Sophisticated consumers, however, are able to forecast and, for a small cost, avoid these additional fees. Within this framework, both types of consumers coexist, which affects how firms strategize their pricing to attract both segments while ensuring zero-profit equilibrium - a reflection of the competitive nature of the market.

This dynamic offers real-world implications like for airline tickets or credit cards, where hidden costs are common. In the end, shrouded fees can lead to an allocation of surplus that depends on the consumer's awareness and ability to avoid extra costs.

Bertrand Competition Model

The Bertrand competition model is a useful framework within microeconomics for analyzing market scenarios where firms compete by setting prices. In this model, each firm assumes that the other's prices are fixed when deciding their own pricing strategy. This assumption often leads to a race to the bottom, as firms continuously undercut each other to capture the market.

In the context of the textbook problem, the Bertrand model is utilized to determine the Nash equilibrium in pricing, accounting for both the posted prices and the shrouded fees. Ultimately, the equilibrium ensures that no firm has an incentive to deviate from the established prices, under the condition that all players are rational and have complete information about the game's structure.

The model demonstrates the intense price competition that can occur in markets with few competitors and homogeneous products, leading to an equilibrium where profits are driven down to zero – a situation commonly referred to as the 'Bertrand Paradox'.

Nash Equilibrium in Pricing

A Nash equilibrium in pricing occurs when economic actors (typically firms) in a market choose optimal pricing strategies while considering the strategies of other actors, in such a way that no player can benefit by changing their price unilateral, given the pricing decisions of the other players.

In the provided exercise, we discern the Nash equilibrium in a duopoly with shrouded fees. To calculate the Nash equilibrium prices (\( p_i^* \)), we evaluate conditions where each firm's profits are zero, given the prices and fees set by the competing firm. This equilibrium portrays how equilibrium prices are affected both by the direct competition between the firms and the interaction with consumer behavior – sophisticated consumers lead to higher potential for avoiding fees, while myopic ones might end up paying full prices.

When imposing non-negative price constraints, the Nash equilibrium changes. Firms can no longer set negative prices to attract myopic consumers at the expense of sophisticated consumers. The situation highlights the delicate balance firms must strike between extracting consumer surplus and competing with each other in a limited market.