Question

Some firms employ the marketing strategy of posting a low price for the good, but then tack on hidden fees or high prices for add-ons that can add up to an "all-in" price that is exorbitant compared to the posted price. A television ad may blare that a perpetually sharp knife sells for \(\$ 20,\) leaving the additional \(\$ 10\) handling charge-or worse, that the \(\$ 20\) is just one of three installments-for the small print. A laser printer printing photo-quality color prints may seem like a bargain at \(\$ 300\) if one doesn't consider that the five toner cartridges must be replaced each year at \(\$ 100\) each. If consumers understand and account for these additional expenses, we are firmly in a neoclassical model, which can be analyzed using standard methods. Behavioral economists worry about the possibility that unsophisticated consumers may underestimate or even ignore these shrouded prices and firms do their best to keep it that way. This question introduces a model of shrouded prices and analyzes their efficiency consequences. a. Consumers' demand for a good whose price they perceive to be \(P\) is given by \(Q=10-P .\) A monopolist produces the good at constant average and marginal cost equal to \(\$ 6 .\) Compute the monopoly price, quantity, profit, consumer surplus, and welfare (the sum of consumer surplus and profit) assuming the perceived is the same as the actual price, so there is no shrouding. b. Now assume that while the perceived price is still \(P\), the actual price charged by the monopolist is \(P+s,\) where \(s\) is the shrouded part, which goes unrecognized by consumers. Compute the monopoly price, quantity, and profit assuming the same demand and cost as in part (a). What amount of shrouding does the firm prefer? c. Compute the consumer surplus (CS) associated with the outcome in (b). This requires some care because consumers spend more than they expect to. Letting \(P_{s}\) and \(Q_{s}\) be the equilibrium price and quantity charged by the monopoly with shrouded prices, \\[ C S=\int_{0}^{Q} P(Q) d Q-P_{s} Q_{s} \\] This equals gross consumer surplus (the area under inverse demand up to the quantity sold) less actual rather than perceived expenditures. d. Compute welfare. Find the welfare-maximizing level of shrouding. Explain why this is positive rather than zero. e. Return to the case of no shrouding in part (a) but now assume the government offers a subsidy s. Show that the welfare-maximizing subsidy equals welfare-maximizing level of shrouding found in part (d). Are the distributional consequences (surplus going to consumers, firm, and government) the same in the two cases? Use the connection between shrouding and a subsidy to argue informally that any amount of shrouding will be inefficient in a perfectly competitive market.

Short answer

Answer: In this scenario, shrouding has no effect on welfare, as both cases without and with shrouding have the same welfare of $8. If the government provides a subsidy equal to the shrouded cost, the consumers would experience no change in welfare, but the distributional consequences may be different, affecting consumer surplus and firm profit in different ways. In a perfectly competitive market, shrouding would not be possible, as firms would not be able to charge a price higher than the market price.

Step-by-step solution

1. Derive the inverse demand function

The demand function is given by \(Q = 10 - P\). To find the inverse demand function, we will solve for P in terms of Q: \(P(Q) = 10 - Q\).

2. Calculate marginal revenue (MR)

Marginal revenue is the derivative of total revenue with respect to quantity. Total revenue (TR) is \(P \times Q = (10-Q)Q\). Taking the derivative with respect to Q, we get: \(MR(Q) = 10 - 2Q\).

3. Set marginal revenue equal to marginal cost (MC)

The monopolist maximizes profits by setting marginal cost equal to marginal revenue. In this case, the marginal cost (MC) is constant at \(6. So: \)10 - 2Q = 6$.

4. Solve for quantity (Q)

Solving for Q, we get: \(Q^* = 2\).

5. Calculate the monopoly price (P)

Using the inverse demand function, we find the monopoly price: \(P^* = 10 - Q^* = 10 - 2 = \$8\).

6. Calculate the monopolist's profit (π)

Profit is given by the equation: \(\pi = (P^* - MC) \times Q^* = (8 - 6) \times 2 = \$4\).

7. Calculate consumer surplus (CS)

Consumer surplus is the area between the inverse demand curve and the monopoly price, up to the quantity sold: \(CS = \int_{0}^{2} (10 - Q)dQ - P^*Q^* = \frac{1}{2}(10)(2) - 8(2) = \$4\).

8. Calculate welfare (W)

Welfare is the sum of consumer surplus and profit: \(W = CS + \pi = 4 + 4 = \$8\). b. Monopoly with shrouding

1. Revise the demand function with shrouding

Now the actual price is given by \(P+s\). Since consumers only recognize the perceived price, the demand function remains the same: \(Q = 10 - (P+s)\).

2. Set up the firm's profit-maximization problem

The firm seeks to maximize profit by choosing P and s such that: \(max_{P,s} \pi((P+s)-6)Q\). Using the demand function, the maximization problem becomes: \(max_{P,s} \pi[(P+s) - 6](10 - (P+s))\).

3. Calculate the first-order conditions (FOCs) and set them to zero

We want to find the values of P and s that maximize the profit function, so we need to calculate the first-order conditions with respect to P and s: \(\frac{\partial \pi}{\partial P} = 10 - (2(P+s)-6)\) and \(\frac{\partial \pi}{\partial s} = 10 - (2(P+s)-6)\).

4. Solve the FOCs for equilibrium values

Setting the FOCs equal to zero, we find the equilibrium values for \(P_s^*\) and \(s^*\): \(P_s* = 4\) and \(s^* = 2\).

5. Calculate the actual price, quantity and profit with shrouding

With these equilibrium values, the actual price is \(P + s = 4 + 2 = \$6\), the quantity is \(Q_s = 10 - (P_s^* + s^*/2) = 4\), and the profit is: \(\pi_s = (6 - 6) \times 4 = \$0\). c. Consumer surplus with shrouding

1. Compute the consumer surplus with shrouding

Using the provided formula, we can calculate the consumer surplus: \(CS_s = \int_{0}^{4} (10 - Q)dQ - P_s^* Q_s^* = \frac{1}{2}(10)(4) - 4(4) = \$8\). d. Welfare with shrouding

1. Compute welfare with shrouded prices

Welfare with shrouding is the sum of consumer surplus and profit: \(W_s = CS_s + \pi_s = 8 + 0 = \$8\).

2. Compare welfare without and with shrouding

Both cases have the same welfare: \(W = W_s = \$8\). Thus, in this case, shrouding has no effect on welfare. e. Government subsidy

1. Compare shrouded price and subsidy

From part (d), we found that the welfare-maximizing level of shrouding is \(2\). To achieve the same welfare with a subsidy, the government should provide a subsidy equal to the shrouded cost, and consumers would experience no change in welfare. However, the distributional consequences may be different, with the government bearing the cost of the subsidy, which could affect consumer surplus and firm profit in different ways.

2. Welfare consequences of shrouding in a perfectly competitive market

In a perfectly competitive market, firms cannot charge a price above the market price, and thus shrouding would not be possible. In such a case, any attempt at shrouding would be recognized by consumers, and they would choose another firm with a lower total cost. Therefore, shrouding is inherently inefficient in a perfectly competitive market.

Key concepts

Monopoly Pricing

In microeconomic theory, monopoly pricing refers to the price-setting behavior of a firm that is the sole supplier of a particular product or service. Unlike firms in competitive markets, a monopolist is not a price taker but has the market power to influence price by altering the quantity supplied.
A key feature of monopoly pricing is the ability of the monopolist to maximize profits by equating marginal cost (MC) to marginal revenue (MR), which is less than the price consumers are willing to pay. This results in a price that is higher than in a competitive market, reducing consumer surplus and potentially causing welfare losses due to decreased market efficiency.
In the textbook exercise, calculating the monopoly price is straightforward. By setting MR equal to MC, the equilibrium quantity and price are determined, thereafter profit and consumer surplus can be computed. This formula assists students in understanding how monopolists use their market power to determine pricing that maximizes their profits but not necessarily the overall welfare.

Consumer Surplus

Consumer surplus (CS) measures the benefit that consumers receive from purchasing goods and services at a price lower than the maximum they are willing to pay. It is represented graphically as the area between the demand curve and the market price, extending up to the quantity purchased. The concept of consumer surplus helps in understanding how much extra value consumers derive from their transactions.
In the context of the exercise, careful calculation of the consumer surplus is essential, especially when prices are 'shrouded'. Students must grasp that when faced with shrouded pricing, consumers may believe they are receiving a greater surplus than they actually are due to not recognizing hidden costs. By instructing students to subtract the actual expenditures from the gross consumer surplus, educators can highlight the deceptive impact that shrouded pricing has on consumer benefits.

Welfare Economics

Welfare economics is a branch of economics that uses microeconomic techniques to evaluate the well-being of individuals within an economy. It seeks to assess the optimal allocation of resources to maximize social welfare, measuring this through concepts like consumer and producer surplus.
In analyzing welfare within the exercise, students must consider both consumer surplus and the monopolist's profit to determine the welfare outcome. Welfare economics emphasizes that while monopoly pricing may benefit the monopolist in terms of profit, it can cause a loss of welfare compared to a competitive market scenario. This is illustrated when students are asked to find a welfare-maximizing level of shrouding, a situation that typically diverges from the normative recommendation of zero shrouding due to its deceptive nature.

Behavioral Economics

Behavioral economics explores the effects of psychological, cognitive, emotional, cultural, and social factors on the economic decisions of individuals and institutions. It challenges the assumption that all agents are perfectly rational and have complete information, introducing realism into economic models.
In the textbook solution, behavioral economics is invoked to analyze the decision-making process of consumers confronted with shrouded prices. It suggests that some consumers may underestimate or ignore additional costs due to bounded rationality or other biases, leading to inefficient market outcomes. Students should recognize how behavioral economics provides insights into why consumers might not behave in accordance with the predictions of classical economic theory in the face of complex pricing strategies.

Price Shrouding

Price shrouding occurs when a firm hides the full cost of a product or service, causing consumers to perceive the price to be lower than it actually is. This can happen through tactics like hidden fees, complicated pricing schemes, or fine print disclosures. Shrouding manipulates consumer perception and can lead to suboptimal purchasing decisions.
Applying this concept to the exercise, students must calculate the firm's preferred level of shrouding and its impact on consumer surplus and overall welfare. They learn that while shrouding can increase a monopolist's perceived profit, the welfare impact may be neutral or negative when accounting for the actual costs to consumers. Such an understanding of price shrouding and its implications empowers students to scrutinize marketing tactics critically and appreciate regulatory efforts to ensure price transparency.